research article particle filtering for obstacle tracking...
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Research ArticleParticle Filtering for Obstacle Tracking inUAS Sense and Avoid Applications
Anna Elena Tirri Giancarmine Fasano Domenico Accardo and Antonio Moccia
University of Naples ldquoFederico IIrdquo I80125 Naples Italy
Correspondence should be addressed to Anna Elena Tirri annaelenatirriuninait
Received 16 January 2014 Revised 13 June 2014 Accepted 13 June 2014 Published 1 July 2014
Academic Editor Liang Lin
Copyright copy 2014 Anna Elena Tirri et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
Obstacle detection and tracking is a key function for UAS sense and avoid applications In fact obstacles in the flight path mustbe detected and tracked in an accurate and timely manner in order to execute a collision avoidance maneuver in case of collisionthreat The most important parameter for the assessment of a collision risk is the Distance at Closest Point of Approach thatis the predicted minimum distance between own aircraft and intruder for assigned current position and speed Since assessedmethodologies can cause some loss of accuracy due to nonlinearities advanced filtering methodologies such as particle filters canprovide more accurate estimates of the target state in case of nonlinear problems thus improving system performance in terms ofcollision risk estimationThe paper focuses on algorithm development and performance evaluation for an obstacle tracking systembased on a particle filter The particle filter algorithm was tested in off-line simulations based on data gathered during flight testsIn particular radar-based tracking was considered in order to evaluate the impact of particle filtering in a single sensor frameworkThe analysis shows some accuracy improvements in the estimation of Distance at Closest Point of Approach thus reducing thedelay in collision detection
1 Introduction
Unmanned aircraft systems (UAS)must guarantee an equiva-lent level of safety compared tomanned aircraft in order to beallowed flying in both controlled and uncontrolled airspace[1] Thus they must have the ability to ldquosee and avoidrdquo otheraircraft andor obstacles in the flight path and they need tobe equipped with an autonomous detect sense and avoid(DSampA) system [2 3] The primary functions of this systemconsist in detecting obstacles in the own trajectory trackingthe detected objects and executing a collision avoidancemaneuver if an intruder is closely approaching thus becom-ing a collision threat ANearMid-Air Collision is determinedwhen the distance between own aircraft and an intruder is lessthan 500 ft [3] thus the prediction of the Distance at ClosestPoint of Approach (DCPA) is considered as a fundamentalparameter for the estimation of a collision risk In order toobtain an accurate DCPA estimate an adequate sensor setuphas to be chosen In fact the autonomous avoidance functioncan be performed installing onboardUAS cooperative andornon-cooperative technologies [4ndash6]
In the framework of TECVOL project carried out bythe Italian Aerospace Research Centre and the Universityof Naples ldquoFederico IIrdquo non-cooperative technology basedon an integrated radarelectro-optical (EO) architecture hasbeen considered as the optimal solution since the projectaimed at demonstrating the full autonomy of the system incase of absenceloss of data link between the aircraft [4 7]The prototype sensing setup has been installed onboard anoptionally piloted very light aircraft named FLARE (flyinglaboratory for aeronautical research) The hardwaresoftwarearchitecture is comprised of radar and four electro-opticalcameras and a central-level fusion algorithm based on anextended Kalman filter (EKF) An intensive flight test cam-paign has been performed taking into account several relativeflight geometries including chasing and frontal encounters[8 9] and considering a non-cooperative intruder of the sameclass of FLARE
In general while EKF is awell-assessed technique suitablefor real time implementation nonlinearities in obstacledynamics andor in the measurement equation can cause
Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 280478 12 pageshttpdxdoiorg1011552014280478
2 The Scientific World Journal
some loss of accuracy in obstacle tracking performance Onthe other hand innovative filtering techniques developed fornonlinear systems such as particle filters are expected toprovide more accurate estimates of obstacle dynamics thanEKF thus improving the accuracy of the DCPA estimate andpotentially reducing the delay in collision detection [10]
Thus a research effort has been carried out in orderto assess the impact of particle filtering approaches in theconsidered application
In general tracking problems comprise several applica-tions such as ocean surveillance submarine tracking carpositioning video surveillance and airborne target trackingDifferent solutions and methods have been proposed andimplemented [11ndash16]
One of the key components of a tracking system isthe filtering and prediction block where target motion ismodeled using a state vector and a dynamic system andsensor observations are related to the state vector by aproper measurement equation Within this framework mostpopular solutions are based onKalmanfiltering [17ndash19]whichcan be demonstrated to be the theoretically optimal approachfor linear systems corrupted by gaussian noise In the latestyears particle filtering techniques have found increasingdiffusion in problems involving nonlinear and non-Gaussiannoise processes [20ndash23]
Particle filtering has been applied to various nonlinearproblems such as bearing-only tracking trackingmultitargetin clutter and jump Markov linear system
In [24] the tracking problem is examined in the contextof autonomous bearing-only tracking of a single appear-ingdisappearing target in the presence of clutter measure-ments The same problem is also analyzed in [21] where acomparison between EKF a pseudo measurement trackingfilter and a PF is pointed out The study aims at tracking atarget from an airborne sensor at an approximately knownaltitude The analysis shows the PF algorithm to be morerobust than EKF Karlsson and Gustafsson [25] make acomparison between the two filters for angle-only trackingin several applications such as air-to-air air-to-sea and sea-to-sea scenarios In the study experimental data are used totest the algorithm in the sea-to-sea caseThe results show thatthe PF outperforms the EKF algorithm Besides PF has beenalso applied to solve problems of tracking multiple targetsin clutter environment [26ndash28] These works provide someimplementation suggestions to improve the PF performancewith extension to bootstrap filter
This paper describes a customized particle filtering algo-rithm based on spherical coordinates and aimed at flyingobstacle detection and tracking for non-cooperative senseand avoid On the basis of application needs the algorithmhas been developed to understand PF potential especially interms of reliability and latency in collision risk estimationThus the predicted DCPA between aircraft has been consid-ered as the key variable of the problem
Besides the application field main innovation aspectsof the developed PF algorithm comprise the treatment andcompensation of sensor latencies in view of real time softwareimplementation with the negative timemeasurement updateproblem dealt with keeping in memory a sliding window
B r
VB
VA
AdAB
VAB = VA minus VB
Figure 1 Definition ofminimum separation distance vector 119889119860119861
and using a Monte Carlo sampling approach and the directparticle-based prediction of minimum separation distance
The paper is organized as follows First a brief descriptionof problem geometry and hardware architecture of the systemused in flight tests is provided Then the tracking algorithmis presented in detail Finally results obtained in off-linesimulations based on flight data gathered during TECVOLtest campaign are presented and discussed
2 Obstacle Detection and Tracking forUAS Sense and Avoid
ADSampA systemhas to be endowedwith an obstacle detectionand tracking system that performs the ldquosenserdquo function anda collision avoidance subsystem that performs a collisionavoidance maneuver as soon as a collision risk is detectedIn order to realize a suitable and reliable sense and avoidsystem a series of requirements concerning the field ofregard range resolution angular resolution detection rangetime to collision and system data rate have to be satisfied inthe case of non-cooperative technologies In particular flightregulations define the scanning volume for collision threatdetection and the maximum relative speed between the twoaircraft Moreover they prescribe that the own aircraft andthe intruder must never be closer than 500 ft that is the so-called bubble distance [3]
Considering the above-mentioned requirements they areessentially relevant to the ability to estimate the Distance atClosest Point of Approach and the Time to Closest Point ofApproach often named ldquotime to gordquo in the literature Theformer parameter indicates the minimum distance that willbe measured between two planes that keep their currentvelocity constant it can be calculated from [4]
119889119860119861=119903 sdot 119881119860119861
100381710038171003817100381711988111986011986110038171003817100381710038172119881119860119861minus 119903 (1)
where 119889119860119861
is the minimum separation distance (whose normis the DCPA) [29]119881
119860119861is the relative speed vector (119881
119860minus119881119861)
between the intruder (aircraft 119860) and the ownship (aircraft119861) and 119903 is the relative position between the aircraft (seeFigure 1) If the intruder is modeled as a spherical object withradius 119877 it can be demonstrated [4] that assuming constantvelocity vectors 119881
119860and 119881
119861 respectively the two aircraft are
headed for collision if and only if the following conditions aresatisfied
10038171003817100381710038171198891198601198611003817100381710038171003817 le 119877 119903 lt 0 (2)
The Scientific World Journal 3
These values are a measure of the collision risk if theseconditions are satisfied a Near Mid-Air Collision threat isconsidered
It is worth noting that in order to obtain an accurateestimate of the DCPA an adequate sensor setup has to beproperly chosen In general this function can be performedinstalling onboard UAS cooperative andor non-cooperativesystems that include both active and passive sensors thechoice depends on size speed maneuverability andmissionsfor which theUASwill be used In case of largeUAS platformsand fully autonomous systems integrated radarelectro-optical architecture seems to be a good option to increasethe collision threat awareness In fact radars provide accuraterange estimates and can operate in all-time all-weatherconditions while EO sensors offer the potential of accurateangular measurements at fast update rates in addition thesesystems do not rely on information from external sources todetect and track other aircraft thus avoiding problems due tothe loss of communication links
As anticipated above within TECVOL project a con-figuration with radar as main sensor and EO as auxiliarysensors has been chosen as the optimal solution in view of theapplication In fact this project aimed at the development andflight demonstration of the technologies needed to supporthigh altitude long endurance UAS flight autonomy Thechoice of a multisensor configuration allows a compensationof single sensor shortcomings by integrating informationfrom heterogeneous sources In the next section for the sakeof clarity the flight system architecture is briefly described
3 Flight System Architecture
During the TECVOL flight test campaign the prototypehardwaresoftware sensing system installed onboard FLARE(Figure 2) was comprised of a Ka-band pulse radar and fourelectro-optical cameras (two visible cameras and two infraredcameras) a CPU devoted to image processing (IP-CPU) anda CPU devoted to real time tracking by sensor data fusion(RTT-CPU) This unit is connected to the onboard flightcontrol computer that performs autonomous navigation andflight control including autonomous collision avoidancemaneuvers [4 7 30] A hierarchical architecture in which theradar is the main sensor that must perform initial detectionand tracking and the EO sensors are used as auxiliary infor-mation sources in order to increase accuracy and data ratehas been consideredThe choice of a hierarchical architectureis determined by different levels of sensor performance infact the conventional EO sensors perform initial detectionat closer ranges than radar The standalone radar trackingestimates can be effective in reducing the computation timeand false alarm rate of EO image processing by selecting prop-erly defined search windows to apply the obstacle detectionprocess
In Figure 3 the adopted hardware system is depictedFor more details on the hardware and logical architecturesadopted within TECVOL project the reader is referred to[4 7]
Figure 2 Sensing system onboard FLARE
AHRS
Radar Panchro vis Color vis Infrared Infrared
Ethernet
EthernetFirewire link
Can BUS
GNC systemGPS
AIR
ALT
Navigation sensors
Image processingcomputer
Real timecomputer
Figure 3 The onboard hardware architecture
The tracking system can operate in two different modes
(1) standalone radar tracking mode that performs cur-rent estimates of obstacle relative position and veloc-ity on the basis of measurements from radar and theinertial unit
(2) radarEO tracking mode where current estimates ofobstacle relative position and velocity are determinedalso on the basis of EO sensor measurements
In this paper the radar-only tracking configuration wasconsidered in order to evaluate the impact of particle filteringtechniques first in a single sensor framework Indeed giventhe hierarchical architecture of the considered system radar-only tracking performance has a significant impact on datafusion operation In particular while in TECVOL projectthe tracking module was based on an EKF-based central-level fusion system for real time applications this paperdiscusses the development of a particle filter technique whichhas been tested in off-line simulations in fact innovativetechniques are expected to provide more accurate estimatesof obstacle dynamics than EKF in case of nonlinear systemsthus reducing the delay in collision detection
4 The Scientific World Journal
4 Developed Software Description
In general the tracking software allows effective fusion ofinformation provided by different sensors such as radar andinertial unit moreover it performs the gatingassociationfunctions in order to associate at the same intruder mea-surements gathered in different scans and to eliminate falsealarms and clutter returns In fact the inputs to the algorithmare sensor measurements which represent in general objectof interest false alarm and clutter In this case most ofthe clutter return will likely come from ground echoesTrackmeasurement association is carried out using ellip-soidal gating and a centralized statistic [31] defined as
120585 = [119910 minus 119910]1015840[119877 + 119867119875119867
1015840]minus1
[119910 minus 119910] (3)
where 119910 is the measurement vector at the time of detection 119910is the predicted measurement vector at the time of detection119875 is the predicted covariance matrix 119867 is the measurementtransition matrix and 119877 is the measurement covariancematrix This statistics is a normalized distance betweenmeasurement and prediction which takes into account allthe relevant uncertainties Assuming a statistical distributionfor 120585 it is then possible to define a threshold based onthe probability of a correct measurement falling inside thegate As an example in common radar applications 120585 isassumed to be distributed as a chi-square variable with anumber of degrees of freedom equal to the dimension of themeasurement vector
After the association phase based on a common nearestneighbour approach since a dense multitarget environmentis unlikely to be found in the considered civil collision avoid-ance scenario the track status must be properly handled Inparticular tracks are divided in three categories one-plot(single observation not associated with any existing track)tentative (at least two observations but confirmation logicis still required) and firm (confirmed track) The transitiontentative firm can be based on different techniques Tracks aredeleted if they are not updated within a reasonable interval
The filtering and prediction phase allows combining trackprediction and sensormeasurements and produces new trackpredictions The tracking system is based on a particle filterwith nonlinear dynamic model and linear measurementequation The state vector is comprised of 6 componentsthat are the obstacle positions in terms of range azimuthand elevation in north-east-down (NED) reference frame andtheir first time derivatives Besides the PF tracker providesalso an estimate of the Distance at Closest Point of ApproachThe obstacle dynamic model is based on a nearly constantvelocity model better described in the following sectionImportant points are related to the sensor latency and theproper inclusion of aircraft navigation measurements Thusproper data registration techniques have been considered asa prerequisite for the developed algorithm [32] Regardingtime registration the radar sends its measurements at theend of each pass with maximum latency of the order of 1 sSince the tracker works at 10Hz in the developed system ameasurement is assigned a time stamp which is the nearesttime on the tracker 01 s scale Since the radar delay is typically
larger than the 01 s scale it is likely that a measurementrelative to time 119905
1arrives when the state has already been
propagated to a later time 119905119899 In this case the state and
covariance must be updated at time 1199051 Also the gating and
association processes have to be performed with values ofstate and covariance at time 119905
1 Then the problem is how to
produce updated parameters from measurement at time 1199051
In order to perform gating association and track updat-ing the solution is to keep inmemory a slidingwindowwherenavigation and track data are stored The considered timewindow dimensions correspond to the largest possible radardata latency Given that state and covariance at time 119905
1have
to be known and stored in the developed PF tracker the keyidea is to consider all the variables at time 119905
1 to perform the
filtering step taking into account the radar measurement atthat time and then update the state (and covariance) untiltime 119905
119899by means of a Monte Carlo approach
41 Particle Filter Algorithm Particle filters are Bayesianestimators that resolve the state estimation problems bydetermining the probability density function (PDF) of anunknown random vector using a weighted sum of delta func-tionsThese filters have less limitations than the Kalman filterIndeed they can exploit nonlinear process and measurementmodels and they can be used with any form of system noisestatistical distribution
The implemented particle filter is based on the samplingimportance resampling algorithm [33] constituted by threemain steps generation of particles calculation of the weightsassociated with the particles and resampling procedureThen the state space is propagated through a nonlineardynamic equation A brief overview of the PF phases isreported
Let us consider a set of points and associated weights inthe target state space 119908(119894)
119896minus1 119909(119894)
119896minus1 for 119894 = 1 119873
119904 which
represent samples from the updated target state PDF at time119896minus1The latter can be represented by a weighted sum of deltafunctions as
119901 (119909119896minus1| 119885119896minus1) asymp
119873
sum
119894=1
119908(119894)
119896minus1120575 (119909119896minus1minus 119909(119894)
119896minus1) (4)
where 119908(119894)119896minus1
is the weight associated with the 119894th particle andsum119873
119894=1119908(119894)
119896minus1= 1
In the developed algorithm the target state space (iethe points and related weights) is initialized generating theparticles from a multivariate normal distribution with meanequal to the first radar measurements and specified standarddeviation values In particular the uncertainties have beenestimated on the basis of obstacle dynamic behavior and radaraccuracy (120590
119903= 9m 120590
120599= 2∘ 120590
120601= 2∘) Choosing a large
initial uncertainty on obstacle position allows letting a goodnumber of particles representing the state in important orhigh likelihood regions Consequently radar measurementshave non-negligible importance in the track initializationphase At the first step all the particles are generated withthe same weight set equal to 1N After that the set of pointsrepresenting 119901(119909
119896minus1| 119885119896minus1) have to be transformed into a set
The Scientific World Journal 5
Estimate at k + 1
State at k + 1
PF initialization
Transition to k + 1
xik+1 = f(xik) + nk
Measurement at k + 1
zik+1 = H(xik+1) + k+1
Prediction at k + 1
xi(k+1|k) = f(xi(k|k)) + nk
Measurement prediction at k + 1
zi(k+1|k) = H(xi(k+1|k)) + k
Weights update at k + 1
Resamplingxi(k+1|k+1) = resampling(xi(k+1|k) wi
k+1)
Generation of particles xikand weights wi
k
exp
Figure 4 Particle filtering algorithm
of points 119908(119894)119896 119909(119894)
119896 representing 119901(119909
119896| 119885119896) This is done by
PF in two steps prediction and filteringThe prediction step exploits the system model to predict
the state distribution function from one measurement timeto another one It transforms the updated density at time119896 minus 1 into a set of points representing the predicted density119901(119909119896| 119885119896minus1) by substituting each sample 119909(119894)
119896minus1in the dynamic
equation Since the state is subject to a process noise modeledas an independent and identically distributed process noisesequence the prediction step translates deforms and spreadsthe state distribution
The filtering step utilizes a measurement at time 119896 toupdate the set of particles representing the propagated density119901(119909119896| 119885119896minus1) to a set of particles 119908(119894)
119896 119909(119894)
119896 sim 119901(119909
119896| 119885119896) with
updated weights The optimal choice is to sample from theupdated density 119901(119909
119896| 119885119896) directly since this is impossible
because it is unknown the solution is to sample from thepropagated density (as in this specific analysis)Then given ameasurement 119911
119896and the set of propagated points 119908(119894)
119896minus1 119909(119894)
119896
the updated set of particles is given by
119908(119894)
119896=
119908(119894)
119896minus1119901 (119911119896| 119909(119894)
119896)
sum119873
119895=1119908(119895)
119896minus1119901 (119911119896| 119909(119895)
119896)
(5)
where 119901(119911119896| 119909(119894)
119896) is the measurement likelihood in this
application it has been defined as
119901 (119911119896| 119909119896) =
1
radic21205871198772
exp(minus(119911119896minus 119896)1015840119877minus1(119911119896minus 119896)
2)
(6)where
119896is the predicted measurement at the time of
detection and 119877 is the measurement covariance matrix
In the software the resampling procedure is based on asystematic resampling scheme [33] which is performed ateach time step and not only when the number of particleswith non-negligible weight falls below a threshold valueThe resampling phase enables a great quantity of particlesto survive during the propagation of the state space thusavoiding the degeneracy phenomenon
The software outputs based on range azimuth elevationand their first time derivatives are then calculated on the basisof the state estimates weighted on all particles
In Figure 4 a particle filtering scheme is reported in orderto better clarify how the developed software has been con-ceived The scheme exploits the main steps of the algorithminitialization prediction filtering and resampling In partic-ular the filtering phase is based on weights update obtainedconsidering measurement prediction sensor outputs andmeasurement covariance matrix 119877
42 Obstacle Tracking Dynamic Model The selection of adynamic model is a nontrivial problem for airborne obstacletracking systems since an accurate estimate of the obstacleposition is considered fundamental for the evaluation of theDistance at Closest Point of Approach In the developedsoftware a nearly constant velocity model in spherical coor-dinates has been implemented to represent the target relativetrajectory [34 35] The target state is propagated through anonlinear dynamic equation since the state variables are inspherical coordinates and thus closer to sensormeasurementsoutputs
The state vector is comprised of obstacle position interms of range azimuth and elevation in north-east-downreference frame and their first time derivatives Hereinafterthe obstacle dynamic model is reported for the sake of clarity
6 The Scientific World Journal
52505
52505
52505
52505
52506
52506
52506
times104
1080
1070
1060
1050
1040
1030
1020
1010
1000
990
GPS time of day (s)
Rang
e (m
)
Spherical PF
GPSRadar
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104
4000
3000
2000
1000
0
GPS time of day (s)
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
Rang
e (m
)
GPSRadar
RadarPF tracker
20
0
minus20
minus40
Erro
r in
rang
e (m
)
Spherical PF
Figure 5 Range as estimated by GPS by radar and by radar-only tracker and estimation error as a function of GPS time of day The upperfigure highlights the trajectory of each particle
The target state vector in spherical coordinates is definedas
119909 = [119903 119903 120599 120599 120601 120601] (7)
where 119903 is the range 120599 is the azimuth 120601 is the elevation angleand 119903 120599 120601 are their first time derivatives
In order to evaluate the velocity components let usconsider
V = [
[
V119903
V120599
V120601
]
]
= [
[
119903
119903 120599 cos120601119903 120601
]
]
(8)
where the velocity vector has been defined as V = [V119903 V120599 V120601]
for the sake of simplicity
For a spherical constant velocity dynamic model repre-senting the objectmotion it is assumed that V
119903= V120599= V120601= 0
Taking the time derivative of each component in (8) yields
V119903= 119903 = 0
V120599= 119903 120599 cos 120593 + 119903 120599 cos 120593 minus 119903 120599 sin 120593 = 0
V120601= 119903 + 119903 = 0
(9)
Rearranging the above expressions in terms of angu-lar velocities and considering discrete-time domain with
The Scientific World Journal 7
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
Radar
RadarPF tracker
Spherical PF
Spherical PF
100
0
minus100
minus200Azi
mut
h in
NED
refe
renc
e fra
me (
∘ )PF tracker
6
4
2
Erro
r in
stab
ilize
daz
imut
h (∘
)
Figure 6 Azimuth in NED reference frame as estimated by GPS by radar and by radar-only tracker and estimation error as a function ofGPS time of day
sampling time 119879 the components of the dynamic motionequation are given by
119903119899= 119903119899minus1+ 119879 119903119899minus1
119903119899= 119903119899minus1
120599119899= 120599119899minus1+ 119879 120599119899minus1[1 +
119879
2119903119899minus1
(119903119899minus1120601119899minus1119905119892120601119899minus1minus 119903119899minus1)]
120599119899= 120599119899minus1[1 + 119879( 120601
119899minus1119905119892120601119899minus1minus119903119899minus1
119903119899minus1
)]
120601119899= 120601119899minus1+ 119879 120601119899minus1[1 minus
119879
2119903119899minus1
119903119899minus1]
120601119899= 120601119899minus1[1 minus
119879
2119903119899minus1
119903119899minus1]
(10)
The nonlinear dynamicmotion equation for the sphericalstate vector can be written as
119909119899= 119891 (119909
119899minus1) + 119899119899minus1 (11)
with the zero-mean Gaussian dynamic acceleration noisedistribution
119899119899sim 119873(0 119876
120588) (12)
The components of 119891(119909119899minus1) are given by the nonlinear
equation (10) and the process noise matrix is
119876120588= [
[
119902119903119876102
02
02119902ℎ119876102
02
02119902V1198761
]
]
(13)
with
1198761=
[[[[
[
1198793
3
1198792
2
1198792
2119879
]]]]
]
(14)
where 119902119903 119902ℎ and 119902V must be set depending on the target
maneuvers [34]Since the model is in spherical coordinates the measure-
ment equation is linear and it can be expressed as
119911119899= 119867119909119899+ 119908119899 (15)
with
119867 = [
[
1 0 0 0 0 0
0 0 1 0 0 0
0 0 0 0 1 0
]
]
(16)
and 119908119899is the observation noise which is considered to be
independent zero-mean Gaussian noise defined by
119908119899sim 119873 (0 119877
119899) (17)
8 The Scientific World Journal
52494
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
Radar
RadarPF tracker
Spherical PF
Spherical PFEl
evat
ion
in N
EDre
fere
nce f
ram
e (∘ )
PF tracker
40
minus4minus8minus12
1505
minus05minus15minus25Er
ror i
n st
abili
zed
elev
atio
n (∘
)
Figure 7 Elevation in NED reference frame as estimated by GPS by radar and by radar-only tracker and estimation error as a function ofGPS time of day
52494
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
PF tracker
Spherical PF
Spherical PFPF tracker
minus72
minus76
minus80
minus84
Rang
e rat
e(m
s)
6
2
minus2
minus6Erro
r in
rang
era
te (m
s)
Figure 8 Range rate as estimated by GPS and by radar-only tracker and estimation error as a function of GPS time of day
where 119877119899is the measurement covariance matrix as stated
aboveThe developed obstacle detection and tracking software
provides also an estimate of the Distance at Closest Pointof Approach (see (1)) Since the particles are characterizedby own positions and velocities and given the nonlineardependencies between 119903119881 andDCPA the latter is calculatedfor each particle In this way in order to avoid furtherapproximations due to the evaluation of this distance from
position and velocitymean values DCPA has been calculatedas mean value of the different distances evaluated as
DCPA119899=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
119903 sdot 119881
1003817100381710038171003817100381711988110038171003817100381710038171003817
2119881 minus 119903
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(18)
This is a form of ldquodeep integrationrdquo of a collision detectionsensor since an estimate of the level of collision threat isdetermined by means of the same data fusion algorithm
The Scientific World Journal 9
52494
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
PF tracker
Spherical PF
Spherical PFPF tracker
0
minus1
minus2
minus3
050301
minus01minus03
Azi
mut
h ra
te in
NED
refe
renc
e fra
me (
∘ s)
Erro
r in
stab
ilize
daz
imut
h ra
te (∘
s)
Figure 9 Azimuth rate in NED reference frame as estimated by GPS and by radar-only tracker and estimation error as a function of GPStime of day
This is an additional advantage of using PF rather than EKFsince the need of linearized models in EKF does not allowestimating DCPA by the filter itself
5 Results
The developed obstacle tracking algorithm has been testedin off-line simulations based on flight data gathered duringan intensive test campaign Flight tests were carried out byexploiting the following configuration of test facilities
(a) FLARE aircraft piloted by a human pilot or by theautonomous flight control system
(b) a piloted intruder VLA aircraft in the same class ofFLARE equipped with GPS antennas and receiversand an onboard CPU for navigation data storage
(c) a ground control station (GCS) for real time flightcoordination and test monitoring [36]
(d) a full-duplex data link between FLARE and GCSused to send commands to initiate or terminate testsand to receive synthetic filter output and navigationmeasurements
(e) a downlink between intruder and GCS used for flightmonitoring
During the tests two types of maneuvers were executedsuch as chasing tests with FLARE pursuing the intruder andquasi-frontal encounters performed to estimate detectionand tracking performance in the most interesting scenariosfrom the application point of view
In particular the scenario selected in this paper forperformance analysis is a single quasi-frontal encounterbetween FLARE and the intruder The algorithm has beentested in standalone radar tracking configuration that is
estimates of obstacle relative position and velocity are basedon measurements from radar (update frequency of 1Hz) andthe own-ship navigation system
The number of particles has been set equal to 500 Thisnumber was selected since increasing it up to one orderof magnitude did not produced significant performanceincrease The algorithm is initialized taking into accountthe first radar sensor measurement the covariance matrix iscalculated on the basis of sensor measurements and then it isupdated with estimated values of software output
The algorithm outputs are based on obstacle position andvelocity in terms of range azimuth and elevation and DCPAin a stabilized north-east-down reference frame with originin FLARE center of mass The considered flight segment hasduration of about 20 s with an initial range of about 2000m
In Figure 5 obstacle range as estimated by radar radar-based tracker and GPS (reference) together with errorestimate with respect to GPS measurements is reportedAfter a firm track has been generated on the basis of radarmeasurements the tracker is able to characterize the obstacletrajectory The radar-only tracker provides a range estimatewith an accuracy of the order of few meters that derives fromthe good radar range accuracy and the absence of intrudermaneuvers In Figure 5 the upper plot illustrates the obstaclerange in a small interval time (of about 1 s) in order to showthe particles trajectories (colored lines)
Figures 6 and 7 report the obstacle angular dynamicsin terms of azimuth and elevation As expected the orderof magnitude of these errors is comparable to the radaraccuracy In particular the estimation uncertainty in termsof root mean square is of about 25∘ for azimuth and 13∘ forelevation Being computed in NED these RMS errors includeattitude measurement error biases In fact error biases in theestimation of magnetic heading are the main reason of thelarger error in azimuth It is worth noting that these biases
10 The Scientific World Journal
Table 1 PF performance in the selected scenario in terms of RMSerror
RMS Particle filter EKFRange (m) 84 37Range rate (m∘) 30 23Azimuth (∘) 25 17Azimuth rate (∘s) 02 04Elevation (∘) 13 21Elevation rate (∘s) 02 08
have a little effect on the estimation of angular rates and ofDistance at Closest Point of Approach
The range and angular rates as estimated by GPS (ref-erence) and particle filter tracker are reported in Figures 89 and 10 These variables are very important informationsources for collision detection assessment even though theyare not directly provided by the radar sensor The plots showthat the tracker estimates are very accurate with a very smallvalue in terms of standard deviation
Simulation results confirm how the resampling proce-dure is a key factor for tracking performance avoiding thedegeneracy phenomenon and thus enabling a great quantityof particles to survive to the prediction step
In order to better understand the particle filter trackingcapability PF and EKF estimation errors are reported inTable 1 in terms of root mean square (RMS) errors computedas
RMS = radic 1119873
119873
sum
119905=1
(119909119905minus 119909119905)2 (19)
where 119873 is the number of measurements 119909119905is the generic
PF tracker estimate (computed after resampling and repre-senting the mean value over all the particles) and 119909
119905is the
reference value computed on the basis of FLARE and intruderGPS measurements
The results show that PF tracker performance is com-parable to EKF in terms of order of magnitude Of coursethe introduction of electro-optical data can improve angularaccuracy since these sensors have a faster update rate thanradar In particular while the range rate error is very similarfor the two filters obstacle angular velocities provided byPF algorithm are slightly more accurate than EKF in theconsidered scenario These variables are very importantinformation sources for collision detection assessment eventhough they are not directly provided by the radar
In fact in near collision conditions angular rates are themost important variables influencing collision detection Asshown in [7] in these conditions DCPA uncertainty for givenrange and range rate shows a linear dependence on angularrate errors while range rate essentially impacts the time-to-go estimate
In the considered scenario DCPA as computed on thebasis of GPS measurement has been used as a reference forcomparing DCPA estimated by EKF tracker and PF trackerFigure 11 shows that the PF algorithm is more accuratethan EKF for the estimation of the DCPA in the initial
52494
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
PF tracker
Spherical PF
Spherical PFPF tracker
Elev
atio
nh ra
te in
NED
refe
renc
e fra
me (
∘ s)
08
04
0
minus04
minus01minus02minus03minus04minus05Er
ror i
n st
abili
zed
elev
atio
n ra
te (∘
s)
Figure 10 Elevation rate in NED reference frame as estimated byGPS and by radar-only tracker and estimation error as a function ofGPS time of day
450
400
350
300
250
200
150
100
50
Distance at Closest Point of Approach (DCPA) (m)
PF trackerEKF trackerGPS
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
Figure 11 Distance at Closest Point of Approach as estimated byGPS (reference) by radar and by radar-only tracker as function ofGPS time of the day
phase of firm tracking (at larger range) thus providing animprovement in collision risk assessment and a potentialreduction in the delay in declaring a collision threat Analysisof GPS data demonstrates that the considered encounterrepresents a real Near Mid-Air Collision (NMAC) scenariosince the reference DCPA keeps a very small value and liesbelow the bubble distance threshold almost in the whole firmtracking phase
The Scientific World Journal 11
6 Conclusion and Future Works
This paper focused on algorithm and test results fromobstacle tracking software based on particle filter and aimedat demonstrating UAS autonomous collision detection capa-bility in terms of reliable estimation of Distance at ClosestPoint of Approach The algorithm performance has beeninitially evaluated in radar-only configuration since the maininterest was addressed to the analysis of the potential impactof nonlinear filters on tracking capabilities with respect toassessed EKF first in a single sensor framework
The software has been tested in off-line simulations basedon real data recorded during a flight test campaign and aquasi-frontal encounter between the own aircraft and theintruder has been presented as test case The results pointedout that the developed algorithm is able to detect and trackthe obstacle trajectory with accuracy comparable to the EKFIn particular some advantages were highlighted in the directdetermination of Distance at Closest Point of Approach witha potential reduction of the delay for collision detectionThis result permits planning additional future investigationactivities such as
(i) performing the comparison on a larger experimentaldata set thus increasing the statistical significance
(ii) developing a multisensor-based analysis to confirmthe results obtained by the developed PF tracker whenadditional data sources are available such as electro-optical sensors indeed they can provide higheraccuracy in angular measurements and better datarate than radar sensors with a great impact on DCPAperformance
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The PhD grant of Miss Anna Elena Tirri is cofunded byEUROCONTROL through the research network HALA inthe framework of the WP-E of SESAR project
References
[1] EUROCONTROL in Proceedings of the EUROCONTROL Spec-ifications for the Use of Military Unmanned Aerial Vehicles asOperational Air Traffic Outside Segregated Airspace Version10 DocNo EUROCONTROL-SPEC-0102 Bruxelles BelgiumJuly 2007
[2] US Federal Aviation Administration (FAA) ldquoAirworthinesscertification of unmanned aircraft systemsrdquo Order 813034US Federal Aviation Administration (FAA) Washington DCUSA 2008
[3] US Federal Aviation Administration (FAA) ldquoInvestigate aNear Mid Air Collisionrdquo FAA Order 89001 vol 7 chapter 4Washington DC USA 2007
[4] G Fasano D Accardo A Moccia et al ldquoMulti-sensor-basedfully autonomous non-cooperative collision avoidance system
for unmanned air vehiclesrdquo Journal of Aerospace ComputingInformation and Communication vol 5 no 10 pp 338ndash3602008
[5] MTSI ldquoNon-cooperative detect see amp avoid (DSA) sensorstudyrdquo Tech Rep NASA ERAST 2002
[6] O Shakernia W Chen S Graham et al ldquoSense and Avoid(SAA) flight test and lessons learnedrdquo in Proceedings of the 2ndAIAA InfotechAerospace Conference and Exhibit (AIAA rsquo07)pp 2781ndash2795 Rohnert Park Calif USA May 2007
[7] D Accardo G Fasano L Forlenza A Moccia and A RispolildquoFlight test of a radar-based tracking system for UAS sense andavoidrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 49 no 2 pp 1139ndash1160 2013
[8] USFAA SpecialOperations FAAOrder 76104M January 2007[9] S J Julier and J K Uhlmann ldquoA new extension of the Kalman
filter to nonlinear systemsrdquo in Signal Processing Sensor Fusionand Target Recognition VI vol 3068 of Proceedings of SPIE pp182ndash193 Orlando Fla USA 1997
[10] N E Smith R G Cobb S J Pierce and V M Raska ldquoOptimalcollision avoidance trajectories for unmannedremotely pilotedaircraftrdquo in Proceedings of the AIAA Guidance Navigation andControl Conference (GNC 13) AIAA 2013-4619 Boston MassUSA August 2013
[11] L Lin Y Wang Y Liu C Xiong and K Zeng ldquoMarker-lessregistration based on template tracking for augmented realityrdquoMultimedia Tools and Applications vol 41 no 2 pp 235ndash2522009
[12] X Liu L Lin S Yan H Jin and W Jiang ldquoAdaptive objecttracking by learning hybrid template onlinerdquo IEEE Transactionson Circuits and Systems for Video Technology vol 21 no 11 pp1588ndash1599 2011
[13] L Lin Y Lu Y Pan and X Chen ldquoIntegrating graph partition-ing and matching for trajectory analysis in video surveillancerdquoIEEE Transactions on Image Processing vol 21 no 12 pp 4844ndash4857 2012
[14] L Xia P Li Y Guo and Z Shen ldquoResearch of maneuveringtarget tracking based on particle filterrdquo in Proceedings of the Chi-nese Automation Congress (CAC rsquo13) pp 567ndash570 ChangshaChina 2013
[15] F Gustafsson F Gunnarsson N Bergman et al ldquoParticle filtersfor positioning navigation and trackingrdquo IEEE Transactions onSignal Processing vol 50 no 2 pp 425ndash437 2002
[16] S Challa and G W Pulford ldquoJoint target tracking and classi-fication using radar and ESM sensorsrdquo IEEE Transactions onAerospace and Electronic Systems vol 37 no 3 pp 1039ndash10552001
[17] M S Grewal and A P Andrews Kalman Filtering Theory andPractice Using Matlab John Wiley amp Sons 2nd edition 2001
[18] S Haykin Kalman Filtering and Neural Networks John Wileyand Sons 2001
[19] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Transactions of the ASME Series D Journal of BasicEngineering vol 82 no 1 pp 35ndash45 1960
[20] S Arulampalam and B Ristic ldquoComparison of the particle filterwith range-parameterised and modified polar EKFs for angle-only trackingrdquo in Signal and Data Processing of Small Targetsvol 4048 of Proceedings of SPIE pp 288ndash299 Orlando FlaUSA April 2000
[21] X Lin T Kirubarajan Y Bar-Shalom and S Maskell ldquoCom-parison of EKF pseudomeasurement and particle filters fora bearing-only target tracking problemrdquo in Signal and Data
12 The Scientific World Journal
Processing of Small Targets vol 4728 of Proceedings of SPIE pp240ndash250 April 2002
[22] M S Arulampalam S Maskell N Gordon and T Clapp ldquoAtutorial on particle filters for online nonlinearnon-GaussianBayesian trackingrdquo IEEE Transactions on Signal Processing vol50 no 2 pp 174ndash188 2002
[23] A Doucet N de Freitas and N Gordon ldquoAn introduction tosequential Monte Carlo methodsrdquo in Sequential Monte CarloMethods in Practice Statistics for Engineering and InformationScience pp 3ndash14 Springer New York NY USA 2001
[24] B Liu andCHao ldquoSequential bearings-only-tracking initiationwith particle filteringmethodrdquoThe ScientificWorld Journal vol2013 Article ID 489121 7 pages 2013
[25] R Karlsson and F Gustafsson ldquoRecursive Bayesian estimationbearings-only applicationsrdquo IEE Proceedings Radar Sonar andNavigation vol 152 no 5 pp 305ndash313 2005
[26] N Gordon ldquoHybrid bootstrap filter for target tracking inclutterrdquo in Proceedings of the American Control Conference vol1 pp 628ndash632 June 1995
[27] S Mcginnity and G W Irwin ldquoMultiple model bootstrapfilter for maneuvering target trackingrdquo IEEE Transactions onAerospace and Electronic Systems vol 36 no 3 pp 1006ndash10122000
[28] M R Morelande and S Challa ldquoManoeuvring target trackingin clutter using particle filtersrdquo IEEE Transactions on Aerospaceand Electronic Systems vol 41 no 1 pp 252ndash270 2005
[29] D Lerro and Y Bar-Shalom ldquoTracking with de-biased consis-tent converted measurements versus EKFrdquo IEEE TransactionsonAerospace and Electronic Systems vol 29 no 3 pp 1015ndash10221993
[30] G Fasano L Forlenza D Accardo A Moccia and A RispolildquoIntegrated obstacle detection system based on radar andoptical sensorsrdquo inProceedings of the AIAA Infotech at Aerospace(AIAA rsquo10) Atlanta Ga USA April 2010
[31] S S Blackman and R F Popoli Design and Analysis of ModernTracking Systems Artech House Norwood Mass USA 1999
[32] G Fasano D Accardo A Moccia and A Rispoli ldquoAn inno-vative procedure for calibration of strapdown electro-opticalsensors onboard unmanned air vehiclesrdquo Sensors vol 10 no 1pp 639ndash654 2010
[33] B Ristic S Arulampalam and N Gordon Beyond the KalmanFilter Particle Filter for Tracking Applications Artech HouseNew York NY USA 2004
[34] A Haug and L Williams ldquoA spherical constant velocity modelfor target tracking in three dimensionsrdquo in IEEE AerospaceConference pp 1ndash15 Big Sky Mont USA March 2012
[35] X R Li and V P Jilkov ldquoA survey of maneuvering target track-ing dynamic modelsrdquo in Proceedings of the SPIE Conference onsignal and Data Processing of Small Targets vol 39 pp 1333ndash1364 Orlando Fla USA April 2000
[36] G Fasano A Moccia D Accardo and A Rispoli ldquoDevelop-ment and test of an integrated sensor system for autonomouscollision avoidancerdquo in Proceedings of the 26th Congress ofInternational Council of the Aeronautical Sciences (ICAS rsquo08) pp3625ndash3634 Anchorage Alaska USA September 2008
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2 The Scientific World Journal
some loss of accuracy in obstacle tracking performance Onthe other hand innovative filtering techniques developed fornonlinear systems such as particle filters are expected toprovide more accurate estimates of obstacle dynamics thanEKF thus improving the accuracy of the DCPA estimate andpotentially reducing the delay in collision detection [10]
Thus a research effort has been carried out in orderto assess the impact of particle filtering approaches in theconsidered application
In general tracking problems comprise several applica-tions such as ocean surveillance submarine tracking carpositioning video surveillance and airborne target trackingDifferent solutions and methods have been proposed andimplemented [11ndash16]
One of the key components of a tracking system isthe filtering and prediction block where target motion ismodeled using a state vector and a dynamic system andsensor observations are related to the state vector by aproper measurement equation Within this framework mostpopular solutions are based onKalmanfiltering [17ndash19]whichcan be demonstrated to be the theoretically optimal approachfor linear systems corrupted by gaussian noise In the latestyears particle filtering techniques have found increasingdiffusion in problems involving nonlinear and non-Gaussiannoise processes [20ndash23]
Particle filtering has been applied to various nonlinearproblems such as bearing-only tracking trackingmultitargetin clutter and jump Markov linear system
In [24] the tracking problem is examined in the contextof autonomous bearing-only tracking of a single appear-ingdisappearing target in the presence of clutter measure-ments The same problem is also analyzed in [21] where acomparison between EKF a pseudo measurement trackingfilter and a PF is pointed out The study aims at tracking atarget from an airborne sensor at an approximately knownaltitude The analysis shows the PF algorithm to be morerobust than EKF Karlsson and Gustafsson [25] make acomparison between the two filters for angle-only trackingin several applications such as air-to-air air-to-sea and sea-to-sea scenarios In the study experimental data are used totest the algorithm in the sea-to-sea caseThe results show thatthe PF outperforms the EKF algorithm Besides PF has beenalso applied to solve problems of tracking multiple targetsin clutter environment [26ndash28] These works provide someimplementation suggestions to improve the PF performancewith extension to bootstrap filter
This paper describes a customized particle filtering algo-rithm based on spherical coordinates and aimed at flyingobstacle detection and tracking for non-cooperative senseand avoid On the basis of application needs the algorithmhas been developed to understand PF potential especially interms of reliability and latency in collision risk estimationThus the predicted DCPA between aircraft has been consid-ered as the key variable of the problem
Besides the application field main innovation aspectsof the developed PF algorithm comprise the treatment andcompensation of sensor latencies in view of real time softwareimplementation with the negative timemeasurement updateproblem dealt with keeping in memory a sliding window
B r
VB
VA
AdAB
VAB = VA minus VB
Figure 1 Definition ofminimum separation distance vector 119889119860119861
and using a Monte Carlo sampling approach and the directparticle-based prediction of minimum separation distance
The paper is organized as follows First a brief descriptionof problem geometry and hardware architecture of the systemused in flight tests is provided Then the tracking algorithmis presented in detail Finally results obtained in off-linesimulations based on flight data gathered during TECVOLtest campaign are presented and discussed
2 Obstacle Detection and Tracking forUAS Sense and Avoid
ADSampA systemhas to be endowedwith an obstacle detectionand tracking system that performs the ldquosenserdquo function anda collision avoidance subsystem that performs a collisionavoidance maneuver as soon as a collision risk is detectedIn order to realize a suitable and reliable sense and avoidsystem a series of requirements concerning the field ofregard range resolution angular resolution detection rangetime to collision and system data rate have to be satisfied inthe case of non-cooperative technologies In particular flightregulations define the scanning volume for collision threatdetection and the maximum relative speed between the twoaircraft Moreover they prescribe that the own aircraft andthe intruder must never be closer than 500 ft that is the so-called bubble distance [3]
Considering the above-mentioned requirements they areessentially relevant to the ability to estimate the Distance atClosest Point of Approach and the Time to Closest Point ofApproach often named ldquotime to gordquo in the literature Theformer parameter indicates the minimum distance that willbe measured between two planes that keep their currentvelocity constant it can be calculated from [4]
119889119860119861=119903 sdot 119881119860119861
100381710038171003817100381711988111986011986110038171003817100381710038172119881119860119861minus 119903 (1)
where 119889119860119861
is the minimum separation distance (whose normis the DCPA) [29]119881
119860119861is the relative speed vector (119881
119860minus119881119861)
between the intruder (aircraft 119860) and the ownship (aircraft119861) and 119903 is the relative position between the aircraft (seeFigure 1) If the intruder is modeled as a spherical object withradius 119877 it can be demonstrated [4] that assuming constantvelocity vectors 119881
119860and 119881
119861 respectively the two aircraft are
headed for collision if and only if the following conditions aresatisfied
10038171003817100381710038171198891198601198611003817100381710038171003817 le 119877 119903 lt 0 (2)
The Scientific World Journal 3
These values are a measure of the collision risk if theseconditions are satisfied a Near Mid-Air Collision threat isconsidered
It is worth noting that in order to obtain an accurateestimate of the DCPA an adequate sensor setup has to beproperly chosen In general this function can be performedinstalling onboard UAS cooperative andor non-cooperativesystems that include both active and passive sensors thechoice depends on size speed maneuverability andmissionsfor which theUASwill be used In case of largeUAS platformsand fully autonomous systems integrated radarelectro-optical architecture seems to be a good option to increasethe collision threat awareness In fact radars provide accuraterange estimates and can operate in all-time all-weatherconditions while EO sensors offer the potential of accurateangular measurements at fast update rates in addition thesesystems do not rely on information from external sources todetect and track other aircraft thus avoiding problems due tothe loss of communication links
As anticipated above within TECVOL project a con-figuration with radar as main sensor and EO as auxiliarysensors has been chosen as the optimal solution in view of theapplication In fact this project aimed at the development andflight demonstration of the technologies needed to supporthigh altitude long endurance UAS flight autonomy Thechoice of a multisensor configuration allows a compensationof single sensor shortcomings by integrating informationfrom heterogeneous sources In the next section for the sakeof clarity the flight system architecture is briefly described
3 Flight System Architecture
During the TECVOL flight test campaign the prototypehardwaresoftware sensing system installed onboard FLARE(Figure 2) was comprised of a Ka-band pulse radar and fourelectro-optical cameras (two visible cameras and two infraredcameras) a CPU devoted to image processing (IP-CPU) anda CPU devoted to real time tracking by sensor data fusion(RTT-CPU) This unit is connected to the onboard flightcontrol computer that performs autonomous navigation andflight control including autonomous collision avoidancemaneuvers [4 7 30] A hierarchical architecture in which theradar is the main sensor that must perform initial detectionand tracking and the EO sensors are used as auxiliary infor-mation sources in order to increase accuracy and data ratehas been consideredThe choice of a hierarchical architectureis determined by different levels of sensor performance infact the conventional EO sensors perform initial detectionat closer ranges than radar The standalone radar trackingestimates can be effective in reducing the computation timeand false alarm rate of EO image processing by selecting prop-erly defined search windows to apply the obstacle detectionprocess
In Figure 3 the adopted hardware system is depictedFor more details on the hardware and logical architecturesadopted within TECVOL project the reader is referred to[4 7]
Figure 2 Sensing system onboard FLARE
AHRS
Radar Panchro vis Color vis Infrared Infrared
Ethernet
EthernetFirewire link
Can BUS
GNC systemGPS
AIR
ALT
Navigation sensors
Image processingcomputer
Real timecomputer
Figure 3 The onboard hardware architecture
The tracking system can operate in two different modes
(1) standalone radar tracking mode that performs cur-rent estimates of obstacle relative position and veloc-ity on the basis of measurements from radar and theinertial unit
(2) radarEO tracking mode where current estimates ofobstacle relative position and velocity are determinedalso on the basis of EO sensor measurements
In this paper the radar-only tracking configuration wasconsidered in order to evaluate the impact of particle filteringtechniques first in a single sensor framework Indeed giventhe hierarchical architecture of the considered system radar-only tracking performance has a significant impact on datafusion operation In particular while in TECVOL projectthe tracking module was based on an EKF-based central-level fusion system for real time applications this paperdiscusses the development of a particle filter technique whichhas been tested in off-line simulations in fact innovativetechniques are expected to provide more accurate estimatesof obstacle dynamics than EKF in case of nonlinear systemsthus reducing the delay in collision detection
4 The Scientific World Journal
4 Developed Software Description
In general the tracking software allows effective fusion ofinformation provided by different sensors such as radar andinertial unit moreover it performs the gatingassociationfunctions in order to associate at the same intruder mea-surements gathered in different scans and to eliminate falsealarms and clutter returns In fact the inputs to the algorithmare sensor measurements which represent in general objectof interest false alarm and clutter In this case most ofthe clutter return will likely come from ground echoesTrackmeasurement association is carried out using ellip-soidal gating and a centralized statistic [31] defined as
120585 = [119910 minus 119910]1015840[119877 + 119867119875119867
1015840]minus1
[119910 minus 119910] (3)
where 119910 is the measurement vector at the time of detection 119910is the predicted measurement vector at the time of detection119875 is the predicted covariance matrix 119867 is the measurementtransition matrix and 119877 is the measurement covariancematrix This statistics is a normalized distance betweenmeasurement and prediction which takes into account allthe relevant uncertainties Assuming a statistical distributionfor 120585 it is then possible to define a threshold based onthe probability of a correct measurement falling inside thegate As an example in common radar applications 120585 isassumed to be distributed as a chi-square variable with anumber of degrees of freedom equal to the dimension of themeasurement vector
After the association phase based on a common nearestneighbour approach since a dense multitarget environmentis unlikely to be found in the considered civil collision avoid-ance scenario the track status must be properly handled Inparticular tracks are divided in three categories one-plot(single observation not associated with any existing track)tentative (at least two observations but confirmation logicis still required) and firm (confirmed track) The transitiontentative firm can be based on different techniques Tracks aredeleted if they are not updated within a reasonable interval
The filtering and prediction phase allows combining trackprediction and sensormeasurements and produces new trackpredictions The tracking system is based on a particle filterwith nonlinear dynamic model and linear measurementequation The state vector is comprised of 6 componentsthat are the obstacle positions in terms of range azimuthand elevation in north-east-down (NED) reference frame andtheir first time derivatives Besides the PF tracker providesalso an estimate of the Distance at Closest Point of ApproachThe obstacle dynamic model is based on a nearly constantvelocity model better described in the following sectionImportant points are related to the sensor latency and theproper inclusion of aircraft navigation measurements Thusproper data registration techniques have been considered asa prerequisite for the developed algorithm [32] Regardingtime registration the radar sends its measurements at theend of each pass with maximum latency of the order of 1 sSince the tracker works at 10Hz in the developed system ameasurement is assigned a time stamp which is the nearesttime on the tracker 01 s scale Since the radar delay is typically
larger than the 01 s scale it is likely that a measurementrelative to time 119905
1arrives when the state has already been
propagated to a later time 119905119899 In this case the state and
covariance must be updated at time 1199051 Also the gating and
association processes have to be performed with values ofstate and covariance at time 119905
1 Then the problem is how to
produce updated parameters from measurement at time 1199051
In order to perform gating association and track updat-ing the solution is to keep inmemory a slidingwindowwherenavigation and track data are stored The considered timewindow dimensions correspond to the largest possible radardata latency Given that state and covariance at time 119905
1have
to be known and stored in the developed PF tracker the keyidea is to consider all the variables at time 119905
1 to perform the
filtering step taking into account the radar measurement atthat time and then update the state (and covariance) untiltime 119905
119899by means of a Monte Carlo approach
41 Particle Filter Algorithm Particle filters are Bayesianestimators that resolve the state estimation problems bydetermining the probability density function (PDF) of anunknown random vector using a weighted sum of delta func-tionsThese filters have less limitations than the Kalman filterIndeed they can exploit nonlinear process and measurementmodels and they can be used with any form of system noisestatistical distribution
The implemented particle filter is based on the samplingimportance resampling algorithm [33] constituted by threemain steps generation of particles calculation of the weightsassociated with the particles and resampling procedureThen the state space is propagated through a nonlineardynamic equation A brief overview of the PF phases isreported
Let us consider a set of points and associated weights inthe target state space 119908(119894)
119896minus1 119909(119894)
119896minus1 for 119894 = 1 119873
119904 which
represent samples from the updated target state PDF at time119896minus1The latter can be represented by a weighted sum of deltafunctions as
119901 (119909119896minus1| 119885119896minus1) asymp
119873
sum
119894=1
119908(119894)
119896minus1120575 (119909119896minus1minus 119909(119894)
119896minus1) (4)
where 119908(119894)119896minus1
is the weight associated with the 119894th particle andsum119873
119894=1119908(119894)
119896minus1= 1
In the developed algorithm the target state space (iethe points and related weights) is initialized generating theparticles from a multivariate normal distribution with meanequal to the first radar measurements and specified standarddeviation values In particular the uncertainties have beenestimated on the basis of obstacle dynamic behavior and radaraccuracy (120590
119903= 9m 120590
120599= 2∘ 120590
120601= 2∘) Choosing a large
initial uncertainty on obstacle position allows letting a goodnumber of particles representing the state in important orhigh likelihood regions Consequently radar measurementshave non-negligible importance in the track initializationphase At the first step all the particles are generated withthe same weight set equal to 1N After that the set of pointsrepresenting 119901(119909
119896minus1| 119885119896minus1) have to be transformed into a set
The Scientific World Journal 5
Estimate at k + 1
State at k + 1
PF initialization
Transition to k + 1
xik+1 = f(xik) + nk
Measurement at k + 1
zik+1 = H(xik+1) + k+1
Prediction at k + 1
xi(k+1|k) = f(xi(k|k)) + nk
Measurement prediction at k + 1
zi(k+1|k) = H(xi(k+1|k)) + k
Weights update at k + 1
Resamplingxi(k+1|k+1) = resampling(xi(k+1|k) wi
k+1)
Generation of particles xikand weights wi
k
exp
Figure 4 Particle filtering algorithm
of points 119908(119894)119896 119909(119894)
119896 representing 119901(119909
119896| 119885119896) This is done by
PF in two steps prediction and filteringThe prediction step exploits the system model to predict
the state distribution function from one measurement timeto another one It transforms the updated density at time119896 minus 1 into a set of points representing the predicted density119901(119909119896| 119885119896minus1) by substituting each sample 119909(119894)
119896minus1in the dynamic
equation Since the state is subject to a process noise modeledas an independent and identically distributed process noisesequence the prediction step translates deforms and spreadsthe state distribution
The filtering step utilizes a measurement at time 119896 toupdate the set of particles representing the propagated density119901(119909119896| 119885119896minus1) to a set of particles 119908(119894)
119896 119909(119894)
119896 sim 119901(119909
119896| 119885119896) with
updated weights The optimal choice is to sample from theupdated density 119901(119909
119896| 119885119896) directly since this is impossible
because it is unknown the solution is to sample from thepropagated density (as in this specific analysis)Then given ameasurement 119911
119896and the set of propagated points 119908(119894)
119896minus1 119909(119894)
119896
the updated set of particles is given by
119908(119894)
119896=
119908(119894)
119896minus1119901 (119911119896| 119909(119894)
119896)
sum119873
119895=1119908(119895)
119896minus1119901 (119911119896| 119909(119895)
119896)
(5)
where 119901(119911119896| 119909(119894)
119896) is the measurement likelihood in this
application it has been defined as
119901 (119911119896| 119909119896) =
1
radic21205871198772
exp(minus(119911119896minus 119896)1015840119877minus1(119911119896minus 119896)
2)
(6)where
119896is the predicted measurement at the time of
detection and 119877 is the measurement covariance matrix
In the software the resampling procedure is based on asystematic resampling scheme [33] which is performed ateach time step and not only when the number of particleswith non-negligible weight falls below a threshold valueThe resampling phase enables a great quantity of particlesto survive during the propagation of the state space thusavoiding the degeneracy phenomenon
The software outputs based on range azimuth elevationand their first time derivatives are then calculated on the basisof the state estimates weighted on all particles
In Figure 4 a particle filtering scheme is reported in orderto better clarify how the developed software has been con-ceived The scheme exploits the main steps of the algorithminitialization prediction filtering and resampling In partic-ular the filtering phase is based on weights update obtainedconsidering measurement prediction sensor outputs andmeasurement covariance matrix 119877
42 Obstacle Tracking Dynamic Model The selection of adynamic model is a nontrivial problem for airborne obstacletracking systems since an accurate estimate of the obstacleposition is considered fundamental for the evaluation of theDistance at Closest Point of Approach In the developedsoftware a nearly constant velocity model in spherical coor-dinates has been implemented to represent the target relativetrajectory [34 35] The target state is propagated through anonlinear dynamic equation since the state variables are inspherical coordinates and thus closer to sensormeasurementsoutputs
The state vector is comprised of obstacle position interms of range azimuth and elevation in north-east-downreference frame and their first time derivatives Hereinafterthe obstacle dynamic model is reported for the sake of clarity
6 The Scientific World Journal
52505
52505
52505
52505
52506
52506
52506
times104
1080
1070
1060
1050
1040
1030
1020
1010
1000
990
GPS time of day (s)
Rang
e (m
)
Spherical PF
GPSRadar
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104
4000
3000
2000
1000
0
GPS time of day (s)
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
Rang
e (m
)
GPSRadar
RadarPF tracker
20
0
minus20
minus40
Erro
r in
rang
e (m
)
Spherical PF
Figure 5 Range as estimated by GPS by radar and by radar-only tracker and estimation error as a function of GPS time of day The upperfigure highlights the trajectory of each particle
The target state vector in spherical coordinates is definedas
119909 = [119903 119903 120599 120599 120601 120601] (7)
where 119903 is the range 120599 is the azimuth 120601 is the elevation angleand 119903 120599 120601 are their first time derivatives
In order to evaluate the velocity components let usconsider
V = [
[
V119903
V120599
V120601
]
]
= [
[
119903
119903 120599 cos120601119903 120601
]
]
(8)
where the velocity vector has been defined as V = [V119903 V120599 V120601]
for the sake of simplicity
For a spherical constant velocity dynamic model repre-senting the objectmotion it is assumed that V
119903= V120599= V120601= 0
Taking the time derivative of each component in (8) yields
V119903= 119903 = 0
V120599= 119903 120599 cos 120593 + 119903 120599 cos 120593 minus 119903 120599 sin 120593 = 0
V120601= 119903 + 119903 = 0
(9)
Rearranging the above expressions in terms of angu-lar velocities and considering discrete-time domain with
The Scientific World Journal 7
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
Radar
RadarPF tracker
Spherical PF
Spherical PF
100
0
minus100
minus200Azi
mut
h in
NED
refe
renc
e fra
me (
∘ )PF tracker
6
4
2
Erro
r in
stab
ilize
daz
imut
h (∘
)
Figure 6 Azimuth in NED reference frame as estimated by GPS by radar and by radar-only tracker and estimation error as a function ofGPS time of day
sampling time 119879 the components of the dynamic motionequation are given by
119903119899= 119903119899minus1+ 119879 119903119899minus1
119903119899= 119903119899minus1
120599119899= 120599119899minus1+ 119879 120599119899minus1[1 +
119879
2119903119899minus1
(119903119899minus1120601119899minus1119905119892120601119899minus1minus 119903119899minus1)]
120599119899= 120599119899minus1[1 + 119879( 120601
119899minus1119905119892120601119899minus1minus119903119899minus1
119903119899minus1
)]
120601119899= 120601119899minus1+ 119879 120601119899minus1[1 minus
119879
2119903119899minus1
119903119899minus1]
120601119899= 120601119899minus1[1 minus
119879
2119903119899minus1
119903119899minus1]
(10)
The nonlinear dynamicmotion equation for the sphericalstate vector can be written as
119909119899= 119891 (119909
119899minus1) + 119899119899minus1 (11)
with the zero-mean Gaussian dynamic acceleration noisedistribution
119899119899sim 119873(0 119876
120588) (12)
The components of 119891(119909119899minus1) are given by the nonlinear
equation (10) and the process noise matrix is
119876120588= [
[
119902119903119876102
02
02119902ℎ119876102
02
02119902V1198761
]
]
(13)
with
1198761=
[[[[
[
1198793
3
1198792
2
1198792
2119879
]]]]
]
(14)
where 119902119903 119902ℎ and 119902V must be set depending on the target
maneuvers [34]Since the model is in spherical coordinates the measure-
ment equation is linear and it can be expressed as
119911119899= 119867119909119899+ 119908119899 (15)
with
119867 = [
[
1 0 0 0 0 0
0 0 1 0 0 0
0 0 0 0 1 0
]
]
(16)
and 119908119899is the observation noise which is considered to be
independent zero-mean Gaussian noise defined by
119908119899sim 119873 (0 119877
119899) (17)
8 The Scientific World Journal
52494
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
Radar
RadarPF tracker
Spherical PF
Spherical PFEl
evat
ion
in N
EDre
fere
nce f
ram
e (∘ )
PF tracker
40
minus4minus8minus12
1505
minus05minus15minus25Er
ror i
n st
abili
zed
elev
atio
n (∘
)
Figure 7 Elevation in NED reference frame as estimated by GPS by radar and by radar-only tracker and estimation error as a function ofGPS time of day
52494
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
PF tracker
Spherical PF
Spherical PFPF tracker
minus72
minus76
minus80
minus84
Rang
e rat
e(m
s)
6
2
minus2
minus6Erro
r in
rang
era
te (m
s)
Figure 8 Range rate as estimated by GPS and by radar-only tracker and estimation error as a function of GPS time of day
where 119877119899is the measurement covariance matrix as stated
aboveThe developed obstacle detection and tracking software
provides also an estimate of the Distance at Closest Pointof Approach (see (1)) Since the particles are characterizedby own positions and velocities and given the nonlineardependencies between 119903119881 andDCPA the latter is calculatedfor each particle In this way in order to avoid furtherapproximations due to the evaluation of this distance from
position and velocitymean values DCPA has been calculatedas mean value of the different distances evaluated as
DCPA119899=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
119903 sdot 119881
1003817100381710038171003817100381711988110038171003817100381710038171003817
2119881 minus 119903
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(18)
This is a form of ldquodeep integrationrdquo of a collision detectionsensor since an estimate of the level of collision threat isdetermined by means of the same data fusion algorithm
The Scientific World Journal 9
52494
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
PF tracker
Spherical PF
Spherical PFPF tracker
0
minus1
minus2
minus3
050301
minus01minus03
Azi
mut
h ra
te in
NED
refe
renc
e fra
me (
∘ s)
Erro
r in
stab
ilize
daz
imut
h ra
te (∘
s)
Figure 9 Azimuth rate in NED reference frame as estimated by GPS and by radar-only tracker and estimation error as a function of GPStime of day
This is an additional advantage of using PF rather than EKFsince the need of linearized models in EKF does not allowestimating DCPA by the filter itself
5 Results
The developed obstacle tracking algorithm has been testedin off-line simulations based on flight data gathered duringan intensive test campaign Flight tests were carried out byexploiting the following configuration of test facilities
(a) FLARE aircraft piloted by a human pilot or by theautonomous flight control system
(b) a piloted intruder VLA aircraft in the same class ofFLARE equipped with GPS antennas and receiversand an onboard CPU for navigation data storage
(c) a ground control station (GCS) for real time flightcoordination and test monitoring [36]
(d) a full-duplex data link between FLARE and GCSused to send commands to initiate or terminate testsand to receive synthetic filter output and navigationmeasurements
(e) a downlink between intruder and GCS used for flightmonitoring
During the tests two types of maneuvers were executedsuch as chasing tests with FLARE pursuing the intruder andquasi-frontal encounters performed to estimate detectionand tracking performance in the most interesting scenariosfrom the application point of view
In particular the scenario selected in this paper forperformance analysis is a single quasi-frontal encounterbetween FLARE and the intruder The algorithm has beentested in standalone radar tracking configuration that is
estimates of obstacle relative position and velocity are basedon measurements from radar (update frequency of 1Hz) andthe own-ship navigation system
The number of particles has been set equal to 500 Thisnumber was selected since increasing it up to one orderof magnitude did not produced significant performanceincrease The algorithm is initialized taking into accountthe first radar sensor measurement the covariance matrix iscalculated on the basis of sensor measurements and then it isupdated with estimated values of software output
The algorithm outputs are based on obstacle position andvelocity in terms of range azimuth and elevation and DCPAin a stabilized north-east-down reference frame with originin FLARE center of mass The considered flight segment hasduration of about 20 s with an initial range of about 2000m
In Figure 5 obstacle range as estimated by radar radar-based tracker and GPS (reference) together with errorestimate with respect to GPS measurements is reportedAfter a firm track has been generated on the basis of radarmeasurements the tracker is able to characterize the obstacletrajectory The radar-only tracker provides a range estimatewith an accuracy of the order of few meters that derives fromthe good radar range accuracy and the absence of intrudermaneuvers In Figure 5 the upper plot illustrates the obstaclerange in a small interval time (of about 1 s) in order to showthe particles trajectories (colored lines)
Figures 6 and 7 report the obstacle angular dynamicsin terms of azimuth and elevation As expected the orderof magnitude of these errors is comparable to the radaraccuracy In particular the estimation uncertainty in termsof root mean square is of about 25∘ for azimuth and 13∘ forelevation Being computed in NED these RMS errors includeattitude measurement error biases In fact error biases in theestimation of magnetic heading are the main reason of thelarger error in azimuth It is worth noting that these biases
10 The Scientific World Journal
Table 1 PF performance in the selected scenario in terms of RMSerror
RMS Particle filter EKFRange (m) 84 37Range rate (m∘) 30 23Azimuth (∘) 25 17Azimuth rate (∘s) 02 04Elevation (∘) 13 21Elevation rate (∘s) 02 08
have a little effect on the estimation of angular rates and ofDistance at Closest Point of Approach
The range and angular rates as estimated by GPS (ref-erence) and particle filter tracker are reported in Figures 89 and 10 These variables are very important informationsources for collision detection assessment even though theyare not directly provided by the radar sensor The plots showthat the tracker estimates are very accurate with a very smallvalue in terms of standard deviation
Simulation results confirm how the resampling proce-dure is a key factor for tracking performance avoiding thedegeneracy phenomenon and thus enabling a great quantityof particles to survive to the prediction step
In order to better understand the particle filter trackingcapability PF and EKF estimation errors are reported inTable 1 in terms of root mean square (RMS) errors computedas
RMS = radic 1119873
119873
sum
119905=1
(119909119905minus 119909119905)2 (19)
where 119873 is the number of measurements 119909119905is the generic
PF tracker estimate (computed after resampling and repre-senting the mean value over all the particles) and 119909
119905is the
reference value computed on the basis of FLARE and intruderGPS measurements
The results show that PF tracker performance is com-parable to EKF in terms of order of magnitude Of coursethe introduction of electro-optical data can improve angularaccuracy since these sensors have a faster update rate thanradar In particular while the range rate error is very similarfor the two filters obstacle angular velocities provided byPF algorithm are slightly more accurate than EKF in theconsidered scenario These variables are very importantinformation sources for collision detection assessment eventhough they are not directly provided by the radar
In fact in near collision conditions angular rates are themost important variables influencing collision detection Asshown in [7] in these conditions DCPA uncertainty for givenrange and range rate shows a linear dependence on angularrate errors while range rate essentially impacts the time-to-go estimate
In the considered scenario DCPA as computed on thebasis of GPS measurement has been used as a reference forcomparing DCPA estimated by EKF tracker and PF trackerFigure 11 shows that the PF algorithm is more accuratethan EKF for the estimation of the DCPA in the initial
52494
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
PF tracker
Spherical PF
Spherical PFPF tracker
Elev
atio
nh ra
te in
NED
refe
renc
e fra
me (
∘ s)
08
04
0
minus04
minus01minus02minus03minus04minus05Er
ror i
n st
abili
zed
elev
atio
n ra
te (∘
s)
Figure 10 Elevation rate in NED reference frame as estimated byGPS and by radar-only tracker and estimation error as a function ofGPS time of day
450
400
350
300
250
200
150
100
50
Distance at Closest Point of Approach (DCPA) (m)
PF trackerEKF trackerGPS
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
Figure 11 Distance at Closest Point of Approach as estimated byGPS (reference) by radar and by radar-only tracker as function ofGPS time of the day
phase of firm tracking (at larger range) thus providing animprovement in collision risk assessment and a potentialreduction in the delay in declaring a collision threat Analysisof GPS data demonstrates that the considered encounterrepresents a real Near Mid-Air Collision (NMAC) scenariosince the reference DCPA keeps a very small value and liesbelow the bubble distance threshold almost in the whole firmtracking phase
The Scientific World Journal 11
6 Conclusion and Future Works
This paper focused on algorithm and test results fromobstacle tracking software based on particle filter and aimedat demonstrating UAS autonomous collision detection capa-bility in terms of reliable estimation of Distance at ClosestPoint of Approach The algorithm performance has beeninitially evaluated in radar-only configuration since the maininterest was addressed to the analysis of the potential impactof nonlinear filters on tracking capabilities with respect toassessed EKF first in a single sensor framework
The software has been tested in off-line simulations basedon real data recorded during a flight test campaign and aquasi-frontal encounter between the own aircraft and theintruder has been presented as test case The results pointedout that the developed algorithm is able to detect and trackthe obstacle trajectory with accuracy comparable to the EKFIn particular some advantages were highlighted in the directdetermination of Distance at Closest Point of Approach witha potential reduction of the delay for collision detectionThis result permits planning additional future investigationactivities such as
(i) performing the comparison on a larger experimentaldata set thus increasing the statistical significance
(ii) developing a multisensor-based analysis to confirmthe results obtained by the developed PF tracker whenadditional data sources are available such as electro-optical sensors indeed they can provide higheraccuracy in angular measurements and better datarate than radar sensors with a great impact on DCPAperformance
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The PhD grant of Miss Anna Elena Tirri is cofunded byEUROCONTROL through the research network HALA inthe framework of the WP-E of SESAR project
References
[1] EUROCONTROL in Proceedings of the EUROCONTROL Spec-ifications for the Use of Military Unmanned Aerial Vehicles asOperational Air Traffic Outside Segregated Airspace Version10 DocNo EUROCONTROL-SPEC-0102 Bruxelles BelgiumJuly 2007
[2] US Federal Aviation Administration (FAA) ldquoAirworthinesscertification of unmanned aircraft systemsrdquo Order 813034US Federal Aviation Administration (FAA) Washington DCUSA 2008
[3] US Federal Aviation Administration (FAA) ldquoInvestigate aNear Mid Air Collisionrdquo FAA Order 89001 vol 7 chapter 4Washington DC USA 2007
[4] G Fasano D Accardo A Moccia et al ldquoMulti-sensor-basedfully autonomous non-cooperative collision avoidance system
for unmanned air vehiclesrdquo Journal of Aerospace ComputingInformation and Communication vol 5 no 10 pp 338ndash3602008
[5] MTSI ldquoNon-cooperative detect see amp avoid (DSA) sensorstudyrdquo Tech Rep NASA ERAST 2002
[6] O Shakernia W Chen S Graham et al ldquoSense and Avoid(SAA) flight test and lessons learnedrdquo in Proceedings of the 2ndAIAA InfotechAerospace Conference and Exhibit (AIAA rsquo07)pp 2781ndash2795 Rohnert Park Calif USA May 2007
[7] D Accardo G Fasano L Forlenza A Moccia and A RispolildquoFlight test of a radar-based tracking system for UAS sense andavoidrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 49 no 2 pp 1139ndash1160 2013
[8] USFAA SpecialOperations FAAOrder 76104M January 2007[9] S J Julier and J K Uhlmann ldquoA new extension of the Kalman
filter to nonlinear systemsrdquo in Signal Processing Sensor Fusionand Target Recognition VI vol 3068 of Proceedings of SPIE pp182ndash193 Orlando Fla USA 1997
[10] N E Smith R G Cobb S J Pierce and V M Raska ldquoOptimalcollision avoidance trajectories for unmannedremotely pilotedaircraftrdquo in Proceedings of the AIAA Guidance Navigation andControl Conference (GNC 13) AIAA 2013-4619 Boston MassUSA August 2013
[11] L Lin Y Wang Y Liu C Xiong and K Zeng ldquoMarker-lessregistration based on template tracking for augmented realityrdquoMultimedia Tools and Applications vol 41 no 2 pp 235ndash2522009
[12] X Liu L Lin S Yan H Jin and W Jiang ldquoAdaptive objecttracking by learning hybrid template onlinerdquo IEEE Transactionson Circuits and Systems for Video Technology vol 21 no 11 pp1588ndash1599 2011
[13] L Lin Y Lu Y Pan and X Chen ldquoIntegrating graph partition-ing and matching for trajectory analysis in video surveillancerdquoIEEE Transactions on Image Processing vol 21 no 12 pp 4844ndash4857 2012
[14] L Xia P Li Y Guo and Z Shen ldquoResearch of maneuveringtarget tracking based on particle filterrdquo in Proceedings of the Chi-nese Automation Congress (CAC rsquo13) pp 567ndash570 ChangshaChina 2013
[15] F Gustafsson F Gunnarsson N Bergman et al ldquoParticle filtersfor positioning navigation and trackingrdquo IEEE Transactions onSignal Processing vol 50 no 2 pp 425ndash437 2002
[16] S Challa and G W Pulford ldquoJoint target tracking and classi-fication using radar and ESM sensorsrdquo IEEE Transactions onAerospace and Electronic Systems vol 37 no 3 pp 1039ndash10552001
[17] M S Grewal and A P Andrews Kalman Filtering Theory andPractice Using Matlab John Wiley amp Sons 2nd edition 2001
[18] S Haykin Kalman Filtering and Neural Networks John Wileyand Sons 2001
[19] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Transactions of the ASME Series D Journal of BasicEngineering vol 82 no 1 pp 35ndash45 1960
[20] S Arulampalam and B Ristic ldquoComparison of the particle filterwith range-parameterised and modified polar EKFs for angle-only trackingrdquo in Signal and Data Processing of Small Targetsvol 4048 of Proceedings of SPIE pp 288ndash299 Orlando FlaUSA April 2000
[21] X Lin T Kirubarajan Y Bar-Shalom and S Maskell ldquoCom-parison of EKF pseudomeasurement and particle filters fora bearing-only target tracking problemrdquo in Signal and Data
12 The Scientific World Journal
Processing of Small Targets vol 4728 of Proceedings of SPIE pp240ndash250 April 2002
[22] M S Arulampalam S Maskell N Gordon and T Clapp ldquoAtutorial on particle filters for online nonlinearnon-GaussianBayesian trackingrdquo IEEE Transactions on Signal Processing vol50 no 2 pp 174ndash188 2002
[23] A Doucet N de Freitas and N Gordon ldquoAn introduction tosequential Monte Carlo methodsrdquo in Sequential Monte CarloMethods in Practice Statistics for Engineering and InformationScience pp 3ndash14 Springer New York NY USA 2001
[24] B Liu andCHao ldquoSequential bearings-only-tracking initiationwith particle filteringmethodrdquoThe ScientificWorld Journal vol2013 Article ID 489121 7 pages 2013
[25] R Karlsson and F Gustafsson ldquoRecursive Bayesian estimationbearings-only applicationsrdquo IEE Proceedings Radar Sonar andNavigation vol 152 no 5 pp 305ndash313 2005
[26] N Gordon ldquoHybrid bootstrap filter for target tracking inclutterrdquo in Proceedings of the American Control Conference vol1 pp 628ndash632 June 1995
[27] S Mcginnity and G W Irwin ldquoMultiple model bootstrapfilter for maneuvering target trackingrdquo IEEE Transactions onAerospace and Electronic Systems vol 36 no 3 pp 1006ndash10122000
[28] M R Morelande and S Challa ldquoManoeuvring target trackingin clutter using particle filtersrdquo IEEE Transactions on Aerospaceand Electronic Systems vol 41 no 1 pp 252ndash270 2005
[29] D Lerro and Y Bar-Shalom ldquoTracking with de-biased consis-tent converted measurements versus EKFrdquo IEEE TransactionsonAerospace and Electronic Systems vol 29 no 3 pp 1015ndash10221993
[30] G Fasano L Forlenza D Accardo A Moccia and A RispolildquoIntegrated obstacle detection system based on radar andoptical sensorsrdquo inProceedings of the AIAA Infotech at Aerospace(AIAA rsquo10) Atlanta Ga USA April 2010
[31] S S Blackman and R F Popoli Design and Analysis of ModernTracking Systems Artech House Norwood Mass USA 1999
[32] G Fasano D Accardo A Moccia and A Rispoli ldquoAn inno-vative procedure for calibration of strapdown electro-opticalsensors onboard unmanned air vehiclesrdquo Sensors vol 10 no 1pp 639ndash654 2010
[33] B Ristic S Arulampalam and N Gordon Beyond the KalmanFilter Particle Filter for Tracking Applications Artech HouseNew York NY USA 2004
[34] A Haug and L Williams ldquoA spherical constant velocity modelfor target tracking in three dimensionsrdquo in IEEE AerospaceConference pp 1ndash15 Big Sky Mont USA March 2012
[35] X R Li and V P Jilkov ldquoA survey of maneuvering target track-ing dynamic modelsrdquo in Proceedings of the SPIE Conference onsignal and Data Processing of Small Targets vol 39 pp 1333ndash1364 Orlando Fla USA April 2000
[36] G Fasano A Moccia D Accardo and A Rispoli ldquoDevelop-ment and test of an integrated sensor system for autonomouscollision avoidancerdquo in Proceedings of the 26th Congress ofInternational Council of the Aeronautical Sciences (ICAS rsquo08) pp3625ndash3634 Anchorage Alaska USA September 2008
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Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
The Scientific World Journal 3
These values are a measure of the collision risk if theseconditions are satisfied a Near Mid-Air Collision threat isconsidered
It is worth noting that in order to obtain an accurateestimate of the DCPA an adequate sensor setup has to beproperly chosen In general this function can be performedinstalling onboard UAS cooperative andor non-cooperativesystems that include both active and passive sensors thechoice depends on size speed maneuverability andmissionsfor which theUASwill be used In case of largeUAS platformsand fully autonomous systems integrated radarelectro-optical architecture seems to be a good option to increasethe collision threat awareness In fact radars provide accuraterange estimates and can operate in all-time all-weatherconditions while EO sensors offer the potential of accurateangular measurements at fast update rates in addition thesesystems do not rely on information from external sources todetect and track other aircraft thus avoiding problems due tothe loss of communication links
As anticipated above within TECVOL project a con-figuration with radar as main sensor and EO as auxiliarysensors has been chosen as the optimal solution in view of theapplication In fact this project aimed at the development andflight demonstration of the technologies needed to supporthigh altitude long endurance UAS flight autonomy Thechoice of a multisensor configuration allows a compensationof single sensor shortcomings by integrating informationfrom heterogeneous sources In the next section for the sakeof clarity the flight system architecture is briefly described
3 Flight System Architecture
During the TECVOL flight test campaign the prototypehardwaresoftware sensing system installed onboard FLARE(Figure 2) was comprised of a Ka-band pulse radar and fourelectro-optical cameras (two visible cameras and two infraredcameras) a CPU devoted to image processing (IP-CPU) anda CPU devoted to real time tracking by sensor data fusion(RTT-CPU) This unit is connected to the onboard flightcontrol computer that performs autonomous navigation andflight control including autonomous collision avoidancemaneuvers [4 7 30] A hierarchical architecture in which theradar is the main sensor that must perform initial detectionand tracking and the EO sensors are used as auxiliary infor-mation sources in order to increase accuracy and data ratehas been consideredThe choice of a hierarchical architectureis determined by different levels of sensor performance infact the conventional EO sensors perform initial detectionat closer ranges than radar The standalone radar trackingestimates can be effective in reducing the computation timeand false alarm rate of EO image processing by selecting prop-erly defined search windows to apply the obstacle detectionprocess
In Figure 3 the adopted hardware system is depictedFor more details on the hardware and logical architecturesadopted within TECVOL project the reader is referred to[4 7]
Figure 2 Sensing system onboard FLARE
AHRS
Radar Panchro vis Color vis Infrared Infrared
Ethernet
EthernetFirewire link
Can BUS
GNC systemGPS
AIR
ALT
Navigation sensors
Image processingcomputer
Real timecomputer
Figure 3 The onboard hardware architecture
The tracking system can operate in two different modes
(1) standalone radar tracking mode that performs cur-rent estimates of obstacle relative position and veloc-ity on the basis of measurements from radar and theinertial unit
(2) radarEO tracking mode where current estimates ofobstacle relative position and velocity are determinedalso on the basis of EO sensor measurements
In this paper the radar-only tracking configuration wasconsidered in order to evaluate the impact of particle filteringtechniques first in a single sensor framework Indeed giventhe hierarchical architecture of the considered system radar-only tracking performance has a significant impact on datafusion operation In particular while in TECVOL projectthe tracking module was based on an EKF-based central-level fusion system for real time applications this paperdiscusses the development of a particle filter technique whichhas been tested in off-line simulations in fact innovativetechniques are expected to provide more accurate estimatesof obstacle dynamics than EKF in case of nonlinear systemsthus reducing the delay in collision detection
4 The Scientific World Journal
4 Developed Software Description
In general the tracking software allows effective fusion ofinformation provided by different sensors such as radar andinertial unit moreover it performs the gatingassociationfunctions in order to associate at the same intruder mea-surements gathered in different scans and to eliminate falsealarms and clutter returns In fact the inputs to the algorithmare sensor measurements which represent in general objectof interest false alarm and clutter In this case most ofthe clutter return will likely come from ground echoesTrackmeasurement association is carried out using ellip-soidal gating and a centralized statistic [31] defined as
120585 = [119910 minus 119910]1015840[119877 + 119867119875119867
1015840]minus1
[119910 minus 119910] (3)
where 119910 is the measurement vector at the time of detection 119910is the predicted measurement vector at the time of detection119875 is the predicted covariance matrix 119867 is the measurementtransition matrix and 119877 is the measurement covariancematrix This statistics is a normalized distance betweenmeasurement and prediction which takes into account allthe relevant uncertainties Assuming a statistical distributionfor 120585 it is then possible to define a threshold based onthe probability of a correct measurement falling inside thegate As an example in common radar applications 120585 isassumed to be distributed as a chi-square variable with anumber of degrees of freedom equal to the dimension of themeasurement vector
After the association phase based on a common nearestneighbour approach since a dense multitarget environmentis unlikely to be found in the considered civil collision avoid-ance scenario the track status must be properly handled Inparticular tracks are divided in three categories one-plot(single observation not associated with any existing track)tentative (at least two observations but confirmation logicis still required) and firm (confirmed track) The transitiontentative firm can be based on different techniques Tracks aredeleted if they are not updated within a reasonable interval
The filtering and prediction phase allows combining trackprediction and sensormeasurements and produces new trackpredictions The tracking system is based on a particle filterwith nonlinear dynamic model and linear measurementequation The state vector is comprised of 6 componentsthat are the obstacle positions in terms of range azimuthand elevation in north-east-down (NED) reference frame andtheir first time derivatives Besides the PF tracker providesalso an estimate of the Distance at Closest Point of ApproachThe obstacle dynamic model is based on a nearly constantvelocity model better described in the following sectionImportant points are related to the sensor latency and theproper inclusion of aircraft navigation measurements Thusproper data registration techniques have been considered asa prerequisite for the developed algorithm [32] Regardingtime registration the radar sends its measurements at theend of each pass with maximum latency of the order of 1 sSince the tracker works at 10Hz in the developed system ameasurement is assigned a time stamp which is the nearesttime on the tracker 01 s scale Since the radar delay is typically
larger than the 01 s scale it is likely that a measurementrelative to time 119905
1arrives when the state has already been
propagated to a later time 119905119899 In this case the state and
covariance must be updated at time 1199051 Also the gating and
association processes have to be performed with values ofstate and covariance at time 119905
1 Then the problem is how to
produce updated parameters from measurement at time 1199051
In order to perform gating association and track updat-ing the solution is to keep inmemory a slidingwindowwherenavigation and track data are stored The considered timewindow dimensions correspond to the largest possible radardata latency Given that state and covariance at time 119905
1have
to be known and stored in the developed PF tracker the keyidea is to consider all the variables at time 119905
1 to perform the
filtering step taking into account the radar measurement atthat time and then update the state (and covariance) untiltime 119905
119899by means of a Monte Carlo approach
41 Particle Filter Algorithm Particle filters are Bayesianestimators that resolve the state estimation problems bydetermining the probability density function (PDF) of anunknown random vector using a weighted sum of delta func-tionsThese filters have less limitations than the Kalman filterIndeed they can exploit nonlinear process and measurementmodels and they can be used with any form of system noisestatistical distribution
The implemented particle filter is based on the samplingimportance resampling algorithm [33] constituted by threemain steps generation of particles calculation of the weightsassociated with the particles and resampling procedureThen the state space is propagated through a nonlineardynamic equation A brief overview of the PF phases isreported
Let us consider a set of points and associated weights inthe target state space 119908(119894)
119896minus1 119909(119894)
119896minus1 for 119894 = 1 119873
119904 which
represent samples from the updated target state PDF at time119896minus1The latter can be represented by a weighted sum of deltafunctions as
119901 (119909119896minus1| 119885119896minus1) asymp
119873
sum
119894=1
119908(119894)
119896minus1120575 (119909119896minus1minus 119909(119894)
119896minus1) (4)
where 119908(119894)119896minus1
is the weight associated with the 119894th particle andsum119873
119894=1119908(119894)
119896minus1= 1
In the developed algorithm the target state space (iethe points and related weights) is initialized generating theparticles from a multivariate normal distribution with meanequal to the first radar measurements and specified standarddeviation values In particular the uncertainties have beenestimated on the basis of obstacle dynamic behavior and radaraccuracy (120590
119903= 9m 120590
120599= 2∘ 120590
120601= 2∘) Choosing a large
initial uncertainty on obstacle position allows letting a goodnumber of particles representing the state in important orhigh likelihood regions Consequently radar measurementshave non-negligible importance in the track initializationphase At the first step all the particles are generated withthe same weight set equal to 1N After that the set of pointsrepresenting 119901(119909
119896minus1| 119885119896minus1) have to be transformed into a set
The Scientific World Journal 5
Estimate at k + 1
State at k + 1
PF initialization
Transition to k + 1
xik+1 = f(xik) + nk
Measurement at k + 1
zik+1 = H(xik+1) + k+1
Prediction at k + 1
xi(k+1|k) = f(xi(k|k)) + nk
Measurement prediction at k + 1
zi(k+1|k) = H(xi(k+1|k)) + k
Weights update at k + 1
Resamplingxi(k+1|k+1) = resampling(xi(k+1|k) wi
k+1)
Generation of particles xikand weights wi
k
exp
Figure 4 Particle filtering algorithm
of points 119908(119894)119896 119909(119894)
119896 representing 119901(119909
119896| 119885119896) This is done by
PF in two steps prediction and filteringThe prediction step exploits the system model to predict
the state distribution function from one measurement timeto another one It transforms the updated density at time119896 minus 1 into a set of points representing the predicted density119901(119909119896| 119885119896minus1) by substituting each sample 119909(119894)
119896minus1in the dynamic
equation Since the state is subject to a process noise modeledas an independent and identically distributed process noisesequence the prediction step translates deforms and spreadsthe state distribution
The filtering step utilizes a measurement at time 119896 toupdate the set of particles representing the propagated density119901(119909119896| 119885119896minus1) to a set of particles 119908(119894)
119896 119909(119894)
119896 sim 119901(119909
119896| 119885119896) with
updated weights The optimal choice is to sample from theupdated density 119901(119909
119896| 119885119896) directly since this is impossible
because it is unknown the solution is to sample from thepropagated density (as in this specific analysis)Then given ameasurement 119911
119896and the set of propagated points 119908(119894)
119896minus1 119909(119894)
119896
the updated set of particles is given by
119908(119894)
119896=
119908(119894)
119896minus1119901 (119911119896| 119909(119894)
119896)
sum119873
119895=1119908(119895)
119896minus1119901 (119911119896| 119909(119895)
119896)
(5)
where 119901(119911119896| 119909(119894)
119896) is the measurement likelihood in this
application it has been defined as
119901 (119911119896| 119909119896) =
1
radic21205871198772
exp(minus(119911119896minus 119896)1015840119877minus1(119911119896minus 119896)
2)
(6)where
119896is the predicted measurement at the time of
detection and 119877 is the measurement covariance matrix
In the software the resampling procedure is based on asystematic resampling scheme [33] which is performed ateach time step and not only when the number of particleswith non-negligible weight falls below a threshold valueThe resampling phase enables a great quantity of particlesto survive during the propagation of the state space thusavoiding the degeneracy phenomenon
The software outputs based on range azimuth elevationand their first time derivatives are then calculated on the basisof the state estimates weighted on all particles
In Figure 4 a particle filtering scheme is reported in orderto better clarify how the developed software has been con-ceived The scheme exploits the main steps of the algorithminitialization prediction filtering and resampling In partic-ular the filtering phase is based on weights update obtainedconsidering measurement prediction sensor outputs andmeasurement covariance matrix 119877
42 Obstacle Tracking Dynamic Model The selection of adynamic model is a nontrivial problem for airborne obstacletracking systems since an accurate estimate of the obstacleposition is considered fundamental for the evaluation of theDistance at Closest Point of Approach In the developedsoftware a nearly constant velocity model in spherical coor-dinates has been implemented to represent the target relativetrajectory [34 35] The target state is propagated through anonlinear dynamic equation since the state variables are inspherical coordinates and thus closer to sensormeasurementsoutputs
The state vector is comprised of obstacle position interms of range azimuth and elevation in north-east-downreference frame and their first time derivatives Hereinafterthe obstacle dynamic model is reported for the sake of clarity
6 The Scientific World Journal
52505
52505
52505
52505
52506
52506
52506
times104
1080
1070
1060
1050
1040
1030
1020
1010
1000
990
GPS time of day (s)
Rang
e (m
)
Spherical PF
GPSRadar
52494
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52498
525
52502
52504
52506
52508
5251
52512
52514
times104
4000
3000
2000
1000
0
GPS time of day (s)
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52508
5251
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52514
times104GPS time of day (s)
Rang
e (m
)
GPSRadar
RadarPF tracker
20
0
minus20
minus40
Erro
r in
rang
e (m
)
Spherical PF
Figure 5 Range as estimated by GPS by radar and by radar-only tracker and estimation error as a function of GPS time of day The upperfigure highlights the trajectory of each particle
The target state vector in spherical coordinates is definedas
119909 = [119903 119903 120599 120599 120601 120601] (7)
where 119903 is the range 120599 is the azimuth 120601 is the elevation angleand 119903 120599 120601 are their first time derivatives
In order to evaluate the velocity components let usconsider
V = [
[
V119903
V120599
V120601
]
]
= [
[
119903
119903 120599 cos120601119903 120601
]
]
(8)
where the velocity vector has been defined as V = [V119903 V120599 V120601]
for the sake of simplicity
For a spherical constant velocity dynamic model repre-senting the objectmotion it is assumed that V
119903= V120599= V120601= 0
Taking the time derivative of each component in (8) yields
V119903= 119903 = 0
V120599= 119903 120599 cos 120593 + 119903 120599 cos 120593 minus 119903 120599 sin 120593 = 0
V120601= 119903 + 119903 = 0
(9)
Rearranging the above expressions in terms of angu-lar velocities and considering discrete-time domain with
The Scientific World Journal 7
52494
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525
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times104GPS time of day (s)
52496
52498
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5251
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52514
times104GPS time of day (s)
GPS
Radar
RadarPF tracker
Spherical PF
Spherical PF
100
0
minus100
minus200Azi
mut
h in
NED
refe
renc
e fra
me (
∘ )PF tracker
6
4
2
Erro
r in
stab
ilize
daz
imut
h (∘
)
Figure 6 Azimuth in NED reference frame as estimated by GPS by radar and by radar-only tracker and estimation error as a function ofGPS time of day
sampling time 119879 the components of the dynamic motionequation are given by
119903119899= 119903119899minus1+ 119879 119903119899minus1
119903119899= 119903119899minus1
120599119899= 120599119899minus1+ 119879 120599119899minus1[1 +
119879
2119903119899minus1
(119903119899minus1120601119899minus1119905119892120601119899minus1minus 119903119899minus1)]
120599119899= 120599119899minus1[1 + 119879( 120601
119899minus1119905119892120601119899minus1minus119903119899minus1
119903119899minus1
)]
120601119899= 120601119899minus1+ 119879 120601119899minus1[1 minus
119879
2119903119899minus1
119903119899minus1]
120601119899= 120601119899minus1[1 minus
119879
2119903119899minus1
119903119899minus1]
(10)
The nonlinear dynamicmotion equation for the sphericalstate vector can be written as
119909119899= 119891 (119909
119899minus1) + 119899119899minus1 (11)
with the zero-mean Gaussian dynamic acceleration noisedistribution
119899119899sim 119873(0 119876
120588) (12)
The components of 119891(119909119899minus1) are given by the nonlinear
equation (10) and the process noise matrix is
119876120588= [
[
119902119903119876102
02
02119902ℎ119876102
02
02119902V1198761
]
]
(13)
with
1198761=
[[[[
[
1198793
3
1198792
2
1198792
2119879
]]]]
]
(14)
where 119902119903 119902ℎ and 119902V must be set depending on the target
maneuvers [34]Since the model is in spherical coordinates the measure-
ment equation is linear and it can be expressed as
119911119899= 119867119909119899+ 119908119899 (15)
with
119867 = [
[
1 0 0 0 0 0
0 0 1 0 0 0
0 0 0 0 1 0
]
]
(16)
and 119908119899is the observation noise which is considered to be
independent zero-mean Gaussian noise defined by
119908119899sim 119873 (0 119877
119899) (17)
8 The Scientific World Journal
52494
52494
52496
52498
525
52502
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5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
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5251
52512
52514
times104GPS time of day (s)
GPS
Radar
RadarPF tracker
Spherical PF
Spherical PFEl
evat
ion
in N
EDre
fere
nce f
ram
e (∘ )
PF tracker
40
minus4minus8minus12
1505
minus05minus15minus25Er
ror i
n st
abili
zed
elev
atio
n (∘
)
Figure 7 Elevation in NED reference frame as estimated by GPS by radar and by radar-only tracker and estimation error as a function ofGPS time of day
52494
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times104GPS time of day (s)
GPS
PF tracker
Spherical PF
Spherical PFPF tracker
minus72
minus76
minus80
minus84
Rang
e rat
e(m
s)
6
2
minus2
minus6Erro
r in
rang
era
te (m
s)
Figure 8 Range rate as estimated by GPS and by radar-only tracker and estimation error as a function of GPS time of day
where 119877119899is the measurement covariance matrix as stated
aboveThe developed obstacle detection and tracking software
provides also an estimate of the Distance at Closest Pointof Approach (see (1)) Since the particles are characterizedby own positions and velocities and given the nonlineardependencies between 119903119881 andDCPA the latter is calculatedfor each particle In this way in order to avoid furtherapproximations due to the evaluation of this distance from
position and velocitymean values DCPA has been calculatedas mean value of the different distances evaluated as
DCPA119899=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
119903 sdot 119881
1003817100381710038171003817100381711988110038171003817100381710038171003817
2119881 minus 119903
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(18)
This is a form of ldquodeep integrationrdquo of a collision detectionsensor since an estimate of the level of collision threat isdetermined by means of the same data fusion algorithm
The Scientific World Journal 9
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times104GPS time of day (s)
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times104GPS time of day (s)
GPS
PF tracker
Spherical PF
Spherical PFPF tracker
0
minus1
minus2
minus3
050301
minus01minus03
Azi
mut
h ra
te in
NED
refe
renc
e fra
me (
∘ s)
Erro
r in
stab
ilize
daz
imut
h ra
te (∘
s)
Figure 9 Azimuth rate in NED reference frame as estimated by GPS and by radar-only tracker and estimation error as a function of GPStime of day
This is an additional advantage of using PF rather than EKFsince the need of linearized models in EKF does not allowestimating DCPA by the filter itself
5 Results
The developed obstacle tracking algorithm has been testedin off-line simulations based on flight data gathered duringan intensive test campaign Flight tests were carried out byexploiting the following configuration of test facilities
(a) FLARE aircraft piloted by a human pilot or by theautonomous flight control system
(b) a piloted intruder VLA aircraft in the same class ofFLARE equipped with GPS antennas and receiversand an onboard CPU for navigation data storage
(c) a ground control station (GCS) for real time flightcoordination and test monitoring [36]
(d) a full-duplex data link between FLARE and GCSused to send commands to initiate or terminate testsand to receive synthetic filter output and navigationmeasurements
(e) a downlink between intruder and GCS used for flightmonitoring
During the tests two types of maneuvers were executedsuch as chasing tests with FLARE pursuing the intruder andquasi-frontal encounters performed to estimate detectionand tracking performance in the most interesting scenariosfrom the application point of view
In particular the scenario selected in this paper forperformance analysis is a single quasi-frontal encounterbetween FLARE and the intruder The algorithm has beentested in standalone radar tracking configuration that is
estimates of obstacle relative position and velocity are basedon measurements from radar (update frequency of 1Hz) andthe own-ship navigation system
The number of particles has been set equal to 500 Thisnumber was selected since increasing it up to one orderof magnitude did not produced significant performanceincrease The algorithm is initialized taking into accountthe first radar sensor measurement the covariance matrix iscalculated on the basis of sensor measurements and then it isupdated with estimated values of software output
The algorithm outputs are based on obstacle position andvelocity in terms of range azimuth and elevation and DCPAin a stabilized north-east-down reference frame with originin FLARE center of mass The considered flight segment hasduration of about 20 s with an initial range of about 2000m
In Figure 5 obstacle range as estimated by radar radar-based tracker and GPS (reference) together with errorestimate with respect to GPS measurements is reportedAfter a firm track has been generated on the basis of radarmeasurements the tracker is able to characterize the obstacletrajectory The radar-only tracker provides a range estimatewith an accuracy of the order of few meters that derives fromthe good radar range accuracy and the absence of intrudermaneuvers In Figure 5 the upper plot illustrates the obstaclerange in a small interval time (of about 1 s) in order to showthe particles trajectories (colored lines)
Figures 6 and 7 report the obstacle angular dynamicsin terms of azimuth and elevation As expected the orderof magnitude of these errors is comparable to the radaraccuracy In particular the estimation uncertainty in termsof root mean square is of about 25∘ for azimuth and 13∘ forelevation Being computed in NED these RMS errors includeattitude measurement error biases In fact error biases in theestimation of magnetic heading are the main reason of thelarger error in azimuth It is worth noting that these biases
10 The Scientific World Journal
Table 1 PF performance in the selected scenario in terms of RMSerror
RMS Particle filter EKFRange (m) 84 37Range rate (m∘) 30 23Azimuth (∘) 25 17Azimuth rate (∘s) 02 04Elevation (∘) 13 21Elevation rate (∘s) 02 08
have a little effect on the estimation of angular rates and ofDistance at Closest Point of Approach
The range and angular rates as estimated by GPS (ref-erence) and particle filter tracker are reported in Figures 89 and 10 These variables are very important informationsources for collision detection assessment even though theyare not directly provided by the radar sensor The plots showthat the tracker estimates are very accurate with a very smallvalue in terms of standard deviation
Simulation results confirm how the resampling proce-dure is a key factor for tracking performance avoiding thedegeneracy phenomenon and thus enabling a great quantityof particles to survive to the prediction step
In order to better understand the particle filter trackingcapability PF and EKF estimation errors are reported inTable 1 in terms of root mean square (RMS) errors computedas
RMS = radic 1119873
119873
sum
119905=1
(119909119905minus 119909119905)2 (19)
where 119873 is the number of measurements 119909119905is the generic
PF tracker estimate (computed after resampling and repre-senting the mean value over all the particles) and 119909
119905is the
reference value computed on the basis of FLARE and intruderGPS measurements
The results show that PF tracker performance is com-parable to EKF in terms of order of magnitude Of coursethe introduction of electro-optical data can improve angularaccuracy since these sensors have a faster update rate thanradar In particular while the range rate error is very similarfor the two filters obstacle angular velocities provided byPF algorithm are slightly more accurate than EKF in theconsidered scenario These variables are very importantinformation sources for collision detection assessment eventhough they are not directly provided by the radar
In fact in near collision conditions angular rates are themost important variables influencing collision detection Asshown in [7] in these conditions DCPA uncertainty for givenrange and range rate shows a linear dependence on angularrate errors while range rate essentially impacts the time-to-go estimate
In the considered scenario DCPA as computed on thebasis of GPS measurement has been used as a reference forcomparing DCPA estimated by EKF tracker and PF trackerFigure 11 shows that the PF algorithm is more accuratethan EKF for the estimation of the DCPA in the initial
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GPS
PF tracker
Spherical PF
Spherical PFPF tracker
Elev
atio
nh ra
te in
NED
refe
renc
e fra
me (
∘ s)
08
04
0
minus04
minus01minus02minus03minus04minus05Er
ror i
n st
abili
zed
elev
atio
n ra
te (∘
s)
Figure 10 Elevation rate in NED reference frame as estimated byGPS and by radar-only tracker and estimation error as a function ofGPS time of day
450
400
350
300
250
200
150
100
50
Distance at Closest Point of Approach (DCPA) (m)
PF trackerEKF trackerGPS
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times104GPS time of day (s)
Figure 11 Distance at Closest Point of Approach as estimated byGPS (reference) by radar and by radar-only tracker as function ofGPS time of the day
phase of firm tracking (at larger range) thus providing animprovement in collision risk assessment and a potentialreduction in the delay in declaring a collision threat Analysisof GPS data demonstrates that the considered encounterrepresents a real Near Mid-Air Collision (NMAC) scenariosince the reference DCPA keeps a very small value and liesbelow the bubble distance threshold almost in the whole firmtracking phase
The Scientific World Journal 11
6 Conclusion and Future Works
This paper focused on algorithm and test results fromobstacle tracking software based on particle filter and aimedat demonstrating UAS autonomous collision detection capa-bility in terms of reliable estimation of Distance at ClosestPoint of Approach The algorithm performance has beeninitially evaluated in radar-only configuration since the maininterest was addressed to the analysis of the potential impactof nonlinear filters on tracking capabilities with respect toassessed EKF first in a single sensor framework
The software has been tested in off-line simulations basedon real data recorded during a flight test campaign and aquasi-frontal encounter between the own aircraft and theintruder has been presented as test case The results pointedout that the developed algorithm is able to detect and trackthe obstacle trajectory with accuracy comparable to the EKFIn particular some advantages were highlighted in the directdetermination of Distance at Closest Point of Approach witha potential reduction of the delay for collision detectionThis result permits planning additional future investigationactivities such as
(i) performing the comparison on a larger experimentaldata set thus increasing the statistical significance
(ii) developing a multisensor-based analysis to confirmthe results obtained by the developed PF tracker whenadditional data sources are available such as electro-optical sensors indeed they can provide higheraccuracy in angular measurements and better datarate than radar sensors with a great impact on DCPAperformance
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The PhD grant of Miss Anna Elena Tirri is cofunded byEUROCONTROL through the research network HALA inthe framework of the WP-E of SESAR project
References
[1] EUROCONTROL in Proceedings of the EUROCONTROL Spec-ifications for the Use of Military Unmanned Aerial Vehicles asOperational Air Traffic Outside Segregated Airspace Version10 DocNo EUROCONTROL-SPEC-0102 Bruxelles BelgiumJuly 2007
[2] US Federal Aviation Administration (FAA) ldquoAirworthinesscertification of unmanned aircraft systemsrdquo Order 813034US Federal Aviation Administration (FAA) Washington DCUSA 2008
[3] US Federal Aviation Administration (FAA) ldquoInvestigate aNear Mid Air Collisionrdquo FAA Order 89001 vol 7 chapter 4Washington DC USA 2007
[4] G Fasano D Accardo A Moccia et al ldquoMulti-sensor-basedfully autonomous non-cooperative collision avoidance system
for unmanned air vehiclesrdquo Journal of Aerospace ComputingInformation and Communication vol 5 no 10 pp 338ndash3602008
[5] MTSI ldquoNon-cooperative detect see amp avoid (DSA) sensorstudyrdquo Tech Rep NASA ERAST 2002
[6] O Shakernia W Chen S Graham et al ldquoSense and Avoid(SAA) flight test and lessons learnedrdquo in Proceedings of the 2ndAIAA InfotechAerospace Conference and Exhibit (AIAA rsquo07)pp 2781ndash2795 Rohnert Park Calif USA May 2007
[7] D Accardo G Fasano L Forlenza A Moccia and A RispolildquoFlight test of a radar-based tracking system for UAS sense andavoidrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 49 no 2 pp 1139ndash1160 2013
[8] USFAA SpecialOperations FAAOrder 76104M January 2007[9] S J Julier and J K Uhlmann ldquoA new extension of the Kalman
filter to nonlinear systemsrdquo in Signal Processing Sensor Fusionand Target Recognition VI vol 3068 of Proceedings of SPIE pp182ndash193 Orlando Fla USA 1997
[10] N E Smith R G Cobb S J Pierce and V M Raska ldquoOptimalcollision avoidance trajectories for unmannedremotely pilotedaircraftrdquo in Proceedings of the AIAA Guidance Navigation andControl Conference (GNC 13) AIAA 2013-4619 Boston MassUSA August 2013
[11] L Lin Y Wang Y Liu C Xiong and K Zeng ldquoMarker-lessregistration based on template tracking for augmented realityrdquoMultimedia Tools and Applications vol 41 no 2 pp 235ndash2522009
[12] X Liu L Lin S Yan H Jin and W Jiang ldquoAdaptive objecttracking by learning hybrid template onlinerdquo IEEE Transactionson Circuits and Systems for Video Technology vol 21 no 11 pp1588ndash1599 2011
[13] L Lin Y Lu Y Pan and X Chen ldquoIntegrating graph partition-ing and matching for trajectory analysis in video surveillancerdquoIEEE Transactions on Image Processing vol 21 no 12 pp 4844ndash4857 2012
[14] L Xia P Li Y Guo and Z Shen ldquoResearch of maneuveringtarget tracking based on particle filterrdquo in Proceedings of the Chi-nese Automation Congress (CAC rsquo13) pp 567ndash570 ChangshaChina 2013
[15] F Gustafsson F Gunnarsson N Bergman et al ldquoParticle filtersfor positioning navigation and trackingrdquo IEEE Transactions onSignal Processing vol 50 no 2 pp 425ndash437 2002
[16] S Challa and G W Pulford ldquoJoint target tracking and classi-fication using radar and ESM sensorsrdquo IEEE Transactions onAerospace and Electronic Systems vol 37 no 3 pp 1039ndash10552001
[17] M S Grewal and A P Andrews Kalman Filtering Theory andPractice Using Matlab John Wiley amp Sons 2nd edition 2001
[18] S Haykin Kalman Filtering and Neural Networks John Wileyand Sons 2001
[19] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Transactions of the ASME Series D Journal of BasicEngineering vol 82 no 1 pp 35ndash45 1960
[20] S Arulampalam and B Ristic ldquoComparison of the particle filterwith range-parameterised and modified polar EKFs for angle-only trackingrdquo in Signal and Data Processing of Small Targetsvol 4048 of Proceedings of SPIE pp 288ndash299 Orlando FlaUSA April 2000
[21] X Lin T Kirubarajan Y Bar-Shalom and S Maskell ldquoCom-parison of EKF pseudomeasurement and particle filters fora bearing-only target tracking problemrdquo in Signal and Data
12 The Scientific World Journal
Processing of Small Targets vol 4728 of Proceedings of SPIE pp240ndash250 April 2002
[22] M S Arulampalam S Maskell N Gordon and T Clapp ldquoAtutorial on particle filters for online nonlinearnon-GaussianBayesian trackingrdquo IEEE Transactions on Signal Processing vol50 no 2 pp 174ndash188 2002
[23] A Doucet N de Freitas and N Gordon ldquoAn introduction tosequential Monte Carlo methodsrdquo in Sequential Monte CarloMethods in Practice Statistics for Engineering and InformationScience pp 3ndash14 Springer New York NY USA 2001
[24] B Liu andCHao ldquoSequential bearings-only-tracking initiationwith particle filteringmethodrdquoThe ScientificWorld Journal vol2013 Article ID 489121 7 pages 2013
[25] R Karlsson and F Gustafsson ldquoRecursive Bayesian estimationbearings-only applicationsrdquo IEE Proceedings Radar Sonar andNavigation vol 152 no 5 pp 305ndash313 2005
[26] N Gordon ldquoHybrid bootstrap filter for target tracking inclutterrdquo in Proceedings of the American Control Conference vol1 pp 628ndash632 June 1995
[27] S Mcginnity and G W Irwin ldquoMultiple model bootstrapfilter for maneuvering target trackingrdquo IEEE Transactions onAerospace and Electronic Systems vol 36 no 3 pp 1006ndash10122000
[28] M R Morelande and S Challa ldquoManoeuvring target trackingin clutter using particle filtersrdquo IEEE Transactions on Aerospaceand Electronic Systems vol 41 no 1 pp 252ndash270 2005
[29] D Lerro and Y Bar-Shalom ldquoTracking with de-biased consis-tent converted measurements versus EKFrdquo IEEE TransactionsonAerospace and Electronic Systems vol 29 no 3 pp 1015ndash10221993
[30] G Fasano L Forlenza D Accardo A Moccia and A RispolildquoIntegrated obstacle detection system based on radar andoptical sensorsrdquo inProceedings of the AIAA Infotech at Aerospace(AIAA rsquo10) Atlanta Ga USA April 2010
[31] S S Blackman and R F Popoli Design and Analysis of ModernTracking Systems Artech House Norwood Mass USA 1999
[32] G Fasano D Accardo A Moccia and A Rispoli ldquoAn inno-vative procedure for calibration of strapdown electro-opticalsensors onboard unmanned air vehiclesrdquo Sensors vol 10 no 1pp 639ndash654 2010
[33] B Ristic S Arulampalam and N Gordon Beyond the KalmanFilter Particle Filter for Tracking Applications Artech HouseNew York NY USA 2004
[34] A Haug and L Williams ldquoA spherical constant velocity modelfor target tracking in three dimensionsrdquo in IEEE AerospaceConference pp 1ndash15 Big Sky Mont USA March 2012
[35] X R Li and V P Jilkov ldquoA survey of maneuvering target track-ing dynamic modelsrdquo in Proceedings of the SPIE Conference onsignal and Data Processing of Small Targets vol 39 pp 1333ndash1364 Orlando Fla USA April 2000
[36] G Fasano A Moccia D Accardo and A Rispoli ldquoDevelop-ment and test of an integrated sensor system for autonomouscollision avoidancerdquo in Proceedings of the 26th Congress ofInternational Council of the Aeronautical Sciences (ICAS rsquo08) pp3625ndash3634 Anchorage Alaska USA September 2008
International Journal of
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Navigation and Observation
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DistributedSensor Networks
International Journal of
4 The Scientific World Journal
4 Developed Software Description
In general the tracking software allows effective fusion ofinformation provided by different sensors such as radar andinertial unit moreover it performs the gatingassociationfunctions in order to associate at the same intruder mea-surements gathered in different scans and to eliminate falsealarms and clutter returns In fact the inputs to the algorithmare sensor measurements which represent in general objectof interest false alarm and clutter In this case most ofthe clutter return will likely come from ground echoesTrackmeasurement association is carried out using ellip-soidal gating and a centralized statistic [31] defined as
120585 = [119910 minus 119910]1015840[119877 + 119867119875119867
1015840]minus1
[119910 minus 119910] (3)
where 119910 is the measurement vector at the time of detection 119910is the predicted measurement vector at the time of detection119875 is the predicted covariance matrix 119867 is the measurementtransition matrix and 119877 is the measurement covariancematrix This statistics is a normalized distance betweenmeasurement and prediction which takes into account allthe relevant uncertainties Assuming a statistical distributionfor 120585 it is then possible to define a threshold based onthe probability of a correct measurement falling inside thegate As an example in common radar applications 120585 isassumed to be distributed as a chi-square variable with anumber of degrees of freedom equal to the dimension of themeasurement vector
After the association phase based on a common nearestneighbour approach since a dense multitarget environmentis unlikely to be found in the considered civil collision avoid-ance scenario the track status must be properly handled Inparticular tracks are divided in three categories one-plot(single observation not associated with any existing track)tentative (at least two observations but confirmation logicis still required) and firm (confirmed track) The transitiontentative firm can be based on different techniques Tracks aredeleted if they are not updated within a reasonable interval
The filtering and prediction phase allows combining trackprediction and sensormeasurements and produces new trackpredictions The tracking system is based on a particle filterwith nonlinear dynamic model and linear measurementequation The state vector is comprised of 6 componentsthat are the obstacle positions in terms of range azimuthand elevation in north-east-down (NED) reference frame andtheir first time derivatives Besides the PF tracker providesalso an estimate of the Distance at Closest Point of ApproachThe obstacle dynamic model is based on a nearly constantvelocity model better described in the following sectionImportant points are related to the sensor latency and theproper inclusion of aircraft navigation measurements Thusproper data registration techniques have been considered asa prerequisite for the developed algorithm [32] Regardingtime registration the radar sends its measurements at theend of each pass with maximum latency of the order of 1 sSince the tracker works at 10Hz in the developed system ameasurement is assigned a time stamp which is the nearesttime on the tracker 01 s scale Since the radar delay is typically
larger than the 01 s scale it is likely that a measurementrelative to time 119905
1arrives when the state has already been
propagated to a later time 119905119899 In this case the state and
covariance must be updated at time 1199051 Also the gating and
association processes have to be performed with values ofstate and covariance at time 119905
1 Then the problem is how to
produce updated parameters from measurement at time 1199051
In order to perform gating association and track updat-ing the solution is to keep inmemory a slidingwindowwherenavigation and track data are stored The considered timewindow dimensions correspond to the largest possible radardata latency Given that state and covariance at time 119905
1have
to be known and stored in the developed PF tracker the keyidea is to consider all the variables at time 119905
1 to perform the
filtering step taking into account the radar measurement atthat time and then update the state (and covariance) untiltime 119905
119899by means of a Monte Carlo approach
41 Particle Filter Algorithm Particle filters are Bayesianestimators that resolve the state estimation problems bydetermining the probability density function (PDF) of anunknown random vector using a weighted sum of delta func-tionsThese filters have less limitations than the Kalman filterIndeed they can exploit nonlinear process and measurementmodels and they can be used with any form of system noisestatistical distribution
The implemented particle filter is based on the samplingimportance resampling algorithm [33] constituted by threemain steps generation of particles calculation of the weightsassociated with the particles and resampling procedureThen the state space is propagated through a nonlineardynamic equation A brief overview of the PF phases isreported
Let us consider a set of points and associated weights inthe target state space 119908(119894)
119896minus1 119909(119894)
119896minus1 for 119894 = 1 119873
119904 which
represent samples from the updated target state PDF at time119896minus1The latter can be represented by a weighted sum of deltafunctions as
119901 (119909119896minus1| 119885119896minus1) asymp
119873
sum
119894=1
119908(119894)
119896minus1120575 (119909119896minus1minus 119909(119894)
119896minus1) (4)
where 119908(119894)119896minus1
is the weight associated with the 119894th particle andsum119873
119894=1119908(119894)
119896minus1= 1
In the developed algorithm the target state space (iethe points and related weights) is initialized generating theparticles from a multivariate normal distribution with meanequal to the first radar measurements and specified standarddeviation values In particular the uncertainties have beenestimated on the basis of obstacle dynamic behavior and radaraccuracy (120590
119903= 9m 120590
120599= 2∘ 120590
120601= 2∘) Choosing a large
initial uncertainty on obstacle position allows letting a goodnumber of particles representing the state in important orhigh likelihood regions Consequently radar measurementshave non-negligible importance in the track initializationphase At the first step all the particles are generated withthe same weight set equal to 1N After that the set of pointsrepresenting 119901(119909
119896minus1| 119885119896minus1) have to be transformed into a set
The Scientific World Journal 5
Estimate at k + 1
State at k + 1
PF initialization
Transition to k + 1
xik+1 = f(xik) + nk
Measurement at k + 1
zik+1 = H(xik+1) + k+1
Prediction at k + 1
xi(k+1|k) = f(xi(k|k)) + nk
Measurement prediction at k + 1
zi(k+1|k) = H(xi(k+1|k)) + k
Weights update at k + 1
Resamplingxi(k+1|k+1) = resampling(xi(k+1|k) wi
k+1)
Generation of particles xikand weights wi
k
exp
Figure 4 Particle filtering algorithm
of points 119908(119894)119896 119909(119894)
119896 representing 119901(119909
119896| 119885119896) This is done by
PF in two steps prediction and filteringThe prediction step exploits the system model to predict
the state distribution function from one measurement timeto another one It transforms the updated density at time119896 minus 1 into a set of points representing the predicted density119901(119909119896| 119885119896minus1) by substituting each sample 119909(119894)
119896minus1in the dynamic
equation Since the state is subject to a process noise modeledas an independent and identically distributed process noisesequence the prediction step translates deforms and spreadsthe state distribution
The filtering step utilizes a measurement at time 119896 toupdate the set of particles representing the propagated density119901(119909119896| 119885119896minus1) to a set of particles 119908(119894)
119896 119909(119894)
119896 sim 119901(119909
119896| 119885119896) with
updated weights The optimal choice is to sample from theupdated density 119901(119909
119896| 119885119896) directly since this is impossible
because it is unknown the solution is to sample from thepropagated density (as in this specific analysis)Then given ameasurement 119911
119896and the set of propagated points 119908(119894)
119896minus1 119909(119894)
119896
the updated set of particles is given by
119908(119894)
119896=
119908(119894)
119896minus1119901 (119911119896| 119909(119894)
119896)
sum119873
119895=1119908(119895)
119896minus1119901 (119911119896| 119909(119895)
119896)
(5)
where 119901(119911119896| 119909(119894)
119896) is the measurement likelihood in this
application it has been defined as
119901 (119911119896| 119909119896) =
1
radic21205871198772
exp(minus(119911119896minus 119896)1015840119877minus1(119911119896minus 119896)
2)
(6)where
119896is the predicted measurement at the time of
detection and 119877 is the measurement covariance matrix
In the software the resampling procedure is based on asystematic resampling scheme [33] which is performed ateach time step and not only when the number of particleswith non-negligible weight falls below a threshold valueThe resampling phase enables a great quantity of particlesto survive during the propagation of the state space thusavoiding the degeneracy phenomenon
The software outputs based on range azimuth elevationand their first time derivatives are then calculated on the basisof the state estimates weighted on all particles
In Figure 4 a particle filtering scheme is reported in orderto better clarify how the developed software has been con-ceived The scheme exploits the main steps of the algorithminitialization prediction filtering and resampling In partic-ular the filtering phase is based on weights update obtainedconsidering measurement prediction sensor outputs andmeasurement covariance matrix 119877
42 Obstacle Tracking Dynamic Model The selection of adynamic model is a nontrivial problem for airborne obstacletracking systems since an accurate estimate of the obstacleposition is considered fundamental for the evaluation of theDistance at Closest Point of Approach In the developedsoftware a nearly constant velocity model in spherical coor-dinates has been implemented to represent the target relativetrajectory [34 35] The target state is propagated through anonlinear dynamic equation since the state variables are inspherical coordinates and thus closer to sensormeasurementsoutputs
The state vector is comprised of obstacle position interms of range azimuth and elevation in north-east-downreference frame and their first time derivatives Hereinafterthe obstacle dynamic model is reported for the sake of clarity
6 The Scientific World Journal
52505
52505
52505
52505
52506
52506
52506
times104
1080
1070
1060
1050
1040
1030
1020
1010
1000
990
GPS time of day (s)
Rang
e (m
)
Spherical PF
GPSRadar
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104
4000
3000
2000
1000
0
GPS time of day (s)
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
Rang
e (m
)
GPSRadar
RadarPF tracker
20
0
minus20
minus40
Erro
r in
rang
e (m
)
Spherical PF
Figure 5 Range as estimated by GPS by radar and by radar-only tracker and estimation error as a function of GPS time of day The upperfigure highlights the trajectory of each particle
The target state vector in spherical coordinates is definedas
119909 = [119903 119903 120599 120599 120601 120601] (7)
where 119903 is the range 120599 is the azimuth 120601 is the elevation angleand 119903 120599 120601 are their first time derivatives
In order to evaluate the velocity components let usconsider
V = [
[
V119903
V120599
V120601
]
]
= [
[
119903
119903 120599 cos120601119903 120601
]
]
(8)
where the velocity vector has been defined as V = [V119903 V120599 V120601]
for the sake of simplicity
For a spherical constant velocity dynamic model repre-senting the objectmotion it is assumed that V
119903= V120599= V120601= 0
Taking the time derivative of each component in (8) yields
V119903= 119903 = 0
V120599= 119903 120599 cos 120593 + 119903 120599 cos 120593 minus 119903 120599 sin 120593 = 0
V120601= 119903 + 119903 = 0
(9)
Rearranging the above expressions in terms of angu-lar velocities and considering discrete-time domain with
The Scientific World Journal 7
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
Radar
RadarPF tracker
Spherical PF
Spherical PF
100
0
minus100
minus200Azi
mut
h in
NED
refe
renc
e fra
me (
∘ )PF tracker
6
4
2
Erro
r in
stab
ilize
daz
imut
h (∘
)
Figure 6 Azimuth in NED reference frame as estimated by GPS by radar and by radar-only tracker and estimation error as a function ofGPS time of day
sampling time 119879 the components of the dynamic motionequation are given by
119903119899= 119903119899minus1+ 119879 119903119899minus1
119903119899= 119903119899minus1
120599119899= 120599119899minus1+ 119879 120599119899minus1[1 +
119879
2119903119899minus1
(119903119899minus1120601119899minus1119905119892120601119899minus1minus 119903119899minus1)]
120599119899= 120599119899minus1[1 + 119879( 120601
119899minus1119905119892120601119899minus1minus119903119899minus1
119903119899minus1
)]
120601119899= 120601119899minus1+ 119879 120601119899minus1[1 minus
119879
2119903119899minus1
119903119899minus1]
120601119899= 120601119899minus1[1 minus
119879
2119903119899minus1
119903119899minus1]
(10)
The nonlinear dynamicmotion equation for the sphericalstate vector can be written as
119909119899= 119891 (119909
119899minus1) + 119899119899minus1 (11)
with the zero-mean Gaussian dynamic acceleration noisedistribution
119899119899sim 119873(0 119876
120588) (12)
The components of 119891(119909119899minus1) are given by the nonlinear
equation (10) and the process noise matrix is
119876120588= [
[
119902119903119876102
02
02119902ℎ119876102
02
02119902V1198761
]
]
(13)
with
1198761=
[[[[
[
1198793
3
1198792
2
1198792
2119879
]]]]
]
(14)
where 119902119903 119902ℎ and 119902V must be set depending on the target
maneuvers [34]Since the model is in spherical coordinates the measure-
ment equation is linear and it can be expressed as
119911119899= 119867119909119899+ 119908119899 (15)
with
119867 = [
[
1 0 0 0 0 0
0 0 1 0 0 0
0 0 0 0 1 0
]
]
(16)
and 119908119899is the observation noise which is considered to be
independent zero-mean Gaussian noise defined by
119908119899sim 119873 (0 119877
119899) (17)
8 The Scientific World Journal
52494
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
Radar
RadarPF tracker
Spherical PF
Spherical PFEl
evat
ion
in N
EDre
fere
nce f
ram
e (∘ )
PF tracker
40
minus4minus8minus12
1505
minus05minus15minus25Er
ror i
n st
abili
zed
elev
atio
n (∘
)
Figure 7 Elevation in NED reference frame as estimated by GPS by radar and by radar-only tracker and estimation error as a function ofGPS time of day
52494
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
PF tracker
Spherical PF
Spherical PFPF tracker
minus72
minus76
minus80
minus84
Rang
e rat
e(m
s)
6
2
minus2
minus6Erro
r in
rang
era
te (m
s)
Figure 8 Range rate as estimated by GPS and by radar-only tracker and estimation error as a function of GPS time of day
where 119877119899is the measurement covariance matrix as stated
aboveThe developed obstacle detection and tracking software
provides also an estimate of the Distance at Closest Pointof Approach (see (1)) Since the particles are characterizedby own positions and velocities and given the nonlineardependencies between 119903119881 andDCPA the latter is calculatedfor each particle In this way in order to avoid furtherapproximations due to the evaluation of this distance from
position and velocitymean values DCPA has been calculatedas mean value of the different distances evaluated as
DCPA119899=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
119903 sdot 119881
1003817100381710038171003817100381711988110038171003817100381710038171003817
2119881 minus 119903
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(18)
This is a form of ldquodeep integrationrdquo of a collision detectionsensor since an estimate of the level of collision threat isdetermined by means of the same data fusion algorithm
The Scientific World Journal 9
52494
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
PF tracker
Spherical PF
Spherical PFPF tracker
0
minus1
minus2
minus3
050301
minus01minus03
Azi
mut
h ra
te in
NED
refe
renc
e fra
me (
∘ s)
Erro
r in
stab
ilize
daz
imut
h ra
te (∘
s)
Figure 9 Azimuth rate in NED reference frame as estimated by GPS and by radar-only tracker and estimation error as a function of GPStime of day
This is an additional advantage of using PF rather than EKFsince the need of linearized models in EKF does not allowestimating DCPA by the filter itself
5 Results
The developed obstacle tracking algorithm has been testedin off-line simulations based on flight data gathered duringan intensive test campaign Flight tests were carried out byexploiting the following configuration of test facilities
(a) FLARE aircraft piloted by a human pilot or by theautonomous flight control system
(b) a piloted intruder VLA aircraft in the same class ofFLARE equipped with GPS antennas and receiversand an onboard CPU for navigation data storage
(c) a ground control station (GCS) for real time flightcoordination and test monitoring [36]
(d) a full-duplex data link between FLARE and GCSused to send commands to initiate or terminate testsand to receive synthetic filter output and navigationmeasurements
(e) a downlink between intruder and GCS used for flightmonitoring
During the tests two types of maneuvers were executedsuch as chasing tests with FLARE pursuing the intruder andquasi-frontal encounters performed to estimate detectionand tracking performance in the most interesting scenariosfrom the application point of view
In particular the scenario selected in this paper forperformance analysis is a single quasi-frontal encounterbetween FLARE and the intruder The algorithm has beentested in standalone radar tracking configuration that is
estimates of obstacle relative position and velocity are basedon measurements from radar (update frequency of 1Hz) andthe own-ship navigation system
The number of particles has been set equal to 500 Thisnumber was selected since increasing it up to one orderof magnitude did not produced significant performanceincrease The algorithm is initialized taking into accountthe first radar sensor measurement the covariance matrix iscalculated on the basis of sensor measurements and then it isupdated with estimated values of software output
The algorithm outputs are based on obstacle position andvelocity in terms of range azimuth and elevation and DCPAin a stabilized north-east-down reference frame with originin FLARE center of mass The considered flight segment hasduration of about 20 s with an initial range of about 2000m
In Figure 5 obstacle range as estimated by radar radar-based tracker and GPS (reference) together with errorestimate with respect to GPS measurements is reportedAfter a firm track has been generated on the basis of radarmeasurements the tracker is able to characterize the obstacletrajectory The radar-only tracker provides a range estimatewith an accuracy of the order of few meters that derives fromthe good radar range accuracy and the absence of intrudermaneuvers In Figure 5 the upper plot illustrates the obstaclerange in a small interval time (of about 1 s) in order to showthe particles trajectories (colored lines)
Figures 6 and 7 report the obstacle angular dynamicsin terms of azimuth and elevation As expected the orderof magnitude of these errors is comparable to the radaraccuracy In particular the estimation uncertainty in termsof root mean square is of about 25∘ for azimuth and 13∘ forelevation Being computed in NED these RMS errors includeattitude measurement error biases In fact error biases in theestimation of magnetic heading are the main reason of thelarger error in azimuth It is worth noting that these biases
10 The Scientific World Journal
Table 1 PF performance in the selected scenario in terms of RMSerror
RMS Particle filter EKFRange (m) 84 37Range rate (m∘) 30 23Azimuth (∘) 25 17Azimuth rate (∘s) 02 04Elevation (∘) 13 21Elevation rate (∘s) 02 08
have a little effect on the estimation of angular rates and ofDistance at Closest Point of Approach
The range and angular rates as estimated by GPS (ref-erence) and particle filter tracker are reported in Figures 89 and 10 These variables are very important informationsources for collision detection assessment even though theyare not directly provided by the radar sensor The plots showthat the tracker estimates are very accurate with a very smallvalue in terms of standard deviation
Simulation results confirm how the resampling proce-dure is a key factor for tracking performance avoiding thedegeneracy phenomenon and thus enabling a great quantityof particles to survive to the prediction step
In order to better understand the particle filter trackingcapability PF and EKF estimation errors are reported inTable 1 in terms of root mean square (RMS) errors computedas
RMS = radic 1119873
119873
sum
119905=1
(119909119905minus 119909119905)2 (19)
where 119873 is the number of measurements 119909119905is the generic
PF tracker estimate (computed after resampling and repre-senting the mean value over all the particles) and 119909
119905is the
reference value computed on the basis of FLARE and intruderGPS measurements
The results show that PF tracker performance is com-parable to EKF in terms of order of magnitude Of coursethe introduction of electro-optical data can improve angularaccuracy since these sensors have a faster update rate thanradar In particular while the range rate error is very similarfor the two filters obstacle angular velocities provided byPF algorithm are slightly more accurate than EKF in theconsidered scenario These variables are very importantinformation sources for collision detection assessment eventhough they are not directly provided by the radar
In fact in near collision conditions angular rates are themost important variables influencing collision detection Asshown in [7] in these conditions DCPA uncertainty for givenrange and range rate shows a linear dependence on angularrate errors while range rate essentially impacts the time-to-go estimate
In the considered scenario DCPA as computed on thebasis of GPS measurement has been used as a reference forcomparing DCPA estimated by EKF tracker and PF trackerFigure 11 shows that the PF algorithm is more accuratethan EKF for the estimation of the DCPA in the initial
52494
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
PF tracker
Spherical PF
Spherical PFPF tracker
Elev
atio
nh ra
te in
NED
refe
renc
e fra
me (
∘ s)
08
04
0
minus04
minus01minus02minus03minus04minus05Er
ror i
n st
abili
zed
elev
atio
n ra
te (∘
s)
Figure 10 Elevation rate in NED reference frame as estimated byGPS and by radar-only tracker and estimation error as a function ofGPS time of day
450
400
350
300
250
200
150
100
50
Distance at Closest Point of Approach (DCPA) (m)
PF trackerEKF trackerGPS
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
Figure 11 Distance at Closest Point of Approach as estimated byGPS (reference) by radar and by radar-only tracker as function ofGPS time of the day
phase of firm tracking (at larger range) thus providing animprovement in collision risk assessment and a potentialreduction in the delay in declaring a collision threat Analysisof GPS data demonstrates that the considered encounterrepresents a real Near Mid-Air Collision (NMAC) scenariosince the reference DCPA keeps a very small value and liesbelow the bubble distance threshold almost in the whole firmtracking phase
The Scientific World Journal 11
6 Conclusion and Future Works
This paper focused on algorithm and test results fromobstacle tracking software based on particle filter and aimedat demonstrating UAS autonomous collision detection capa-bility in terms of reliable estimation of Distance at ClosestPoint of Approach The algorithm performance has beeninitially evaluated in radar-only configuration since the maininterest was addressed to the analysis of the potential impactof nonlinear filters on tracking capabilities with respect toassessed EKF first in a single sensor framework
The software has been tested in off-line simulations basedon real data recorded during a flight test campaign and aquasi-frontal encounter between the own aircraft and theintruder has been presented as test case The results pointedout that the developed algorithm is able to detect and trackthe obstacle trajectory with accuracy comparable to the EKFIn particular some advantages were highlighted in the directdetermination of Distance at Closest Point of Approach witha potential reduction of the delay for collision detectionThis result permits planning additional future investigationactivities such as
(i) performing the comparison on a larger experimentaldata set thus increasing the statistical significance
(ii) developing a multisensor-based analysis to confirmthe results obtained by the developed PF tracker whenadditional data sources are available such as electro-optical sensors indeed they can provide higheraccuracy in angular measurements and better datarate than radar sensors with a great impact on DCPAperformance
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The PhD grant of Miss Anna Elena Tirri is cofunded byEUROCONTROL through the research network HALA inthe framework of the WP-E of SESAR project
References
[1] EUROCONTROL in Proceedings of the EUROCONTROL Spec-ifications for the Use of Military Unmanned Aerial Vehicles asOperational Air Traffic Outside Segregated Airspace Version10 DocNo EUROCONTROL-SPEC-0102 Bruxelles BelgiumJuly 2007
[2] US Federal Aviation Administration (FAA) ldquoAirworthinesscertification of unmanned aircraft systemsrdquo Order 813034US Federal Aviation Administration (FAA) Washington DCUSA 2008
[3] US Federal Aviation Administration (FAA) ldquoInvestigate aNear Mid Air Collisionrdquo FAA Order 89001 vol 7 chapter 4Washington DC USA 2007
[4] G Fasano D Accardo A Moccia et al ldquoMulti-sensor-basedfully autonomous non-cooperative collision avoidance system
for unmanned air vehiclesrdquo Journal of Aerospace ComputingInformation and Communication vol 5 no 10 pp 338ndash3602008
[5] MTSI ldquoNon-cooperative detect see amp avoid (DSA) sensorstudyrdquo Tech Rep NASA ERAST 2002
[6] O Shakernia W Chen S Graham et al ldquoSense and Avoid(SAA) flight test and lessons learnedrdquo in Proceedings of the 2ndAIAA InfotechAerospace Conference and Exhibit (AIAA rsquo07)pp 2781ndash2795 Rohnert Park Calif USA May 2007
[7] D Accardo G Fasano L Forlenza A Moccia and A RispolildquoFlight test of a radar-based tracking system for UAS sense andavoidrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 49 no 2 pp 1139ndash1160 2013
[8] USFAA SpecialOperations FAAOrder 76104M January 2007[9] S J Julier and J K Uhlmann ldquoA new extension of the Kalman
filter to nonlinear systemsrdquo in Signal Processing Sensor Fusionand Target Recognition VI vol 3068 of Proceedings of SPIE pp182ndash193 Orlando Fla USA 1997
[10] N E Smith R G Cobb S J Pierce and V M Raska ldquoOptimalcollision avoidance trajectories for unmannedremotely pilotedaircraftrdquo in Proceedings of the AIAA Guidance Navigation andControl Conference (GNC 13) AIAA 2013-4619 Boston MassUSA August 2013
[11] L Lin Y Wang Y Liu C Xiong and K Zeng ldquoMarker-lessregistration based on template tracking for augmented realityrdquoMultimedia Tools and Applications vol 41 no 2 pp 235ndash2522009
[12] X Liu L Lin S Yan H Jin and W Jiang ldquoAdaptive objecttracking by learning hybrid template onlinerdquo IEEE Transactionson Circuits and Systems for Video Technology vol 21 no 11 pp1588ndash1599 2011
[13] L Lin Y Lu Y Pan and X Chen ldquoIntegrating graph partition-ing and matching for trajectory analysis in video surveillancerdquoIEEE Transactions on Image Processing vol 21 no 12 pp 4844ndash4857 2012
[14] L Xia P Li Y Guo and Z Shen ldquoResearch of maneuveringtarget tracking based on particle filterrdquo in Proceedings of the Chi-nese Automation Congress (CAC rsquo13) pp 567ndash570 ChangshaChina 2013
[15] F Gustafsson F Gunnarsson N Bergman et al ldquoParticle filtersfor positioning navigation and trackingrdquo IEEE Transactions onSignal Processing vol 50 no 2 pp 425ndash437 2002
[16] S Challa and G W Pulford ldquoJoint target tracking and classi-fication using radar and ESM sensorsrdquo IEEE Transactions onAerospace and Electronic Systems vol 37 no 3 pp 1039ndash10552001
[17] M S Grewal and A P Andrews Kalman Filtering Theory andPractice Using Matlab John Wiley amp Sons 2nd edition 2001
[18] S Haykin Kalman Filtering and Neural Networks John Wileyand Sons 2001
[19] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Transactions of the ASME Series D Journal of BasicEngineering vol 82 no 1 pp 35ndash45 1960
[20] S Arulampalam and B Ristic ldquoComparison of the particle filterwith range-parameterised and modified polar EKFs for angle-only trackingrdquo in Signal and Data Processing of Small Targetsvol 4048 of Proceedings of SPIE pp 288ndash299 Orlando FlaUSA April 2000
[21] X Lin T Kirubarajan Y Bar-Shalom and S Maskell ldquoCom-parison of EKF pseudomeasurement and particle filters fora bearing-only target tracking problemrdquo in Signal and Data
12 The Scientific World Journal
Processing of Small Targets vol 4728 of Proceedings of SPIE pp240ndash250 April 2002
[22] M S Arulampalam S Maskell N Gordon and T Clapp ldquoAtutorial on particle filters for online nonlinearnon-GaussianBayesian trackingrdquo IEEE Transactions on Signal Processing vol50 no 2 pp 174ndash188 2002
[23] A Doucet N de Freitas and N Gordon ldquoAn introduction tosequential Monte Carlo methodsrdquo in Sequential Monte CarloMethods in Practice Statistics for Engineering and InformationScience pp 3ndash14 Springer New York NY USA 2001
[24] B Liu andCHao ldquoSequential bearings-only-tracking initiationwith particle filteringmethodrdquoThe ScientificWorld Journal vol2013 Article ID 489121 7 pages 2013
[25] R Karlsson and F Gustafsson ldquoRecursive Bayesian estimationbearings-only applicationsrdquo IEE Proceedings Radar Sonar andNavigation vol 152 no 5 pp 305ndash313 2005
[26] N Gordon ldquoHybrid bootstrap filter for target tracking inclutterrdquo in Proceedings of the American Control Conference vol1 pp 628ndash632 June 1995
[27] S Mcginnity and G W Irwin ldquoMultiple model bootstrapfilter for maneuvering target trackingrdquo IEEE Transactions onAerospace and Electronic Systems vol 36 no 3 pp 1006ndash10122000
[28] M R Morelande and S Challa ldquoManoeuvring target trackingin clutter using particle filtersrdquo IEEE Transactions on Aerospaceand Electronic Systems vol 41 no 1 pp 252ndash270 2005
[29] D Lerro and Y Bar-Shalom ldquoTracking with de-biased consis-tent converted measurements versus EKFrdquo IEEE TransactionsonAerospace and Electronic Systems vol 29 no 3 pp 1015ndash10221993
[30] G Fasano L Forlenza D Accardo A Moccia and A RispolildquoIntegrated obstacle detection system based on radar andoptical sensorsrdquo inProceedings of the AIAA Infotech at Aerospace(AIAA rsquo10) Atlanta Ga USA April 2010
[31] S S Blackman and R F Popoli Design and Analysis of ModernTracking Systems Artech House Norwood Mass USA 1999
[32] G Fasano D Accardo A Moccia and A Rispoli ldquoAn inno-vative procedure for calibration of strapdown electro-opticalsensors onboard unmanned air vehiclesrdquo Sensors vol 10 no 1pp 639ndash654 2010
[33] B Ristic S Arulampalam and N Gordon Beyond the KalmanFilter Particle Filter for Tracking Applications Artech HouseNew York NY USA 2004
[34] A Haug and L Williams ldquoA spherical constant velocity modelfor target tracking in three dimensionsrdquo in IEEE AerospaceConference pp 1ndash15 Big Sky Mont USA March 2012
[35] X R Li and V P Jilkov ldquoA survey of maneuvering target track-ing dynamic modelsrdquo in Proceedings of the SPIE Conference onsignal and Data Processing of Small Targets vol 39 pp 1333ndash1364 Orlando Fla USA April 2000
[36] G Fasano A Moccia D Accardo and A Rispoli ldquoDevelop-ment and test of an integrated sensor system for autonomouscollision avoidancerdquo in Proceedings of the 26th Congress ofInternational Council of the Aeronautical Sciences (ICAS rsquo08) pp3625ndash3634 Anchorage Alaska USA September 2008
International Journal of
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Active and Passive Electronic Components
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Chemical EngineeringInternational Journal of Antennas and
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Navigation and Observation
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DistributedSensor Networks
International Journal of
The Scientific World Journal 5
Estimate at k + 1
State at k + 1
PF initialization
Transition to k + 1
xik+1 = f(xik) + nk
Measurement at k + 1
zik+1 = H(xik+1) + k+1
Prediction at k + 1
xi(k+1|k) = f(xi(k|k)) + nk
Measurement prediction at k + 1
zi(k+1|k) = H(xi(k+1|k)) + k
Weights update at k + 1
Resamplingxi(k+1|k+1) = resampling(xi(k+1|k) wi
k+1)
Generation of particles xikand weights wi
k
exp
Figure 4 Particle filtering algorithm
of points 119908(119894)119896 119909(119894)
119896 representing 119901(119909
119896| 119885119896) This is done by
PF in two steps prediction and filteringThe prediction step exploits the system model to predict
the state distribution function from one measurement timeto another one It transforms the updated density at time119896 minus 1 into a set of points representing the predicted density119901(119909119896| 119885119896minus1) by substituting each sample 119909(119894)
119896minus1in the dynamic
equation Since the state is subject to a process noise modeledas an independent and identically distributed process noisesequence the prediction step translates deforms and spreadsthe state distribution
The filtering step utilizes a measurement at time 119896 toupdate the set of particles representing the propagated density119901(119909119896| 119885119896minus1) to a set of particles 119908(119894)
119896 119909(119894)
119896 sim 119901(119909
119896| 119885119896) with
updated weights The optimal choice is to sample from theupdated density 119901(119909
119896| 119885119896) directly since this is impossible
because it is unknown the solution is to sample from thepropagated density (as in this specific analysis)Then given ameasurement 119911
119896and the set of propagated points 119908(119894)
119896minus1 119909(119894)
119896
the updated set of particles is given by
119908(119894)
119896=
119908(119894)
119896minus1119901 (119911119896| 119909(119894)
119896)
sum119873
119895=1119908(119895)
119896minus1119901 (119911119896| 119909(119895)
119896)
(5)
where 119901(119911119896| 119909(119894)
119896) is the measurement likelihood in this
application it has been defined as
119901 (119911119896| 119909119896) =
1
radic21205871198772
exp(minus(119911119896minus 119896)1015840119877minus1(119911119896minus 119896)
2)
(6)where
119896is the predicted measurement at the time of
detection and 119877 is the measurement covariance matrix
In the software the resampling procedure is based on asystematic resampling scheme [33] which is performed ateach time step and not only when the number of particleswith non-negligible weight falls below a threshold valueThe resampling phase enables a great quantity of particlesto survive during the propagation of the state space thusavoiding the degeneracy phenomenon
The software outputs based on range azimuth elevationand their first time derivatives are then calculated on the basisof the state estimates weighted on all particles
In Figure 4 a particle filtering scheme is reported in orderto better clarify how the developed software has been con-ceived The scheme exploits the main steps of the algorithminitialization prediction filtering and resampling In partic-ular the filtering phase is based on weights update obtainedconsidering measurement prediction sensor outputs andmeasurement covariance matrix 119877
42 Obstacle Tracking Dynamic Model The selection of adynamic model is a nontrivial problem for airborne obstacletracking systems since an accurate estimate of the obstacleposition is considered fundamental for the evaluation of theDistance at Closest Point of Approach In the developedsoftware a nearly constant velocity model in spherical coor-dinates has been implemented to represent the target relativetrajectory [34 35] The target state is propagated through anonlinear dynamic equation since the state variables are inspherical coordinates and thus closer to sensormeasurementsoutputs
The state vector is comprised of obstacle position interms of range azimuth and elevation in north-east-downreference frame and their first time derivatives Hereinafterthe obstacle dynamic model is reported for the sake of clarity
6 The Scientific World Journal
52505
52505
52505
52505
52506
52506
52506
times104
1080
1070
1060
1050
1040
1030
1020
1010
1000
990
GPS time of day (s)
Rang
e (m
)
Spherical PF
GPSRadar
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104
4000
3000
2000
1000
0
GPS time of day (s)
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
Rang
e (m
)
GPSRadar
RadarPF tracker
20
0
minus20
minus40
Erro
r in
rang
e (m
)
Spherical PF
Figure 5 Range as estimated by GPS by radar and by radar-only tracker and estimation error as a function of GPS time of day The upperfigure highlights the trajectory of each particle
The target state vector in spherical coordinates is definedas
119909 = [119903 119903 120599 120599 120601 120601] (7)
where 119903 is the range 120599 is the azimuth 120601 is the elevation angleand 119903 120599 120601 are their first time derivatives
In order to evaluate the velocity components let usconsider
V = [
[
V119903
V120599
V120601
]
]
= [
[
119903
119903 120599 cos120601119903 120601
]
]
(8)
where the velocity vector has been defined as V = [V119903 V120599 V120601]
for the sake of simplicity
For a spherical constant velocity dynamic model repre-senting the objectmotion it is assumed that V
119903= V120599= V120601= 0
Taking the time derivative of each component in (8) yields
V119903= 119903 = 0
V120599= 119903 120599 cos 120593 + 119903 120599 cos 120593 minus 119903 120599 sin 120593 = 0
V120601= 119903 + 119903 = 0
(9)
Rearranging the above expressions in terms of angu-lar velocities and considering discrete-time domain with
The Scientific World Journal 7
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
Radar
RadarPF tracker
Spherical PF
Spherical PF
100
0
minus100
minus200Azi
mut
h in
NED
refe
renc
e fra
me (
∘ )PF tracker
6
4
2
Erro
r in
stab
ilize
daz
imut
h (∘
)
Figure 6 Azimuth in NED reference frame as estimated by GPS by radar and by radar-only tracker and estimation error as a function ofGPS time of day
sampling time 119879 the components of the dynamic motionequation are given by
119903119899= 119903119899minus1+ 119879 119903119899minus1
119903119899= 119903119899minus1
120599119899= 120599119899minus1+ 119879 120599119899minus1[1 +
119879
2119903119899minus1
(119903119899minus1120601119899minus1119905119892120601119899minus1minus 119903119899minus1)]
120599119899= 120599119899minus1[1 + 119879( 120601
119899minus1119905119892120601119899minus1minus119903119899minus1
119903119899minus1
)]
120601119899= 120601119899minus1+ 119879 120601119899minus1[1 minus
119879
2119903119899minus1
119903119899minus1]
120601119899= 120601119899minus1[1 minus
119879
2119903119899minus1
119903119899minus1]
(10)
The nonlinear dynamicmotion equation for the sphericalstate vector can be written as
119909119899= 119891 (119909
119899minus1) + 119899119899minus1 (11)
with the zero-mean Gaussian dynamic acceleration noisedistribution
119899119899sim 119873(0 119876
120588) (12)
The components of 119891(119909119899minus1) are given by the nonlinear
equation (10) and the process noise matrix is
119876120588= [
[
119902119903119876102
02
02119902ℎ119876102
02
02119902V1198761
]
]
(13)
with
1198761=
[[[[
[
1198793
3
1198792
2
1198792
2119879
]]]]
]
(14)
where 119902119903 119902ℎ and 119902V must be set depending on the target
maneuvers [34]Since the model is in spherical coordinates the measure-
ment equation is linear and it can be expressed as
119911119899= 119867119909119899+ 119908119899 (15)
with
119867 = [
[
1 0 0 0 0 0
0 0 1 0 0 0
0 0 0 0 1 0
]
]
(16)
and 119908119899is the observation noise which is considered to be
independent zero-mean Gaussian noise defined by
119908119899sim 119873 (0 119877
119899) (17)
8 The Scientific World Journal
52494
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
Radar
RadarPF tracker
Spherical PF
Spherical PFEl
evat
ion
in N
EDre
fere
nce f
ram
e (∘ )
PF tracker
40
minus4minus8minus12
1505
minus05minus15minus25Er
ror i
n st
abili
zed
elev
atio
n (∘
)
Figure 7 Elevation in NED reference frame as estimated by GPS by radar and by radar-only tracker and estimation error as a function ofGPS time of day
52494
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
PF tracker
Spherical PF
Spherical PFPF tracker
minus72
minus76
minus80
minus84
Rang
e rat
e(m
s)
6
2
minus2
minus6Erro
r in
rang
era
te (m
s)
Figure 8 Range rate as estimated by GPS and by radar-only tracker and estimation error as a function of GPS time of day
where 119877119899is the measurement covariance matrix as stated
aboveThe developed obstacle detection and tracking software
provides also an estimate of the Distance at Closest Pointof Approach (see (1)) Since the particles are characterizedby own positions and velocities and given the nonlineardependencies between 119903119881 andDCPA the latter is calculatedfor each particle In this way in order to avoid furtherapproximations due to the evaluation of this distance from
position and velocitymean values DCPA has been calculatedas mean value of the different distances evaluated as
DCPA119899=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
119903 sdot 119881
1003817100381710038171003817100381711988110038171003817100381710038171003817
2119881 minus 119903
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(18)
This is a form of ldquodeep integrationrdquo of a collision detectionsensor since an estimate of the level of collision threat isdetermined by means of the same data fusion algorithm
The Scientific World Journal 9
52494
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
PF tracker
Spherical PF
Spherical PFPF tracker
0
minus1
minus2
minus3
050301
minus01minus03
Azi
mut
h ra
te in
NED
refe
renc
e fra
me (
∘ s)
Erro
r in
stab
ilize
daz
imut
h ra
te (∘
s)
Figure 9 Azimuth rate in NED reference frame as estimated by GPS and by radar-only tracker and estimation error as a function of GPStime of day
This is an additional advantage of using PF rather than EKFsince the need of linearized models in EKF does not allowestimating DCPA by the filter itself
5 Results
The developed obstacle tracking algorithm has been testedin off-line simulations based on flight data gathered duringan intensive test campaign Flight tests were carried out byexploiting the following configuration of test facilities
(a) FLARE aircraft piloted by a human pilot or by theautonomous flight control system
(b) a piloted intruder VLA aircraft in the same class ofFLARE equipped with GPS antennas and receiversand an onboard CPU for navigation data storage
(c) a ground control station (GCS) for real time flightcoordination and test monitoring [36]
(d) a full-duplex data link between FLARE and GCSused to send commands to initiate or terminate testsand to receive synthetic filter output and navigationmeasurements
(e) a downlink between intruder and GCS used for flightmonitoring
During the tests two types of maneuvers were executedsuch as chasing tests with FLARE pursuing the intruder andquasi-frontal encounters performed to estimate detectionand tracking performance in the most interesting scenariosfrom the application point of view
In particular the scenario selected in this paper forperformance analysis is a single quasi-frontal encounterbetween FLARE and the intruder The algorithm has beentested in standalone radar tracking configuration that is
estimates of obstacle relative position and velocity are basedon measurements from radar (update frequency of 1Hz) andthe own-ship navigation system
The number of particles has been set equal to 500 Thisnumber was selected since increasing it up to one orderof magnitude did not produced significant performanceincrease The algorithm is initialized taking into accountthe first radar sensor measurement the covariance matrix iscalculated on the basis of sensor measurements and then it isupdated with estimated values of software output
The algorithm outputs are based on obstacle position andvelocity in terms of range azimuth and elevation and DCPAin a stabilized north-east-down reference frame with originin FLARE center of mass The considered flight segment hasduration of about 20 s with an initial range of about 2000m
In Figure 5 obstacle range as estimated by radar radar-based tracker and GPS (reference) together with errorestimate with respect to GPS measurements is reportedAfter a firm track has been generated on the basis of radarmeasurements the tracker is able to characterize the obstacletrajectory The radar-only tracker provides a range estimatewith an accuracy of the order of few meters that derives fromthe good radar range accuracy and the absence of intrudermaneuvers In Figure 5 the upper plot illustrates the obstaclerange in a small interval time (of about 1 s) in order to showthe particles trajectories (colored lines)
Figures 6 and 7 report the obstacle angular dynamicsin terms of azimuth and elevation As expected the orderof magnitude of these errors is comparable to the radaraccuracy In particular the estimation uncertainty in termsof root mean square is of about 25∘ for azimuth and 13∘ forelevation Being computed in NED these RMS errors includeattitude measurement error biases In fact error biases in theestimation of magnetic heading are the main reason of thelarger error in azimuth It is worth noting that these biases
10 The Scientific World Journal
Table 1 PF performance in the selected scenario in terms of RMSerror
RMS Particle filter EKFRange (m) 84 37Range rate (m∘) 30 23Azimuth (∘) 25 17Azimuth rate (∘s) 02 04Elevation (∘) 13 21Elevation rate (∘s) 02 08
have a little effect on the estimation of angular rates and ofDistance at Closest Point of Approach
The range and angular rates as estimated by GPS (ref-erence) and particle filter tracker are reported in Figures 89 and 10 These variables are very important informationsources for collision detection assessment even though theyare not directly provided by the radar sensor The plots showthat the tracker estimates are very accurate with a very smallvalue in terms of standard deviation
Simulation results confirm how the resampling proce-dure is a key factor for tracking performance avoiding thedegeneracy phenomenon and thus enabling a great quantityof particles to survive to the prediction step
In order to better understand the particle filter trackingcapability PF and EKF estimation errors are reported inTable 1 in terms of root mean square (RMS) errors computedas
RMS = radic 1119873
119873
sum
119905=1
(119909119905minus 119909119905)2 (19)
where 119873 is the number of measurements 119909119905is the generic
PF tracker estimate (computed after resampling and repre-senting the mean value over all the particles) and 119909
119905is the
reference value computed on the basis of FLARE and intruderGPS measurements
The results show that PF tracker performance is com-parable to EKF in terms of order of magnitude Of coursethe introduction of electro-optical data can improve angularaccuracy since these sensors have a faster update rate thanradar In particular while the range rate error is very similarfor the two filters obstacle angular velocities provided byPF algorithm are slightly more accurate than EKF in theconsidered scenario These variables are very importantinformation sources for collision detection assessment eventhough they are not directly provided by the radar
In fact in near collision conditions angular rates are themost important variables influencing collision detection Asshown in [7] in these conditions DCPA uncertainty for givenrange and range rate shows a linear dependence on angularrate errors while range rate essentially impacts the time-to-go estimate
In the considered scenario DCPA as computed on thebasis of GPS measurement has been used as a reference forcomparing DCPA estimated by EKF tracker and PF trackerFigure 11 shows that the PF algorithm is more accuratethan EKF for the estimation of the DCPA in the initial
52494
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
PF tracker
Spherical PF
Spherical PFPF tracker
Elev
atio
nh ra
te in
NED
refe
renc
e fra
me (
∘ s)
08
04
0
minus04
minus01minus02minus03minus04minus05Er
ror i
n st
abili
zed
elev
atio
n ra
te (∘
s)
Figure 10 Elevation rate in NED reference frame as estimated byGPS and by radar-only tracker and estimation error as a function ofGPS time of day
450
400
350
300
250
200
150
100
50
Distance at Closest Point of Approach (DCPA) (m)
PF trackerEKF trackerGPS
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
Figure 11 Distance at Closest Point of Approach as estimated byGPS (reference) by radar and by radar-only tracker as function ofGPS time of the day
phase of firm tracking (at larger range) thus providing animprovement in collision risk assessment and a potentialreduction in the delay in declaring a collision threat Analysisof GPS data demonstrates that the considered encounterrepresents a real Near Mid-Air Collision (NMAC) scenariosince the reference DCPA keeps a very small value and liesbelow the bubble distance threshold almost in the whole firmtracking phase
The Scientific World Journal 11
6 Conclusion and Future Works
This paper focused on algorithm and test results fromobstacle tracking software based on particle filter and aimedat demonstrating UAS autonomous collision detection capa-bility in terms of reliable estimation of Distance at ClosestPoint of Approach The algorithm performance has beeninitially evaluated in radar-only configuration since the maininterest was addressed to the analysis of the potential impactof nonlinear filters on tracking capabilities with respect toassessed EKF first in a single sensor framework
The software has been tested in off-line simulations basedon real data recorded during a flight test campaign and aquasi-frontal encounter between the own aircraft and theintruder has been presented as test case The results pointedout that the developed algorithm is able to detect and trackthe obstacle trajectory with accuracy comparable to the EKFIn particular some advantages were highlighted in the directdetermination of Distance at Closest Point of Approach witha potential reduction of the delay for collision detectionThis result permits planning additional future investigationactivities such as
(i) performing the comparison on a larger experimentaldata set thus increasing the statistical significance
(ii) developing a multisensor-based analysis to confirmthe results obtained by the developed PF tracker whenadditional data sources are available such as electro-optical sensors indeed they can provide higheraccuracy in angular measurements and better datarate than radar sensors with a great impact on DCPAperformance
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The PhD grant of Miss Anna Elena Tirri is cofunded byEUROCONTROL through the research network HALA inthe framework of the WP-E of SESAR project
References
[1] EUROCONTROL in Proceedings of the EUROCONTROL Spec-ifications for the Use of Military Unmanned Aerial Vehicles asOperational Air Traffic Outside Segregated Airspace Version10 DocNo EUROCONTROL-SPEC-0102 Bruxelles BelgiumJuly 2007
[2] US Federal Aviation Administration (FAA) ldquoAirworthinesscertification of unmanned aircraft systemsrdquo Order 813034US Federal Aviation Administration (FAA) Washington DCUSA 2008
[3] US Federal Aviation Administration (FAA) ldquoInvestigate aNear Mid Air Collisionrdquo FAA Order 89001 vol 7 chapter 4Washington DC USA 2007
[4] G Fasano D Accardo A Moccia et al ldquoMulti-sensor-basedfully autonomous non-cooperative collision avoidance system
for unmanned air vehiclesrdquo Journal of Aerospace ComputingInformation and Communication vol 5 no 10 pp 338ndash3602008
[5] MTSI ldquoNon-cooperative detect see amp avoid (DSA) sensorstudyrdquo Tech Rep NASA ERAST 2002
[6] O Shakernia W Chen S Graham et al ldquoSense and Avoid(SAA) flight test and lessons learnedrdquo in Proceedings of the 2ndAIAA InfotechAerospace Conference and Exhibit (AIAA rsquo07)pp 2781ndash2795 Rohnert Park Calif USA May 2007
[7] D Accardo G Fasano L Forlenza A Moccia and A RispolildquoFlight test of a radar-based tracking system for UAS sense andavoidrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 49 no 2 pp 1139ndash1160 2013
[8] USFAA SpecialOperations FAAOrder 76104M January 2007[9] S J Julier and J K Uhlmann ldquoA new extension of the Kalman
filter to nonlinear systemsrdquo in Signal Processing Sensor Fusionand Target Recognition VI vol 3068 of Proceedings of SPIE pp182ndash193 Orlando Fla USA 1997
[10] N E Smith R G Cobb S J Pierce and V M Raska ldquoOptimalcollision avoidance trajectories for unmannedremotely pilotedaircraftrdquo in Proceedings of the AIAA Guidance Navigation andControl Conference (GNC 13) AIAA 2013-4619 Boston MassUSA August 2013
[11] L Lin Y Wang Y Liu C Xiong and K Zeng ldquoMarker-lessregistration based on template tracking for augmented realityrdquoMultimedia Tools and Applications vol 41 no 2 pp 235ndash2522009
[12] X Liu L Lin S Yan H Jin and W Jiang ldquoAdaptive objecttracking by learning hybrid template onlinerdquo IEEE Transactionson Circuits and Systems for Video Technology vol 21 no 11 pp1588ndash1599 2011
[13] L Lin Y Lu Y Pan and X Chen ldquoIntegrating graph partition-ing and matching for trajectory analysis in video surveillancerdquoIEEE Transactions on Image Processing vol 21 no 12 pp 4844ndash4857 2012
[14] L Xia P Li Y Guo and Z Shen ldquoResearch of maneuveringtarget tracking based on particle filterrdquo in Proceedings of the Chi-nese Automation Congress (CAC rsquo13) pp 567ndash570 ChangshaChina 2013
[15] F Gustafsson F Gunnarsson N Bergman et al ldquoParticle filtersfor positioning navigation and trackingrdquo IEEE Transactions onSignal Processing vol 50 no 2 pp 425ndash437 2002
[16] S Challa and G W Pulford ldquoJoint target tracking and classi-fication using radar and ESM sensorsrdquo IEEE Transactions onAerospace and Electronic Systems vol 37 no 3 pp 1039ndash10552001
[17] M S Grewal and A P Andrews Kalman Filtering Theory andPractice Using Matlab John Wiley amp Sons 2nd edition 2001
[18] S Haykin Kalman Filtering and Neural Networks John Wileyand Sons 2001
[19] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Transactions of the ASME Series D Journal of BasicEngineering vol 82 no 1 pp 35ndash45 1960
[20] S Arulampalam and B Ristic ldquoComparison of the particle filterwith range-parameterised and modified polar EKFs for angle-only trackingrdquo in Signal and Data Processing of Small Targetsvol 4048 of Proceedings of SPIE pp 288ndash299 Orlando FlaUSA April 2000
[21] X Lin T Kirubarajan Y Bar-Shalom and S Maskell ldquoCom-parison of EKF pseudomeasurement and particle filters fora bearing-only target tracking problemrdquo in Signal and Data
12 The Scientific World Journal
Processing of Small Targets vol 4728 of Proceedings of SPIE pp240ndash250 April 2002
[22] M S Arulampalam S Maskell N Gordon and T Clapp ldquoAtutorial on particle filters for online nonlinearnon-GaussianBayesian trackingrdquo IEEE Transactions on Signal Processing vol50 no 2 pp 174ndash188 2002
[23] A Doucet N de Freitas and N Gordon ldquoAn introduction tosequential Monte Carlo methodsrdquo in Sequential Monte CarloMethods in Practice Statistics for Engineering and InformationScience pp 3ndash14 Springer New York NY USA 2001
[24] B Liu andCHao ldquoSequential bearings-only-tracking initiationwith particle filteringmethodrdquoThe ScientificWorld Journal vol2013 Article ID 489121 7 pages 2013
[25] R Karlsson and F Gustafsson ldquoRecursive Bayesian estimationbearings-only applicationsrdquo IEE Proceedings Radar Sonar andNavigation vol 152 no 5 pp 305ndash313 2005
[26] N Gordon ldquoHybrid bootstrap filter for target tracking inclutterrdquo in Proceedings of the American Control Conference vol1 pp 628ndash632 June 1995
[27] S Mcginnity and G W Irwin ldquoMultiple model bootstrapfilter for maneuvering target trackingrdquo IEEE Transactions onAerospace and Electronic Systems vol 36 no 3 pp 1006ndash10122000
[28] M R Morelande and S Challa ldquoManoeuvring target trackingin clutter using particle filtersrdquo IEEE Transactions on Aerospaceand Electronic Systems vol 41 no 1 pp 252ndash270 2005
[29] D Lerro and Y Bar-Shalom ldquoTracking with de-biased consis-tent converted measurements versus EKFrdquo IEEE TransactionsonAerospace and Electronic Systems vol 29 no 3 pp 1015ndash10221993
[30] G Fasano L Forlenza D Accardo A Moccia and A RispolildquoIntegrated obstacle detection system based on radar andoptical sensorsrdquo inProceedings of the AIAA Infotech at Aerospace(AIAA rsquo10) Atlanta Ga USA April 2010
[31] S S Blackman and R F Popoli Design and Analysis of ModernTracking Systems Artech House Norwood Mass USA 1999
[32] G Fasano D Accardo A Moccia and A Rispoli ldquoAn inno-vative procedure for calibration of strapdown electro-opticalsensors onboard unmanned air vehiclesrdquo Sensors vol 10 no 1pp 639ndash654 2010
[33] B Ristic S Arulampalam and N Gordon Beyond the KalmanFilter Particle Filter for Tracking Applications Artech HouseNew York NY USA 2004
[34] A Haug and L Williams ldquoA spherical constant velocity modelfor target tracking in three dimensionsrdquo in IEEE AerospaceConference pp 1ndash15 Big Sky Mont USA March 2012
[35] X R Li and V P Jilkov ldquoA survey of maneuvering target track-ing dynamic modelsrdquo in Proceedings of the SPIE Conference onsignal and Data Processing of Small Targets vol 39 pp 1333ndash1364 Orlando Fla USA April 2000
[36] G Fasano A Moccia D Accardo and A Rispoli ldquoDevelop-ment and test of an integrated sensor system for autonomouscollision avoidancerdquo in Proceedings of the 26th Congress ofInternational Council of the Aeronautical Sciences (ICAS rsquo08) pp3625ndash3634 Anchorage Alaska USA September 2008
International Journal of
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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Navigation and Observation
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DistributedSensor Networks
International Journal of
6 The Scientific World Journal
52505
52505
52505
52505
52506
52506
52506
times104
1080
1070
1060
1050
1040
1030
1020
1010
1000
990
GPS time of day (s)
Rang
e (m
)
Spherical PF
GPSRadar
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104
4000
3000
2000
1000
0
GPS time of day (s)
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
Rang
e (m
)
GPSRadar
RadarPF tracker
20
0
minus20
minus40
Erro
r in
rang
e (m
)
Spherical PF
Figure 5 Range as estimated by GPS by radar and by radar-only tracker and estimation error as a function of GPS time of day The upperfigure highlights the trajectory of each particle
The target state vector in spherical coordinates is definedas
119909 = [119903 119903 120599 120599 120601 120601] (7)
where 119903 is the range 120599 is the azimuth 120601 is the elevation angleand 119903 120599 120601 are their first time derivatives
In order to evaluate the velocity components let usconsider
V = [
[
V119903
V120599
V120601
]
]
= [
[
119903
119903 120599 cos120601119903 120601
]
]
(8)
where the velocity vector has been defined as V = [V119903 V120599 V120601]
for the sake of simplicity
For a spherical constant velocity dynamic model repre-senting the objectmotion it is assumed that V
119903= V120599= V120601= 0
Taking the time derivative of each component in (8) yields
V119903= 119903 = 0
V120599= 119903 120599 cos 120593 + 119903 120599 cos 120593 minus 119903 120599 sin 120593 = 0
V120601= 119903 + 119903 = 0
(9)
Rearranging the above expressions in terms of angu-lar velocities and considering discrete-time domain with
The Scientific World Journal 7
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
Radar
RadarPF tracker
Spherical PF
Spherical PF
100
0
minus100
minus200Azi
mut
h in
NED
refe
renc
e fra
me (
∘ )PF tracker
6
4
2
Erro
r in
stab
ilize
daz
imut
h (∘
)
Figure 6 Azimuth in NED reference frame as estimated by GPS by radar and by radar-only tracker and estimation error as a function ofGPS time of day
sampling time 119879 the components of the dynamic motionequation are given by
119903119899= 119903119899minus1+ 119879 119903119899minus1
119903119899= 119903119899minus1
120599119899= 120599119899minus1+ 119879 120599119899minus1[1 +
119879
2119903119899minus1
(119903119899minus1120601119899minus1119905119892120601119899minus1minus 119903119899minus1)]
120599119899= 120599119899minus1[1 + 119879( 120601
119899minus1119905119892120601119899minus1minus119903119899minus1
119903119899minus1
)]
120601119899= 120601119899minus1+ 119879 120601119899minus1[1 minus
119879
2119903119899minus1
119903119899minus1]
120601119899= 120601119899minus1[1 minus
119879
2119903119899minus1
119903119899minus1]
(10)
The nonlinear dynamicmotion equation for the sphericalstate vector can be written as
119909119899= 119891 (119909
119899minus1) + 119899119899minus1 (11)
with the zero-mean Gaussian dynamic acceleration noisedistribution
119899119899sim 119873(0 119876
120588) (12)
The components of 119891(119909119899minus1) are given by the nonlinear
equation (10) and the process noise matrix is
119876120588= [
[
119902119903119876102
02
02119902ℎ119876102
02
02119902V1198761
]
]
(13)
with
1198761=
[[[[
[
1198793
3
1198792
2
1198792
2119879
]]]]
]
(14)
where 119902119903 119902ℎ and 119902V must be set depending on the target
maneuvers [34]Since the model is in spherical coordinates the measure-
ment equation is linear and it can be expressed as
119911119899= 119867119909119899+ 119908119899 (15)
with
119867 = [
[
1 0 0 0 0 0
0 0 1 0 0 0
0 0 0 0 1 0
]
]
(16)
and 119908119899is the observation noise which is considered to be
independent zero-mean Gaussian noise defined by
119908119899sim 119873 (0 119877
119899) (17)
8 The Scientific World Journal
52494
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
Radar
RadarPF tracker
Spherical PF
Spherical PFEl
evat
ion
in N
EDre
fere
nce f
ram
e (∘ )
PF tracker
40
minus4minus8minus12
1505
minus05minus15minus25Er
ror i
n st
abili
zed
elev
atio
n (∘
)
Figure 7 Elevation in NED reference frame as estimated by GPS by radar and by radar-only tracker and estimation error as a function ofGPS time of day
52494
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
PF tracker
Spherical PF
Spherical PFPF tracker
minus72
minus76
minus80
minus84
Rang
e rat
e(m
s)
6
2
minus2
minus6Erro
r in
rang
era
te (m
s)
Figure 8 Range rate as estimated by GPS and by radar-only tracker and estimation error as a function of GPS time of day
where 119877119899is the measurement covariance matrix as stated
aboveThe developed obstacle detection and tracking software
provides also an estimate of the Distance at Closest Pointof Approach (see (1)) Since the particles are characterizedby own positions and velocities and given the nonlineardependencies between 119903119881 andDCPA the latter is calculatedfor each particle In this way in order to avoid furtherapproximations due to the evaluation of this distance from
position and velocitymean values DCPA has been calculatedas mean value of the different distances evaluated as
DCPA119899=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
119903 sdot 119881
1003817100381710038171003817100381711988110038171003817100381710038171003817
2119881 minus 119903
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(18)
This is a form of ldquodeep integrationrdquo of a collision detectionsensor since an estimate of the level of collision threat isdetermined by means of the same data fusion algorithm
The Scientific World Journal 9
52494
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
PF tracker
Spherical PF
Spherical PFPF tracker
0
minus1
minus2
minus3
050301
minus01minus03
Azi
mut
h ra
te in
NED
refe
renc
e fra
me (
∘ s)
Erro
r in
stab
ilize
daz
imut
h ra
te (∘
s)
Figure 9 Azimuth rate in NED reference frame as estimated by GPS and by radar-only tracker and estimation error as a function of GPStime of day
This is an additional advantage of using PF rather than EKFsince the need of linearized models in EKF does not allowestimating DCPA by the filter itself
5 Results
The developed obstacle tracking algorithm has been testedin off-line simulations based on flight data gathered duringan intensive test campaign Flight tests were carried out byexploiting the following configuration of test facilities
(a) FLARE aircraft piloted by a human pilot or by theautonomous flight control system
(b) a piloted intruder VLA aircraft in the same class ofFLARE equipped with GPS antennas and receiversand an onboard CPU for navigation data storage
(c) a ground control station (GCS) for real time flightcoordination and test monitoring [36]
(d) a full-duplex data link between FLARE and GCSused to send commands to initiate or terminate testsand to receive synthetic filter output and navigationmeasurements
(e) a downlink between intruder and GCS used for flightmonitoring
During the tests two types of maneuvers were executedsuch as chasing tests with FLARE pursuing the intruder andquasi-frontal encounters performed to estimate detectionand tracking performance in the most interesting scenariosfrom the application point of view
In particular the scenario selected in this paper forperformance analysis is a single quasi-frontal encounterbetween FLARE and the intruder The algorithm has beentested in standalone radar tracking configuration that is
estimates of obstacle relative position and velocity are basedon measurements from radar (update frequency of 1Hz) andthe own-ship navigation system
The number of particles has been set equal to 500 Thisnumber was selected since increasing it up to one orderof magnitude did not produced significant performanceincrease The algorithm is initialized taking into accountthe first radar sensor measurement the covariance matrix iscalculated on the basis of sensor measurements and then it isupdated with estimated values of software output
The algorithm outputs are based on obstacle position andvelocity in terms of range azimuth and elevation and DCPAin a stabilized north-east-down reference frame with originin FLARE center of mass The considered flight segment hasduration of about 20 s with an initial range of about 2000m
In Figure 5 obstacle range as estimated by radar radar-based tracker and GPS (reference) together with errorestimate with respect to GPS measurements is reportedAfter a firm track has been generated on the basis of radarmeasurements the tracker is able to characterize the obstacletrajectory The radar-only tracker provides a range estimatewith an accuracy of the order of few meters that derives fromthe good radar range accuracy and the absence of intrudermaneuvers In Figure 5 the upper plot illustrates the obstaclerange in a small interval time (of about 1 s) in order to showthe particles trajectories (colored lines)
Figures 6 and 7 report the obstacle angular dynamicsin terms of azimuth and elevation As expected the orderof magnitude of these errors is comparable to the radaraccuracy In particular the estimation uncertainty in termsof root mean square is of about 25∘ for azimuth and 13∘ forelevation Being computed in NED these RMS errors includeattitude measurement error biases In fact error biases in theestimation of magnetic heading are the main reason of thelarger error in azimuth It is worth noting that these biases
10 The Scientific World Journal
Table 1 PF performance in the selected scenario in terms of RMSerror
RMS Particle filter EKFRange (m) 84 37Range rate (m∘) 30 23Azimuth (∘) 25 17Azimuth rate (∘s) 02 04Elevation (∘) 13 21Elevation rate (∘s) 02 08
have a little effect on the estimation of angular rates and ofDistance at Closest Point of Approach
The range and angular rates as estimated by GPS (ref-erence) and particle filter tracker are reported in Figures 89 and 10 These variables are very important informationsources for collision detection assessment even though theyare not directly provided by the radar sensor The plots showthat the tracker estimates are very accurate with a very smallvalue in terms of standard deviation
Simulation results confirm how the resampling proce-dure is a key factor for tracking performance avoiding thedegeneracy phenomenon and thus enabling a great quantityof particles to survive to the prediction step
In order to better understand the particle filter trackingcapability PF and EKF estimation errors are reported inTable 1 in terms of root mean square (RMS) errors computedas
RMS = radic 1119873
119873
sum
119905=1
(119909119905minus 119909119905)2 (19)
where 119873 is the number of measurements 119909119905is the generic
PF tracker estimate (computed after resampling and repre-senting the mean value over all the particles) and 119909
119905is the
reference value computed on the basis of FLARE and intruderGPS measurements
The results show that PF tracker performance is com-parable to EKF in terms of order of magnitude Of coursethe introduction of electro-optical data can improve angularaccuracy since these sensors have a faster update rate thanradar In particular while the range rate error is very similarfor the two filters obstacle angular velocities provided byPF algorithm are slightly more accurate than EKF in theconsidered scenario These variables are very importantinformation sources for collision detection assessment eventhough they are not directly provided by the radar
In fact in near collision conditions angular rates are themost important variables influencing collision detection Asshown in [7] in these conditions DCPA uncertainty for givenrange and range rate shows a linear dependence on angularrate errors while range rate essentially impacts the time-to-go estimate
In the considered scenario DCPA as computed on thebasis of GPS measurement has been used as a reference forcomparing DCPA estimated by EKF tracker and PF trackerFigure 11 shows that the PF algorithm is more accuratethan EKF for the estimation of the DCPA in the initial
52494
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
PF tracker
Spherical PF
Spherical PFPF tracker
Elev
atio
nh ra
te in
NED
refe
renc
e fra
me (
∘ s)
08
04
0
minus04
minus01minus02minus03minus04minus05Er
ror i
n st
abili
zed
elev
atio
n ra
te (∘
s)
Figure 10 Elevation rate in NED reference frame as estimated byGPS and by radar-only tracker and estimation error as a function ofGPS time of day
450
400
350
300
250
200
150
100
50
Distance at Closest Point of Approach (DCPA) (m)
PF trackerEKF trackerGPS
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
Figure 11 Distance at Closest Point of Approach as estimated byGPS (reference) by radar and by radar-only tracker as function ofGPS time of the day
phase of firm tracking (at larger range) thus providing animprovement in collision risk assessment and a potentialreduction in the delay in declaring a collision threat Analysisof GPS data demonstrates that the considered encounterrepresents a real Near Mid-Air Collision (NMAC) scenariosince the reference DCPA keeps a very small value and liesbelow the bubble distance threshold almost in the whole firmtracking phase
The Scientific World Journal 11
6 Conclusion and Future Works
This paper focused on algorithm and test results fromobstacle tracking software based on particle filter and aimedat demonstrating UAS autonomous collision detection capa-bility in terms of reliable estimation of Distance at ClosestPoint of Approach The algorithm performance has beeninitially evaluated in radar-only configuration since the maininterest was addressed to the analysis of the potential impactof nonlinear filters on tracking capabilities with respect toassessed EKF first in a single sensor framework
The software has been tested in off-line simulations basedon real data recorded during a flight test campaign and aquasi-frontal encounter between the own aircraft and theintruder has been presented as test case The results pointedout that the developed algorithm is able to detect and trackthe obstacle trajectory with accuracy comparable to the EKFIn particular some advantages were highlighted in the directdetermination of Distance at Closest Point of Approach witha potential reduction of the delay for collision detectionThis result permits planning additional future investigationactivities such as
(i) performing the comparison on a larger experimentaldata set thus increasing the statistical significance
(ii) developing a multisensor-based analysis to confirmthe results obtained by the developed PF tracker whenadditional data sources are available such as electro-optical sensors indeed they can provide higheraccuracy in angular measurements and better datarate than radar sensors with a great impact on DCPAperformance
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The PhD grant of Miss Anna Elena Tirri is cofunded byEUROCONTROL through the research network HALA inthe framework of the WP-E of SESAR project
References
[1] EUROCONTROL in Proceedings of the EUROCONTROL Spec-ifications for the Use of Military Unmanned Aerial Vehicles asOperational Air Traffic Outside Segregated Airspace Version10 DocNo EUROCONTROL-SPEC-0102 Bruxelles BelgiumJuly 2007
[2] US Federal Aviation Administration (FAA) ldquoAirworthinesscertification of unmanned aircraft systemsrdquo Order 813034US Federal Aviation Administration (FAA) Washington DCUSA 2008
[3] US Federal Aviation Administration (FAA) ldquoInvestigate aNear Mid Air Collisionrdquo FAA Order 89001 vol 7 chapter 4Washington DC USA 2007
[4] G Fasano D Accardo A Moccia et al ldquoMulti-sensor-basedfully autonomous non-cooperative collision avoidance system
for unmanned air vehiclesrdquo Journal of Aerospace ComputingInformation and Communication vol 5 no 10 pp 338ndash3602008
[5] MTSI ldquoNon-cooperative detect see amp avoid (DSA) sensorstudyrdquo Tech Rep NASA ERAST 2002
[6] O Shakernia W Chen S Graham et al ldquoSense and Avoid(SAA) flight test and lessons learnedrdquo in Proceedings of the 2ndAIAA InfotechAerospace Conference and Exhibit (AIAA rsquo07)pp 2781ndash2795 Rohnert Park Calif USA May 2007
[7] D Accardo G Fasano L Forlenza A Moccia and A RispolildquoFlight test of a radar-based tracking system for UAS sense andavoidrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 49 no 2 pp 1139ndash1160 2013
[8] USFAA SpecialOperations FAAOrder 76104M January 2007[9] S J Julier and J K Uhlmann ldquoA new extension of the Kalman
filter to nonlinear systemsrdquo in Signal Processing Sensor Fusionand Target Recognition VI vol 3068 of Proceedings of SPIE pp182ndash193 Orlando Fla USA 1997
[10] N E Smith R G Cobb S J Pierce and V M Raska ldquoOptimalcollision avoidance trajectories for unmannedremotely pilotedaircraftrdquo in Proceedings of the AIAA Guidance Navigation andControl Conference (GNC 13) AIAA 2013-4619 Boston MassUSA August 2013
[11] L Lin Y Wang Y Liu C Xiong and K Zeng ldquoMarker-lessregistration based on template tracking for augmented realityrdquoMultimedia Tools and Applications vol 41 no 2 pp 235ndash2522009
[12] X Liu L Lin S Yan H Jin and W Jiang ldquoAdaptive objecttracking by learning hybrid template onlinerdquo IEEE Transactionson Circuits and Systems for Video Technology vol 21 no 11 pp1588ndash1599 2011
[13] L Lin Y Lu Y Pan and X Chen ldquoIntegrating graph partition-ing and matching for trajectory analysis in video surveillancerdquoIEEE Transactions on Image Processing vol 21 no 12 pp 4844ndash4857 2012
[14] L Xia P Li Y Guo and Z Shen ldquoResearch of maneuveringtarget tracking based on particle filterrdquo in Proceedings of the Chi-nese Automation Congress (CAC rsquo13) pp 567ndash570 ChangshaChina 2013
[15] F Gustafsson F Gunnarsson N Bergman et al ldquoParticle filtersfor positioning navigation and trackingrdquo IEEE Transactions onSignal Processing vol 50 no 2 pp 425ndash437 2002
[16] S Challa and G W Pulford ldquoJoint target tracking and classi-fication using radar and ESM sensorsrdquo IEEE Transactions onAerospace and Electronic Systems vol 37 no 3 pp 1039ndash10552001
[17] M S Grewal and A P Andrews Kalman Filtering Theory andPractice Using Matlab John Wiley amp Sons 2nd edition 2001
[18] S Haykin Kalman Filtering and Neural Networks John Wileyand Sons 2001
[19] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Transactions of the ASME Series D Journal of BasicEngineering vol 82 no 1 pp 35ndash45 1960
[20] S Arulampalam and B Ristic ldquoComparison of the particle filterwith range-parameterised and modified polar EKFs for angle-only trackingrdquo in Signal and Data Processing of Small Targetsvol 4048 of Proceedings of SPIE pp 288ndash299 Orlando FlaUSA April 2000
[21] X Lin T Kirubarajan Y Bar-Shalom and S Maskell ldquoCom-parison of EKF pseudomeasurement and particle filters fora bearing-only target tracking problemrdquo in Signal and Data
12 The Scientific World Journal
Processing of Small Targets vol 4728 of Proceedings of SPIE pp240ndash250 April 2002
[22] M S Arulampalam S Maskell N Gordon and T Clapp ldquoAtutorial on particle filters for online nonlinearnon-GaussianBayesian trackingrdquo IEEE Transactions on Signal Processing vol50 no 2 pp 174ndash188 2002
[23] A Doucet N de Freitas and N Gordon ldquoAn introduction tosequential Monte Carlo methodsrdquo in Sequential Monte CarloMethods in Practice Statistics for Engineering and InformationScience pp 3ndash14 Springer New York NY USA 2001
[24] B Liu andCHao ldquoSequential bearings-only-tracking initiationwith particle filteringmethodrdquoThe ScientificWorld Journal vol2013 Article ID 489121 7 pages 2013
[25] R Karlsson and F Gustafsson ldquoRecursive Bayesian estimationbearings-only applicationsrdquo IEE Proceedings Radar Sonar andNavigation vol 152 no 5 pp 305ndash313 2005
[26] N Gordon ldquoHybrid bootstrap filter for target tracking inclutterrdquo in Proceedings of the American Control Conference vol1 pp 628ndash632 June 1995
[27] S Mcginnity and G W Irwin ldquoMultiple model bootstrapfilter for maneuvering target trackingrdquo IEEE Transactions onAerospace and Electronic Systems vol 36 no 3 pp 1006ndash10122000
[28] M R Morelande and S Challa ldquoManoeuvring target trackingin clutter using particle filtersrdquo IEEE Transactions on Aerospaceand Electronic Systems vol 41 no 1 pp 252ndash270 2005
[29] D Lerro and Y Bar-Shalom ldquoTracking with de-biased consis-tent converted measurements versus EKFrdquo IEEE TransactionsonAerospace and Electronic Systems vol 29 no 3 pp 1015ndash10221993
[30] G Fasano L Forlenza D Accardo A Moccia and A RispolildquoIntegrated obstacle detection system based on radar andoptical sensorsrdquo inProceedings of the AIAA Infotech at Aerospace(AIAA rsquo10) Atlanta Ga USA April 2010
[31] S S Blackman and R F Popoli Design and Analysis of ModernTracking Systems Artech House Norwood Mass USA 1999
[32] G Fasano D Accardo A Moccia and A Rispoli ldquoAn inno-vative procedure for calibration of strapdown electro-opticalsensors onboard unmanned air vehiclesrdquo Sensors vol 10 no 1pp 639ndash654 2010
[33] B Ristic S Arulampalam and N Gordon Beyond the KalmanFilter Particle Filter for Tracking Applications Artech HouseNew York NY USA 2004
[34] A Haug and L Williams ldquoA spherical constant velocity modelfor target tracking in three dimensionsrdquo in IEEE AerospaceConference pp 1ndash15 Big Sky Mont USA March 2012
[35] X R Li and V P Jilkov ldquoA survey of maneuvering target track-ing dynamic modelsrdquo in Proceedings of the SPIE Conference onsignal and Data Processing of Small Targets vol 39 pp 1333ndash1364 Orlando Fla USA April 2000
[36] G Fasano A Moccia D Accardo and A Rispoli ldquoDevelop-ment and test of an integrated sensor system for autonomouscollision avoidancerdquo in Proceedings of the 26th Congress ofInternational Council of the Aeronautical Sciences (ICAS rsquo08) pp3625ndash3634 Anchorage Alaska USA September 2008
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Active and Passive Electronic Components
Control Scienceand Engineering
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RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
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Submit your manuscripts athttpwwwhindawicom
VLSI Design
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Shock and Vibration
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Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Electrical and Computer Engineering
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Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
The Scientific World Journal 7
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
Radar
RadarPF tracker
Spherical PF
Spherical PF
100
0
minus100
minus200Azi
mut
h in
NED
refe
renc
e fra
me (
∘ )PF tracker
6
4
2
Erro
r in
stab
ilize
daz
imut
h (∘
)
Figure 6 Azimuth in NED reference frame as estimated by GPS by radar and by radar-only tracker and estimation error as a function ofGPS time of day
sampling time 119879 the components of the dynamic motionequation are given by
119903119899= 119903119899minus1+ 119879 119903119899minus1
119903119899= 119903119899minus1
120599119899= 120599119899minus1+ 119879 120599119899minus1[1 +
119879
2119903119899minus1
(119903119899minus1120601119899minus1119905119892120601119899minus1minus 119903119899minus1)]
120599119899= 120599119899minus1[1 + 119879( 120601
119899minus1119905119892120601119899minus1minus119903119899minus1
119903119899minus1
)]
120601119899= 120601119899minus1+ 119879 120601119899minus1[1 minus
119879
2119903119899minus1
119903119899minus1]
120601119899= 120601119899minus1[1 minus
119879
2119903119899minus1
119903119899minus1]
(10)
The nonlinear dynamicmotion equation for the sphericalstate vector can be written as
119909119899= 119891 (119909
119899minus1) + 119899119899minus1 (11)
with the zero-mean Gaussian dynamic acceleration noisedistribution
119899119899sim 119873(0 119876
120588) (12)
The components of 119891(119909119899minus1) are given by the nonlinear
equation (10) and the process noise matrix is
119876120588= [
[
119902119903119876102
02
02119902ℎ119876102
02
02119902V1198761
]
]
(13)
with
1198761=
[[[[
[
1198793
3
1198792
2
1198792
2119879
]]]]
]
(14)
where 119902119903 119902ℎ and 119902V must be set depending on the target
maneuvers [34]Since the model is in spherical coordinates the measure-
ment equation is linear and it can be expressed as
119911119899= 119867119909119899+ 119908119899 (15)
with
119867 = [
[
1 0 0 0 0 0
0 0 1 0 0 0
0 0 0 0 1 0
]
]
(16)
and 119908119899is the observation noise which is considered to be
independent zero-mean Gaussian noise defined by
119908119899sim 119873 (0 119877
119899) (17)
8 The Scientific World Journal
52494
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
Radar
RadarPF tracker
Spherical PF
Spherical PFEl
evat
ion
in N
EDre
fere
nce f
ram
e (∘ )
PF tracker
40
minus4minus8minus12
1505
minus05minus15minus25Er
ror i
n st
abili
zed
elev
atio
n (∘
)
Figure 7 Elevation in NED reference frame as estimated by GPS by radar and by radar-only tracker and estimation error as a function ofGPS time of day
52494
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
PF tracker
Spherical PF
Spherical PFPF tracker
minus72
minus76
minus80
minus84
Rang
e rat
e(m
s)
6
2
minus2
minus6Erro
r in
rang
era
te (m
s)
Figure 8 Range rate as estimated by GPS and by radar-only tracker and estimation error as a function of GPS time of day
where 119877119899is the measurement covariance matrix as stated
aboveThe developed obstacle detection and tracking software
provides also an estimate of the Distance at Closest Pointof Approach (see (1)) Since the particles are characterizedby own positions and velocities and given the nonlineardependencies between 119903119881 andDCPA the latter is calculatedfor each particle In this way in order to avoid furtherapproximations due to the evaluation of this distance from
position and velocitymean values DCPA has been calculatedas mean value of the different distances evaluated as
DCPA119899=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
119903 sdot 119881
1003817100381710038171003817100381711988110038171003817100381710038171003817
2119881 minus 119903
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(18)
This is a form of ldquodeep integrationrdquo of a collision detectionsensor since an estimate of the level of collision threat isdetermined by means of the same data fusion algorithm
The Scientific World Journal 9
52494
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
PF tracker
Spherical PF
Spherical PFPF tracker
0
minus1
minus2
minus3
050301
minus01minus03
Azi
mut
h ra
te in
NED
refe
renc
e fra
me (
∘ s)
Erro
r in
stab
ilize
daz
imut
h ra
te (∘
s)
Figure 9 Azimuth rate in NED reference frame as estimated by GPS and by radar-only tracker and estimation error as a function of GPStime of day
This is an additional advantage of using PF rather than EKFsince the need of linearized models in EKF does not allowestimating DCPA by the filter itself
5 Results
The developed obstacle tracking algorithm has been testedin off-line simulations based on flight data gathered duringan intensive test campaign Flight tests were carried out byexploiting the following configuration of test facilities
(a) FLARE aircraft piloted by a human pilot or by theautonomous flight control system
(b) a piloted intruder VLA aircraft in the same class ofFLARE equipped with GPS antennas and receiversand an onboard CPU for navigation data storage
(c) a ground control station (GCS) for real time flightcoordination and test monitoring [36]
(d) a full-duplex data link between FLARE and GCSused to send commands to initiate or terminate testsand to receive synthetic filter output and navigationmeasurements
(e) a downlink between intruder and GCS used for flightmonitoring
During the tests two types of maneuvers were executedsuch as chasing tests with FLARE pursuing the intruder andquasi-frontal encounters performed to estimate detectionand tracking performance in the most interesting scenariosfrom the application point of view
In particular the scenario selected in this paper forperformance analysis is a single quasi-frontal encounterbetween FLARE and the intruder The algorithm has beentested in standalone radar tracking configuration that is
estimates of obstacle relative position and velocity are basedon measurements from radar (update frequency of 1Hz) andthe own-ship navigation system
The number of particles has been set equal to 500 Thisnumber was selected since increasing it up to one orderof magnitude did not produced significant performanceincrease The algorithm is initialized taking into accountthe first radar sensor measurement the covariance matrix iscalculated on the basis of sensor measurements and then it isupdated with estimated values of software output
The algorithm outputs are based on obstacle position andvelocity in terms of range azimuth and elevation and DCPAin a stabilized north-east-down reference frame with originin FLARE center of mass The considered flight segment hasduration of about 20 s with an initial range of about 2000m
In Figure 5 obstacle range as estimated by radar radar-based tracker and GPS (reference) together with errorestimate with respect to GPS measurements is reportedAfter a firm track has been generated on the basis of radarmeasurements the tracker is able to characterize the obstacletrajectory The radar-only tracker provides a range estimatewith an accuracy of the order of few meters that derives fromthe good radar range accuracy and the absence of intrudermaneuvers In Figure 5 the upper plot illustrates the obstaclerange in a small interval time (of about 1 s) in order to showthe particles trajectories (colored lines)
Figures 6 and 7 report the obstacle angular dynamicsin terms of azimuth and elevation As expected the orderof magnitude of these errors is comparable to the radaraccuracy In particular the estimation uncertainty in termsof root mean square is of about 25∘ for azimuth and 13∘ forelevation Being computed in NED these RMS errors includeattitude measurement error biases In fact error biases in theestimation of magnetic heading are the main reason of thelarger error in azimuth It is worth noting that these biases
10 The Scientific World Journal
Table 1 PF performance in the selected scenario in terms of RMSerror
RMS Particle filter EKFRange (m) 84 37Range rate (m∘) 30 23Azimuth (∘) 25 17Azimuth rate (∘s) 02 04Elevation (∘) 13 21Elevation rate (∘s) 02 08
have a little effect on the estimation of angular rates and ofDistance at Closest Point of Approach
The range and angular rates as estimated by GPS (ref-erence) and particle filter tracker are reported in Figures 89 and 10 These variables are very important informationsources for collision detection assessment even though theyare not directly provided by the radar sensor The plots showthat the tracker estimates are very accurate with a very smallvalue in terms of standard deviation
Simulation results confirm how the resampling proce-dure is a key factor for tracking performance avoiding thedegeneracy phenomenon and thus enabling a great quantityof particles to survive to the prediction step
In order to better understand the particle filter trackingcapability PF and EKF estimation errors are reported inTable 1 in terms of root mean square (RMS) errors computedas
RMS = radic 1119873
119873
sum
119905=1
(119909119905minus 119909119905)2 (19)
where 119873 is the number of measurements 119909119905is the generic
PF tracker estimate (computed after resampling and repre-senting the mean value over all the particles) and 119909
119905is the
reference value computed on the basis of FLARE and intruderGPS measurements
The results show that PF tracker performance is com-parable to EKF in terms of order of magnitude Of coursethe introduction of electro-optical data can improve angularaccuracy since these sensors have a faster update rate thanradar In particular while the range rate error is very similarfor the two filters obstacle angular velocities provided byPF algorithm are slightly more accurate than EKF in theconsidered scenario These variables are very importantinformation sources for collision detection assessment eventhough they are not directly provided by the radar
In fact in near collision conditions angular rates are themost important variables influencing collision detection Asshown in [7] in these conditions DCPA uncertainty for givenrange and range rate shows a linear dependence on angularrate errors while range rate essentially impacts the time-to-go estimate
In the considered scenario DCPA as computed on thebasis of GPS measurement has been used as a reference forcomparing DCPA estimated by EKF tracker and PF trackerFigure 11 shows that the PF algorithm is more accuratethan EKF for the estimation of the DCPA in the initial
52494
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
PF tracker
Spherical PF
Spherical PFPF tracker
Elev
atio
nh ra
te in
NED
refe
renc
e fra
me (
∘ s)
08
04
0
minus04
minus01minus02minus03minus04minus05Er
ror i
n st
abili
zed
elev
atio
n ra
te (∘
s)
Figure 10 Elevation rate in NED reference frame as estimated byGPS and by radar-only tracker and estimation error as a function ofGPS time of day
450
400
350
300
250
200
150
100
50
Distance at Closest Point of Approach (DCPA) (m)
PF trackerEKF trackerGPS
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
Figure 11 Distance at Closest Point of Approach as estimated byGPS (reference) by radar and by radar-only tracker as function ofGPS time of the day
phase of firm tracking (at larger range) thus providing animprovement in collision risk assessment and a potentialreduction in the delay in declaring a collision threat Analysisof GPS data demonstrates that the considered encounterrepresents a real Near Mid-Air Collision (NMAC) scenariosince the reference DCPA keeps a very small value and liesbelow the bubble distance threshold almost in the whole firmtracking phase
The Scientific World Journal 11
6 Conclusion and Future Works
This paper focused on algorithm and test results fromobstacle tracking software based on particle filter and aimedat demonstrating UAS autonomous collision detection capa-bility in terms of reliable estimation of Distance at ClosestPoint of Approach The algorithm performance has beeninitially evaluated in radar-only configuration since the maininterest was addressed to the analysis of the potential impactof nonlinear filters on tracking capabilities with respect toassessed EKF first in a single sensor framework
The software has been tested in off-line simulations basedon real data recorded during a flight test campaign and aquasi-frontal encounter between the own aircraft and theintruder has been presented as test case The results pointedout that the developed algorithm is able to detect and trackthe obstacle trajectory with accuracy comparable to the EKFIn particular some advantages were highlighted in the directdetermination of Distance at Closest Point of Approach witha potential reduction of the delay for collision detectionThis result permits planning additional future investigationactivities such as
(i) performing the comparison on a larger experimentaldata set thus increasing the statistical significance
(ii) developing a multisensor-based analysis to confirmthe results obtained by the developed PF tracker whenadditional data sources are available such as electro-optical sensors indeed they can provide higheraccuracy in angular measurements and better datarate than radar sensors with a great impact on DCPAperformance
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The PhD grant of Miss Anna Elena Tirri is cofunded byEUROCONTROL through the research network HALA inthe framework of the WP-E of SESAR project
References
[1] EUROCONTROL in Proceedings of the EUROCONTROL Spec-ifications for the Use of Military Unmanned Aerial Vehicles asOperational Air Traffic Outside Segregated Airspace Version10 DocNo EUROCONTROL-SPEC-0102 Bruxelles BelgiumJuly 2007
[2] US Federal Aviation Administration (FAA) ldquoAirworthinesscertification of unmanned aircraft systemsrdquo Order 813034US Federal Aviation Administration (FAA) Washington DCUSA 2008
[3] US Federal Aviation Administration (FAA) ldquoInvestigate aNear Mid Air Collisionrdquo FAA Order 89001 vol 7 chapter 4Washington DC USA 2007
[4] G Fasano D Accardo A Moccia et al ldquoMulti-sensor-basedfully autonomous non-cooperative collision avoidance system
for unmanned air vehiclesrdquo Journal of Aerospace ComputingInformation and Communication vol 5 no 10 pp 338ndash3602008
[5] MTSI ldquoNon-cooperative detect see amp avoid (DSA) sensorstudyrdquo Tech Rep NASA ERAST 2002
[6] O Shakernia W Chen S Graham et al ldquoSense and Avoid(SAA) flight test and lessons learnedrdquo in Proceedings of the 2ndAIAA InfotechAerospace Conference and Exhibit (AIAA rsquo07)pp 2781ndash2795 Rohnert Park Calif USA May 2007
[7] D Accardo G Fasano L Forlenza A Moccia and A RispolildquoFlight test of a radar-based tracking system for UAS sense andavoidrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 49 no 2 pp 1139ndash1160 2013
[8] USFAA SpecialOperations FAAOrder 76104M January 2007[9] S J Julier and J K Uhlmann ldquoA new extension of the Kalman
filter to nonlinear systemsrdquo in Signal Processing Sensor Fusionand Target Recognition VI vol 3068 of Proceedings of SPIE pp182ndash193 Orlando Fla USA 1997
[10] N E Smith R G Cobb S J Pierce and V M Raska ldquoOptimalcollision avoidance trajectories for unmannedremotely pilotedaircraftrdquo in Proceedings of the AIAA Guidance Navigation andControl Conference (GNC 13) AIAA 2013-4619 Boston MassUSA August 2013
[11] L Lin Y Wang Y Liu C Xiong and K Zeng ldquoMarker-lessregistration based on template tracking for augmented realityrdquoMultimedia Tools and Applications vol 41 no 2 pp 235ndash2522009
[12] X Liu L Lin S Yan H Jin and W Jiang ldquoAdaptive objecttracking by learning hybrid template onlinerdquo IEEE Transactionson Circuits and Systems for Video Technology vol 21 no 11 pp1588ndash1599 2011
[13] L Lin Y Lu Y Pan and X Chen ldquoIntegrating graph partition-ing and matching for trajectory analysis in video surveillancerdquoIEEE Transactions on Image Processing vol 21 no 12 pp 4844ndash4857 2012
[14] L Xia P Li Y Guo and Z Shen ldquoResearch of maneuveringtarget tracking based on particle filterrdquo in Proceedings of the Chi-nese Automation Congress (CAC rsquo13) pp 567ndash570 ChangshaChina 2013
[15] F Gustafsson F Gunnarsson N Bergman et al ldquoParticle filtersfor positioning navigation and trackingrdquo IEEE Transactions onSignal Processing vol 50 no 2 pp 425ndash437 2002
[16] S Challa and G W Pulford ldquoJoint target tracking and classi-fication using radar and ESM sensorsrdquo IEEE Transactions onAerospace and Electronic Systems vol 37 no 3 pp 1039ndash10552001
[17] M S Grewal and A P Andrews Kalman Filtering Theory andPractice Using Matlab John Wiley amp Sons 2nd edition 2001
[18] S Haykin Kalman Filtering and Neural Networks John Wileyand Sons 2001
[19] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Transactions of the ASME Series D Journal of BasicEngineering vol 82 no 1 pp 35ndash45 1960
[20] S Arulampalam and B Ristic ldquoComparison of the particle filterwith range-parameterised and modified polar EKFs for angle-only trackingrdquo in Signal and Data Processing of Small Targetsvol 4048 of Proceedings of SPIE pp 288ndash299 Orlando FlaUSA April 2000
[21] X Lin T Kirubarajan Y Bar-Shalom and S Maskell ldquoCom-parison of EKF pseudomeasurement and particle filters fora bearing-only target tracking problemrdquo in Signal and Data
12 The Scientific World Journal
Processing of Small Targets vol 4728 of Proceedings of SPIE pp240ndash250 April 2002
[22] M S Arulampalam S Maskell N Gordon and T Clapp ldquoAtutorial on particle filters for online nonlinearnon-GaussianBayesian trackingrdquo IEEE Transactions on Signal Processing vol50 no 2 pp 174ndash188 2002
[23] A Doucet N de Freitas and N Gordon ldquoAn introduction tosequential Monte Carlo methodsrdquo in Sequential Monte CarloMethods in Practice Statistics for Engineering and InformationScience pp 3ndash14 Springer New York NY USA 2001
[24] B Liu andCHao ldquoSequential bearings-only-tracking initiationwith particle filteringmethodrdquoThe ScientificWorld Journal vol2013 Article ID 489121 7 pages 2013
[25] R Karlsson and F Gustafsson ldquoRecursive Bayesian estimationbearings-only applicationsrdquo IEE Proceedings Radar Sonar andNavigation vol 152 no 5 pp 305ndash313 2005
[26] N Gordon ldquoHybrid bootstrap filter for target tracking inclutterrdquo in Proceedings of the American Control Conference vol1 pp 628ndash632 June 1995
[27] S Mcginnity and G W Irwin ldquoMultiple model bootstrapfilter for maneuvering target trackingrdquo IEEE Transactions onAerospace and Electronic Systems vol 36 no 3 pp 1006ndash10122000
[28] M R Morelande and S Challa ldquoManoeuvring target trackingin clutter using particle filtersrdquo IEEE Transactions on Aerospaceand Electronic Systems vol 41 no 1 pp 252ndash270 2005
[29] D Lerro and Y Bar-Shalom ldquoTracking with de-biased consis-tent converted measurements versus EKFrdquo IEEE TransactionsonAerospace and Electronic Systems vol 29 no 3 pp 1015ndash10221993
[30] G Fasano L Forlenza D Accardo A Moccia and A RispolildquoIntegrated obstacle detection system based on radar andoptical sensorsrdquo inProceedings of the AIAA Infotech at Aerospace(AIAA rsquo10) Atlanta Ga USA April 2010
[31] S S Blackman and R F Popoli Design and Analysis of ModernTracking Systems Artech House Norwood Mass USA 1999
[32] G Fasano D Accardo A Moccia and A Rispoli ldquoAn inno-vative procedure for calibration of strapdown electro-opticalsensors onboard unmanned air vehiclesrdquo Sensors vol 10 no 1pp 639ndash654 2010
[33] B Ristic S Arulampalam and N Gordon Beyond the KalmanFilter Particle Filter for Tracking Applications Artech HouseNew York NY USA 2004
[34] A Haug and L Williams ldquoA spherical constant velocity modelfor target tracking in three dimensionsrdquo in IEEE AerospaceConference pp 1ndash15 Big Sky Mont USA March 2012
[35] X R Li and V P Jilkov ldquoA survey of maneuvering target track-ing dynamic modelsrdquo in Proceedings of the SPIE Conference onsignal and Data Processing of Small Targets vol 39 pp 1333ndash1364 Orlando Fla USA April 2000
[36] G Fasano A Moccia D Accardo and A Rispoli ldquoDevelop-ment and test of an integrated sensor system for autonomouscollision avoidancerdquo in Proceedings of the 26th Congress ofInternational Council of the Aeronautical Sciences (ICAS rsquo08) pp3625ndash3634 Anchorage Alaska USA September 2008
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
8 The Scientific World Journal
52494
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
Radar
RadarPF tracker
Spherical PF
Spherical PFEl
evat
ion
in N
EDre
fere
nce f
ram
e (∘ )
PF tracker
40
minus4minus8minus12
1505
minus05minus15minus25Er
ror i
n st
abili
zed
elev
atio
n (∘
)
Figure 7 Elevation in NED reference frame as estimated by GPS by radar and by radar-only tracker and estimation error as a function ofGPS time of day
52494
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
PF tracker
Spherical PF
Spherical PFPF tracker
minus72
minus76
minus80
minus84
Rang
e rat
e(m
s)
6
2
minus2
minus6Erro
r in
rang
era
te (m
s)
Figure 8 Range rate as estimated by GPS and by radar-only tracker and estimation error as a function of GPS time of day
where 119877119899is the measurement covariance matrix as stated
aboveThe developed obstacle detection and tracking software
provides also an estimate of the Distance at Closest Pointof Approach (see (1)) Since the particles are characterizedby own positions and velocities and given the nonlineardependencies between 119903119881 andDCPA the latter is calculatedfor each particle In this way in order to avoid furtherapproximations due to the evaluation of this distance from
position and velocitymean values DCPA has been calculatedas mean value of the different distances evaluated as
DCPA119899=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
119903 sdot 119881
1003817100381710038171003817100381711988110038171003817100381710038171003817
2119881 minus 119903
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(18)
This is a form of ldquodeep integrationrdquo of a collision detectionsensor since an estimate of the level of collision threat isdetermined by means of the same data fusion algorithm
The Scientific World Journal 9
52494
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
PF tracker
Spherical PF
Spherical PFPF tracker
0
minus1
minus2
minus3
050301
minus01minus03
Azi
mut
h ra
te in
NED
refe
renc
e fra
me (
∘ s)
Erro
r in
stab
ilize
daz
imut
h ra
te (∘
s)
Figure 9 Azimuth rate in NED reference frame as estimated by GPS and by radar-only tracker and estimation error as a function of GPStime of day
This is an additional advantage of using PF rather than EKFsince the need of linearized models in EKF does not allowestimating DCPA by the filter itself
5 Results
The developed obstacle tracking algorithm has been testedin off-line simulations based on flight data gathered duringan intensive test campaign Flight tests were carried out byexploiting the following configuration of test facilities
(a) FLARE aircraft piloted by a human pilot or by theautonomous flight control system
(b) a piloted intruder VLA aircraft in the same class ofFLARE equipped with GPS antennas and receiversand an onboard CPU for navigation data storage
(c) a ground control station (GCS) for real time flightcoordination and test monitoring [36]
(d) a full-duplex data link between FLARE and GCSused to send commands to initiate or terminate testsand to receive synthetic filter output and navigationmeasurements
(e) a downlink between intruder and GCS used for flightmonitoring
During the tests two types of maneuvers were executedsuch as chasing tests with FLARE pursuing the intruder andquasi-frontal encounters performed to estimate detectionand tracking performance in the most interesting scenariosfrom the application point of view
In particular the scenario selected in this paper forperformance analysis is a single quasi-frontal encounterbetween FLARE and the intruder The algorithm has beentested in standalone radar tracking configuration that is
estimates of obstacle relative position and velocity are basedon measurements from radar (update frequency of 1Hz) andthe own-ship navigation system
The number of particles has been set equal to 500 Thisnumber was selected since increasing it up to one orderof magnitude did not produced significant performanceincrease The algorithm is initialized taking into accountthe first radar sensor measurement the covariance matrix iscalculated on the basis of sensor measurements and then it isupdated with estimated values of software output
The algorithm outputs are based on obstacle position andvelocity in terms of range azimuth and elevation and DCPAin a stabilized north-east-down reference frame with originin FLARE center of mass The considered flight segment hasduration of about 20 s with an initial range of about 2000m
In Figure 5 obstacle range as estimated by radar radar-based tracker and GPS (reference) together with errorestimate with respect to GPS measurements is reportedAfter a firm track has been generated on the basis of radarmeasurements the tracker is able to characterize the obstacletrajectory The radar-only tracker provides a range estimatewith an accuracy of the order of few meters that derives fromthe good radar range accuracy and the absence of intrudermaneuvers In Figure 5 the upper plot illustrates the obstaclerange in a small interval time (of about 1 s) in order to showthe particles trajectories (colored lines)
Figures 6 and 7 report the obstacle angular dynamicsin terms of azimuth and elevation As expected the orderof magnitude of these errors is comparable to the radaraccuracy In particular the estimation uncertainty in termsof root mean square is of about 25∘ for azimuth and 13∘ forelevation Being computed in NED these RMS errors includeattitude measurement error biases In fact error biases in theestimation of magnetic heading are the main reason of thelarger error in azimuth It is worth noting that these biases
10 The Scientific World Journal
Table 1 PF performance in the selected scenario in terms of RMSerror
RMS Particle filter EKFRange (m) 84 37Range rate (m∘) 30 23Azimuth (∘) 25 17Azimuth rate (∘s) 02 04Elevation (∘) 13 21Elevation rate (∘s) 02 08
have a little effect on the estimation of angular rates and ofDistance at Closest Point of Approach
The range and angular rates as estimated by GPS (ref-erence) and particle filter tracker are reported in Figures 89 and 10 These variables are very important informationsources for collision detection assessment even though theyare not directly provided by the radar sensor The plots showthat the tracker estimates are very accurate with a very smallvalue in terms of standard deviation
Simulation results confirm how the resampling proce-dure is a key factor for tracking performance avoiding thedegeneracy phenomenon and thus enabling a great quantityof particles to survive to the prediction step
In order to better understand the particle filter trackingcapability PF and EKF estimation errors are reported inTable 1 in terms of root mean square (RMS) errors computedas
RMS = radic 1119873
119873
sum
119905=1
(119909119905minus 119909119905)2 (19)
where 119873 is the number of measurements 119909119905is the generic
PF tracker estimate (computed after resampling and repre-senting the mean value over all the particles) and 119909
119905is the
reference value computed on the basis of FLARE and intruderGPS measurements
The results show that PF tracker performance is com-parable to EKF in terms of order of magnitude Of coursethe introduction of electro-optical data can improve angularaccuracy since these sensors have a faster update rate thanradar In particular while the range rate error is very similarfor the two filters obstacle angular velocities provided byPF algorithm are slightly more accurate than EKF in theconsidered scenario These variables are very importantinformation sources for collision detection assessment eventhough they are not directly provided by the radar
In fact in near collision conditions angular rates are themost important variables influencing collision detection Asshown in [7] in these conditions DCPA uncertainty for givenrange and range rate shows a linear dependence on angularrate errors while range rate essentially impacts the time-to-go estimate
In the considered scenario DCPA as computed on thebasis of GPS measurement has been used as a reference forcomparing DCPA estimated by EKF tracker and PF trackerFigure 11 shows that the PF algorithm is more accuratethan EKF for the estimation of the DCPA in the initial
52494
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
PF tracker
Spherical PF
Spherical PFPF tracker
Elev
atio
nh ra
te in
NED
refe
renc
e fra
me (
∘ s)
08
04
0
minus04
minus01minus02minus03minus04minus05Er
ror i
n st
abili
zed
elev
atio
n ra
te (∘
s)
Figure 10 Elevation rate in NED reference frame as estimated byGPS and by radar-only tracker and estimation error as a function ofGPS time of day
450
400
350
300
250
200
150
100
50
Distance at Closest Point of Approach (DCPA) (m)
PF trackerEKF trackerGPS
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
Figure 11 Distance at Closest Point of Approach as estimated byGPS (reference) by radar and by radar-only tracker as function ofGPS time of the day
phase of firm tracking (at larger range) thus providing animprovement in collision risk assessment and a potentialreduction in the delay in declaring a collision threat Analysisof GPS data demonstrates that the considered encounterrepresents a real Near Mid-Air Collision (NMAC) scenariosince the reference DCPA keeps a very small value and liesbelow the bubble distance threshold almost in the whole firmtracking phase
The Scientific World Journal 11
6 Conclusion and Future Works
This paper focused on algorithm and test results fromobstacle tracking software based on particle filter and aimedat demonstrating UAS autonomous collision detection capa-bility in terms of reliable estimation of Distance at ClosestPoint of Approach The algorithm performance has beeninitially evaluated in radar-only configuration since the maininterest was addressed to the analysis of the potential impactof nonlinear filters on tracking capabilities with respect toassessed EKF first in a single sensor framework
The software has been tested in off-line simulations basedon real data recorded during a flight test campaign and aquasi-frontal encounter between the own aircraft and theintruder has been presented as test case The results pointedout that the developed algorithm is able to detect and trackthe obstacle trajectory with accuracy comparable to the EKFIn particular some advantages were highlighted in the directdetermination of Distance at Closest Point of Approach witha potential reduction of the delay for collision detectionThis result permits planning additional future investigationactivities such as
(i) performing the comparison on a larger experimentaldata set thus increasing the statistical significance
(ii) developing a multisensor-based analysis to confirmthe results obtained by the developed PF tracker whenadditional data sources are available such as electro-optical sensors indeed they can provide higheraccuracy in angular measurements and better datarate than radar sensors with a great impact on DCPAperformance
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The PhD grant of Miss Anna Elena Tirri is cofunded byEUROCONTROL through the research network HALA inthe framework of the WP-E of SESAR project
References
[1] EUROCONTROL in Proceedings of the EUROCONTROL Spec-ifications for the Use of Military Unmanned Aerial Vehicles asOperational Air Traffic Outside Segregated Airspace Version10 DocNo EUROCONTROL-SPEC-0102 Bruxelles BelgiumJuly 2007
[2] US Federal Aviation Administration (FAA) ldquoAirworthinesscertification of unmanned aircraft systemsrdquo Order 813034US Federal Aviation Administration (FAA) Washington DCUSA 2008
[3] US Federal Aviation Administration (FAA) ldquoInvestigate aNear Mid Air Collisionrdquo FAA Order 89001 vol 7 chapter 4Washington DC USA 2007
[4] G Fasano D Accardo A Moccia et al ldquoMulti-sensor-basedfully autonomous non-cooperative collision avoidance system
for unmanned air vehiclesrdquo Journal of Aerospace ComputingInformation and Communication vol 5 no 10 pp 338ndash3602008
[5] MTSI ldquoNon-cooperative detect see amp avoid (DSA) sensorstudyrdquo Tech Rep NASA ERAST 2002
[6] O Shakernia W Chen S Graham et al ldquoSense and Avoid(SAA) flight test and lessons learnedrdquo in Proceedings of the 2ndAIAA InfotechAerospace Conference and Exhibit (AIAA rsquo07)pp 2781ndash2795 Rohnert Park Calif USA May 2007
[7] D Accardo G Fasano L Forlenza A Moccia and A RispolildquoFlight test of a radar-based tracking system for UAS sense andavoidrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 49 no 2 pp 1139ndash1160 2013
[8] USFAA SpecialOperations FAAOrder 76104M January 2007[9] S J Julier and J K Uhlmann ldquoA new extension of the Kalman
filter to nonlinear systemsrdquo in Signal Processing Sensor Fusionand Target Recognition VI vol 3068 of Proceedings of SPIE pp182ndash193 Orlando Fla USA 1997
[10] N E Smith R G Cobb S J Pierce and V M Raska ldquoOptimalcollision avoidance trajectories for unmannedremotely pilotedaircraftrdquo in Proceedings of the AIAA Guidance Navigation andControl Conference (GNC 13) AIAA 2013-4619 Boston MassUSA August 2013
[11] L Lin Y Wang Y Liu C Xiong and K Zeng ldquoMarker-lessregistration based on template tracking for augmented realityrdquoMultimedia Tools and Applications vol 41 no 2 pp 235ndash2522009
[12] X Liu L Lin S Yan H Jin and W Jiang ldquoAdaptive objecttracking by learning hybrid template onlinerdquo IEEE Transactionson Circuits and Systems for Video Technology vol 21 no 11 pp1588ndash1599 2011
[13] L Lin Y Lu Y Pan and X Chen ldquoIntegrating graph partition-ing and matching for trajectory analysis in video surveillancerdquoIEEE Transactions on Image Processing vol 21 no 12 pp 4844ndash4857 2012
[14] L Xia P Li Y Guo and Z Shen ldquoResearch of maneuveringtarget tracking based on particle filterrdquo in Proceedings of the Chi-nese Automation Congress (CAC rsquo13) pp 567ndash570 ChangshaChina 2013
[15] F Gustafsson F Gunnarsson N Bergman et al ldquoParticle filtersfor positioning navigation and trackingrdquo IEEE Transactions onSignal Processing vol 50 no 2 pp 425ndash437 2002
[16] S Challa and G W Pulford ldquoJoint target tracking and classi-fication using radar and ESM sensorsrdquo IEEE Transactions onAerospace and Electronic Systems vol 37 no 3 pp 1039ndash10552001
[17] M S Grewal and A P Andrews Kalman Filtering Theory andPractice Using Matlab John Wiley amp Sons 2nd edition 2001
[18] S Haykin Kalman Filtering and Neural Networks John Wileyand Sons 2001
[19] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Transactions of the ASME Series D Journal of BasicEngineering vol 82 no 1 pp 35ndash45 1960
[20] S Arulampalam and B Ristic ldquoComparison of the particle filterwith range-parameterised and modified polar EKFs for angle-only trackingrdquo in Signal and Data Processing of Small Targetsvol 4048 of Proceedings of SPIE pp 288ndash299 Orlando FlaUSA April 2000
[21] X Lin T Kirubarajan Y Bar-Shalom and S Maskell ldquoCom-parison of EKF pseudomeasurement and particle filters fora bearing-only target tracking problemrdquo in Signal and Data
12 The Scientific World Journal
Processing of Small Targets vol 4728 of Proceedings of SPIE pp240ndash250 April 2002
[22] M S Arulampalam S Maskell N Gordon and T Clapp ldquoAtutorial on particle filters for online nonlinearnon-GaussianBayesian trackingrdquo IEEE Transactions on Signal Processing vol50 no 2 pp 174ndash188 2002
[23] A Doucet N de Freitas and N Gordon ldquoAn introduction tosequential Monte Carlo methodsrdquo in Sequential Monte CarloMethods in Practice Statistics for Engineering and InformationScience pp 3ndash14 Springer New York NY USA 2001
[24] B Liu andCHao ldquoSequential bearings-only-tracking initiationwith particle filteringmethodrdquoThe ScientificWorld Journal vol2013 Article ID 489121 7 pages 2013
[25] R Karlsson and F Gustafsson ldquoRecursive Bayesian estimationbearings-only applicationsrdquo IEE Proceedings Radar Sonar andNavigation vol 152 no 5 pp 305ndash313 2005
[26] N Gordon ldquoHybrid bootstrap filter for target tracking inclutterrdquo in Proceedings of the American Control Conference vol1 pp 628ndash632 June 1995
[27] S Mcginnity and G W Irwin ldquoMultiple model bootstrapfilter for maneuvering target trackingrdquo IEEE Transactions onAerospace and Electronic Systems vol 36 no 3 pp 1006ndash10122000
[28] M R Morelande and S Challa ldquoManoeuvring target trackingin clutter using particle filtersrdquo IEEE Transactions on Aerospaceand Electronic Systems vol 41 no 1 pp 252ndash270 2005
[29] D Lerro and Y Bar-Shalom ldquoTracking with de-biased consis-tent converted measurements versus EKFrdquo IEEE TransactionsonAerospace and Electronic Systems vol 29 no 3 pp 1015ndash10221993
[30] G Fasano L Forlenza D Accardo A Moccia and A RispolildquoIntegrated obstacle detection system based on radar andoptical sensorsrdquo inProceedings of the AIAA Infotech at Aerospace(AIAA rsquo10) Atlanta Ga USA April 2010
[31] S S Blackman and R F Popoli Design and Analysis of ModernTracking Systems Artech House Norwood Mass USA 1999
[32] G Fasano D Accardo A Moccia and A Rispoli ldquoAn inno-vative procedure for calibration of strapdown electro-opticalsensors onboard unmanned air vehiclesrdquo Sensors vol 10 no 1pp 639ndash654 2010
[33] B Ristic S Arulampalam and N Gordon Beyond the KalmanFilter Particle Filter for Tracking Applications Artech HouseNew York NY USA 2004
[34] A Haug and L Williams ldquoA spherical constant velocity modelfor target tracking in three dimensionsrdquo in IEEE AerospaceConference pp 1ndash15 Big Sky Mont USA March 2012
[35] X R Li and V P Jilkov ldquoA survey of maneuvering target track-ing dynamic modelsrdquo in Proceedings of the SPIE Conference onsignal and Data Processing of Small Targets vol 39 pp 1333ndash1364 Orlando Fla USA April 2000
[36] G Fasano A Moccia D Accardo and A Rispoli ldquoDevelop-ment and test of an integrated sensor system for autonomouscollision avoidancerdquo in Proceedings of the 26th Congress ofInternational Council of the Aeronautical Sciences (ICAS rsquo08) pp3625ndash3634 Anchorage Alaska USA September 2008
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
The Scientific World Journal 9
52494
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
PF tracker
Spherical PF
Spherical PFPF tracker
0
minus1
minus2
minus3
050301
minus01minus03
Azi
mut
h ra
te in
NED
refe
renc
e fra
me (
∘ s)
Erro
r in
stab
ilize
daz
imut
h ra
te (∘
s)
Figure 9 Azimuth rate in NED reference frame as estimated by GPS and by radar-only tracker and estimation error as a function of GPStime of day
This is an additional advantage of using PF rather than EKFsince the need of linearized models in EKF does not allowestimating DCPA by the filter itself
5 Results
The developed obstacle tracking algorithm has been testedin off-line simulations based on flight data gathered duringan intensive test campaign Flight tests were carried out byexploiting the following configuration of test facilities
(a) FLARE aircraft piloted by a human pilot or by theautonomous flight control system
(b) a piloted intruder VLA aircraft in the same class ofFLARE equipped with GPS antennas and receiversand an onboard CPU for navigation data storage
(c) a ground control station (GCS) for real time flightcoordination and test monitoring [36]
(d) a full-duplex data link between FLARE and GCSused to send commands to initiate or terminate testsand to receive synthetic filter output and navigationmeasurements
(e) a downlink between intruder and GCS used for flightmonitoring
During the tests two types of maneuvers were executedsuch as chasing tests with FLARE pursuing the intruder andquasi-frontal encounters performed to estimate detectionand tracking performance in the most interesting scenariosfrom the application point of view
In particular the scenario selected in this paper forperformance analysis is a single quasi-frontal encounterbetween FLARE and the intruder The algorithm has beentested in standalone radar tracking configuration that is
estimates of obstacle relative position and velocity are basedon measurements from radar (update frequency of 1Hz) andthe own-ship navigation system
The number of particles has been set equal to 500 Thisnumber was selected since increasing it up to one orderof magnitude did not produced significant performanceincrease The algorithm is initialized taking into accountthe first radar sensor measurement the covariance matrix iscalculated on the basis of sensor measurements and then it isupdated with estimated values of software output
The algorithm outputs are based on obstacle position andvelocity in terms of range azimuth and elevation and DCPAin a stabilized north-east-down reference frame with originin FLARE center of mass The considered flight segment hasduration of about 20 s with an initial range of about 2000m
In Figure 5 obstacle range as estimated by radar radar-based tracker and GPS (reference) together with errorestimate with respect to GPS measurements is reportedAfter a firm track has been generated on the basis of radarmeasurements the tracker is able to characterize the obstacletrajectory The radar-only tracker provides a range estimatewith an accuracy of the order of few meters that derives fromthe good radar range accuracy and the absence of intrudermaneuvers In Figure 5 the upper plot illustrates the obstaclerange in a small interval time (of about 1 s) in order to showthe particles trajectories (colored lines)
Figures 6 and 7 report the obstacle angular dynamicsin terms of azimuth and elevation As expected the orderof magnitude of these errors is comparable to the radaraccuracy In particular the estimation uncertainty in termsof root mean square is of about 25∘ for azimuth and 13∘ forelevation Being computed in NED these RMS errors includeattitude measurement error biases In fact error biases in theestimation of magnetic heading are the main reason of thelarger error in azimuth It is worth noting that these biases
10 The Scientific World Journal
Table 1 PF performance in the selected scenario in terms of RMSerror
RMS Particle filter EKFRange (m) 84 37Range rate (m∘) 30 23Azimuth (∘) 25 17Azimuth rate (∘s) 02 04Elevation (∘) 13 21Elevation rate (∘s) 02 08
have a little effect on the estimation of angular rates and ofDistance at Closest Point of Approach
The range and angular rates as estimated by GPS (ref-erence) and particle filter tracker are reported in Figures 89 and 10 These variables are very important informationsources for collision detection assessment even though theyare not directly provided by the radar sensor The plots showthat the tracker estimates are very accurate with a very smallvalue in terms of standard deviation
Simulation results confirm how the resampling proce-dure is a key factor for tracking performance avoiding thedegeneracy phenomenon and thus enabling a great quantityof particles to survive to the prediction step
In order to better understand the particle filter trackingcapability PF and EKF estimation errors are reported inTable 1 in terms of root mean square (RMS) errors computedas
RMS = radic 1119873
119873
sum
119905=1
(119909119905minus 119909119905)2 (19)
where 119873 is the number of measurements 119909119905is the generic
PF tracker estimate (computed after resampling and repre-senting the mean value over all the particles) and 119909
119905is the
reference value computed on the basis of FLARE and intruderGPS measurements
The results show that PF tracker performance is com-parable to EKF in terms of order of magnitude Of coursethe introduction of electro-optical data can improve angularaccuracy since these sensors have a faster update rate thanradar In particular while the range rate error is very similarfor the two filters obstacle angular velocities provided byPF algorithm are slightly more accurate than EKF in theconsidered scenario These variables are very importantinformation sources for collision detection assessment eventhough they are not directly provided by the radar
In fact in near collision conditions angular rates are themost important variables influencing collision detection Asshown in [7] in these conditions DCPA uncertainty for givenrange and range rate shows a linear dependence on angularrate errors while range rate essentially impacts the time-to-go estimate
In the considered scenario DCPA as computed on thebasis of GPS measurement has been used as a reference forcomparing DCPA estimated by EKF tracker and PF trackerFigure 11 shows that the PF algorithm is more accuratethan EKF for the estimation of the DCPA in the initial
52494
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
PF tracker
Spherical PF
Spherical PFPF tracker
Elev
atio
nh ra
te in
NED
refe
renc
e fra
me (
∘ s)
08
04
0
minus04
minus01minus02minus03minus04minus05Er
ror i
n st
abili
zed
elev
atio
n ra
te (∘
s)
Figure 10 Elevation rate in NED reference frame as estimated byGPS and by radar-only tracker and estimation error as a function ofGPS time of day
450
400
350
300
250
200
150
100
50
Distance at Closest Point of Approach (DCPA) (m)
PF trackerEKF trackerGPS
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
Figure 11 Distance at Closest Point of Approach as estimated byGPS (reference) by radar and by radar-only tracker as function ofGPS time of the day
phase of firm tracking (at larger range) thus providing animprovement in collision risk assessment and a potentialreduction in the delay in declaring a collision threat Analysisof GPS data demonstrates that the considered encounterrepresents a real Near Mid-Air Collision (NMAC) scenariosince the reference DCPA keeps a very small value and liesbelow the bubble distance threshold almost in the whole firmtracking phase
The Scientific World Journal 11
6 Conclusion and Future Works
This paper focused on algorithm and test results fromobstacle tracking software based on particle filter and aimedat demonstrating UAS autonomous collision detection capa-bility in terms of reliable estimation of Distance at ClosestPoint of Approach The algorithm performance has beeninitially evaluated in radar-only configuration since the maininterest was addressed to the analysis of the potential impactof nonlinear filters on tracking capabilities with respect toassessed EKF first in a single sensor framework
The software has been tested in off-line simulations basedon real data recorded during a flight test campaign and aquasi-frontal encounter between the own aircraft and theintruder has been presented as test case The results pointedout that the developed algorithm is able to detect and trackthe obstacle trajectory with accuracy comparable to the EKFIn particular some advantages were highlighted in the directdetermination of Distance at Closest Point of Approach witha potential reduction of the delay for collision detectionThis result permits planning additional future investigationactivities such as
(i) performing the comparison on a larger experimentaldata set thus increasing the statistical significance
(ii) developing a multisensor-based analysis to confirmthe results obtained by the developed PF tracker whenadditional data sources are available such as electro-optical sensors indeed they can provide higheraccuracy in angular measurements and better datarate than radar sensors with a great impact on DCPAperformance
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The PhD grant of Miss Anna Elena Tirri is cofunded byEUROCONTROL through the research network HALA inthe framework of the WP-E of SESAR project
References
[1] EUROCONTROL in Proceedings of the EUROCONTROL Spec-ifications for the Use of Military Unmanned Aerial Vehicles asOperational Air Traffic Outside Segregated Airspace Version10 DocNo EUROCONTROL-SPEC-0102 Bruxelles BelgiumJuly 2007
[2] US Federal Aviation Administration (FAA) ldquoAirworthinesscertification of unmanned aircraft systemsrdquo Order 813034US Federal Aviation Administration (FAA) Washington DCUSA 2008
[3] US Federal Aviation Administration (FAA) ldquoInvestigate aNear Mid Air Collisionrdquo FAA Order 89001 vol 7 chapter 4Washington DC USA 2007
[4] G Fasano D Accardo A Moccia et al ldquoMulti-sensor-basedfully autonomous non-cooperative collision avoidance system
for unmanned air vehiclesrdquo Journal of Aerospace ComputingInformation and Communication vol 5 no 10 pp 338ndash3602008
[5] MTSI ldquoNon-cooperative detect see amp avoid (DSA) sensorstudyrdquo Tech Rep NASA ERAST 2002
[6] O Shakernia W Chen S Graham et al ldquoSense and Avoid(SAA) flight test and lessons learnedrdquo in Proceedings of the 2ndAIAA InfotechAerospace Conference and Exhibit (AIAA rsquo07)pp 2781ndash2795 Rohnert Park Calif USA May 2007
[7] D Accardo G Fasano L Forlenza A Moccia and A RispolildquoFlight test of a radar-based tracking system for UAS sense andavoidrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 49 no 2 pp 1139ndash1160 2013
[8] USFAA SpecialOperations FAAOrder 76104M January 2007[9] S J Julier and J K Uhlmann ldquoA new extension of the Kalman
filter to nonlinear systemsrdquo in Signal Processing Sensor Fusionand Target Recognition VI vol 3068 of Proceedings of SPIE pp182ndash193 Orlando Fla USA 1997
[10] N E Smith R G Cobb S J Pierce and V M Raska ldquoOptimalcollision avoidance trajectories for unmannedremotely pilotedaircraftrdquo in Proceedings of the AIAA Guidance Navigation andControl Conference (GNC 13) AIAA 2013-4619 Boston MassUSA August 2013
[11] L Lin Y Wang Y Liu C Xiong and K Zeng ldquoMarker-lessregistration based on template tracking for augmented realityrdquoMultimedia Tools and Applications vol 41 no 2 pp 235ndash2522009
[12] X Liu L Lin S Yan H Jin and W Jiang ldquoAdaptive objecttracking by learning hybrid template onlinerdquo IEEE Transactionson Circuits and Systems for Video Technology vol 21 no 11 pp1588ndash1599 2011
[13] L Lin Y Lu Y Pan and X Chen ldquoIntegrating graph partition-ing and matching for trajectory analysis in video surveillancerdquoIEEE Transactions on Image Processing vol 21 no 12 pp 4844ndash4857 2012
[14] L Xia P Li Y Guo and Z Shen ldquoResearch of maneuveringtarget tracking based on particle filterrdquo in Proceedings of the Chi-nese Automation Congress (CAC rsquo13) pp 567ndash570 ChangshaChina 2013
[15] F Gustafsson F Gunnarsson N Bergman et al ldquoParticle filtersfor positioning navigation and trackingrdquo IEEE Transactions onSignal Processing vol 50 no 2 pp 425ndash437 2002
[16] S Challa and G W Pulford ldquoJoint target tracking and classi-fication using radar and ESM sensorsrdquo IEEE Transactions onAerospace and Electronic Systems vol 37 no 3 pp 1039ndash10552001
[17] M S Grewal and A P Andrews Kalman Filtering Theory andPractice Using Matlab John Wiley amp Sons 2nd edition 2001
[18] S Haykin Kalman Filtering and Neural Networks John Wileyand Sons 2001
[19] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Transactions of the ASME Series D Journal of BasicEngineering vol 82 no 1 pp 35ndash45 1960
[20] S Arulampalam and B Ristic ldquoComparison of the particle filterwith range-parameterised and modified polar EKFs for angle-only trackingrdquo in Signal and Data Processing of Small Targetsvol 4048 of Proceedings of SPIE pp 288ndash299 Orlando FlaUSA April 2000
[21] X Lin T Kirubarajan Y Bar-Shalom and S Maskell ldquoCom-parison of EKF pseudomeasurement and particle filters fora bearing-only target tracking problemrdquo in Signal and Data
12 The Scientific World Journal
Processing of Small Targets vol 4728 of Proceedings of SPIE pp240ndash250 April 2002
[22] M S Arulampalam S Maskell N Gordon and T Clapp ldquoAtutorial on particle filters for online nonlinearnon-GaussianBayesian trackingrdquo IEEE Transactions on Signal Processing vol50 no 2 pp 174ndash188 2002
[23] A Doucet N de Freitas and N Gordon ldquoAn introduction tosequential Monte Carlo methodsrdquo in Sequential Monte CarloMethods in Practice Statistics for Engineering and InformationScience pp 3ndash14 Springer New York NY USA 2001
[24] B Liu andCHao ldquoSequential bearings-only-tracking initiationwith particle filteringmethodrdquoThe ScientificWorld Journal vol2013 Article ID 489121 7 pages 2013
[25] R Karlsson and F Gustafsson ldquoRecursive Bayesian estimationbearings-only applicationsrdquo IEE Proceedings Radar Sonar andNavigation vol 152 no 5 pp 305ndash313 2005
[26] N Gordon ldquoHybrid bootstrap filter for target tracking inclutterrdquo in Proceedings of the American Control Conference vol1 pp 628ndash632 June 1995
[27] S Mcginnity and G W Irwin ldquoMultiple model bootstrapfilter for maneuvering target trackingrdquo IEEE Transactions onAerospace and Electronic Systems vol 36 no 3 pp 1006ndash10122000
[28] M R Morelande and S Challa ldquoManoeuvring target trackingin clutter using particle filtersrdquo IEEE Transactions on Aerospaceand Electronic Systems vol 41 no 1 pp 252ndash270 2005
[29] D Lerro and Y Bar-Shalom ldquoTracking with de-biased consis-tent converted measurements versus EKFrdquo IEEE TransactionsonAerospace and Electronic Systems vol 29 no 3 pp 1015ndash10221993
[30] G Fasano L Forlenza D Accardo A Moccia and A RispolildquoIntegrated obstacle detection system based on radar andoptical sensorsrdquo inProceedings of the AIAA Infotech at Aerospace(AIAA rsquo10) Atlanta Ga USA April 2010
[31] S S Blackman and R F Popoli Design and Analysis of ModernTracking Systems Artech House Norwood Mass USA 1999
[32] G Fasano D Accardo A Moccia and A Rispoli ldquoAn inno-vative procedure for calibration of strapdown electro-opticalsensors onboard unmanned air vehiclesrdquo Sensors vol 10 no 1pp 639ndash654 2010
[33] B Ristic S Arulampalam and N Gordon Beyond the KalmanFilter Particle Filter for Tracking Applications Artech HouseNew York NY USA 2004
[34] A Haug and L Williams ldquoA spherical constant velocity modelfor target tracking in three dimensionsrdquo in IEEE AerospaceConference pp 1ndash15 Big Sky Mont USA March 2012
[35] X R Li and V P Jilkov ldquoA survey of maneuvering target track-ing dynamic modelsrdquo in Proceedings of the SPIE Conference onsignal and Data Processing of Small Targets vol 39 pp 1333ndash1364 Orlando Fla USA April 2000
[36] G Fasano A Moccia D Accardo and A Rispoli ldquoDevelop-ment and test of an integrated sensor system for autonomouscollision avoidancerdquo in Proceedings of the 26th Congress ofInternational Council of the Aeronautical Sciences (ICAS rsquo08) pp3625ndash3634 Anchorage Alaska USA September 2008
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
10 The Scientific World Journal
Table 1 PF performance in the selected scenario in terms of RMSerror
RMS Particle filter EKFRange (m) 84 37Range rate (m∘) 30 23Azimuth (∘) 25 17Azimuth rate (∘s) 02 04Elevation (∘) 13 21Elevation rate (∘s) 02 08
have a little effect on the estimation of angular rates and ofDistance at Closest Point of Approach
The range and angular rates as estimated by GPS (ref-erence) and particle filter tracker are reported in Figures 89 and 10 These variables are very important informationsources for collision detection assessment even though theyare not directly provided by the radar sensor The plots showthat the tracker estimates are very accurate with a very smallvalue in terms of standard deviation
Simulation results confirm how the resampling proce-dure is a key factor for tracking performance avoiding thedegeneracy phenomenon and thus enabling a great quantityof particles to survive to the prediction step
In order to better understand the particle filter trackingcapability PF and EKF estimation errors are reported inTable 1 in terms of root mean square (RMS) errors computedas
RMS = radic 1119873
119873
sum
119905=1
(119909119905minus 119909119905)2 (19)
where 119873 is the number of measurements 119909119905is the generic
PF tracker estimate (computed after resampling and repre-senting the mean value over all the particles) and 119909
119905is the
reference value computed on the basis of FLARE and intruderGPS measurements
The results show that PF tracker performance is com-parable to EKF in terms of order of magnitude Of coursethe introduction of electro-optical data can improve angularaccuracy since these sensors have a faster update rate thanradar In particular while the range rate error is very similarfor the two filters obstacle angular velocities provided byPF algorithm are slightly more accurate than EKF in theconsidered scenario These variables are very importantinformation sources for collision detection assessment eventhough they are not directly provided by the radar
In fact in near collision conditions angular rates are themost important variables influencing collision detection Asshown in [7] in these conditions DCPA uncertainty for givenrange and range rate shows a linear dependence on angularrate errors while range rate essentially impacts the time-to-go estimate
In the considered scenario DCPA as computed on thebasis of GPS measurement has been used as a reference forcomparing DCPA estimated by EKF tracker and PF trackerFigure 11 shows that the PF algorithm is more accuratethan EKF for the estimation of the DCPA in the initial
52494
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
GPS
PF tracker
Spherical PF
Spherical PFPF tracker
Elev
atio
nh ra
te in
NED
refe
renc
e fra
me (
∘ s)
08
04
0
minus04
minus01minus02minus03minus04minus05Er
ror i
n st
abili
zed
elev
atio
n ra
te (∘
s)
Figure 10 Elevation rate in NED reference frame as estimated byGPS and by radar-only tracker and estimation error as a function ofGPS time of day
450
400
350
300
250
200
150
100
50
Distance at Closest Point of Approach (DCPA) (m)
PF trackerEKF trackerGPS
52494
52496
52498
525
52502
52504
52506
52508
5251
52512
52514
times104GPS time of day (s)
Figure 11 Distance at Closest Point of Approach as estimated byGPS (reference) by radar and by radar-only tracker as function ofGPS time of the day
phase of firm tracking (at larger range) thus providing animprovement in collision risk assessment and a potentialreduction in the delay in declaring a collision threat Analysisof GPS data demonstrates that the considered encounterrepresents a real Near Mid-Air Collision (NMAC) scenariosince the reference DCPA keeps a very small value and liesbelow the bubble distance threshold almost in the whole firmtracking phase
The Scientific World Journal 11
6 Conclusion and Future Works
This paper focused on algorithm and test results fromobstacle tracking software based on particle filter and aimedat demonstrating UAS autonomous collision detection capa-bility in terms of reliable estimation of Distance at ClosestPoint of Approach The algorithm performance has beeninitially evaluated in radar-only configuration since the maininterest was addressed to the analysis of the potential impactof nonlinear filters on tracking capabilities with respect toassessed EKF first in a single sensor framework
The software has been tested in off-line simulations basedon real data recorded during a flight test campaign and aquasi-frontal encounter between the own aircraft and theintruder has been presented as test case The results pointedout that the developed algorithm is able to detect and trackthe obstacle trajectory with accuracy comparable to the EKFIn particular some advantages were highlighted in the directdetermination of Distance at Closest Point of Approach witha potential reduction of the delay for collision detectionThis result permits planning additional future investigationactivities such as
(i) performing the comparison on a larger experimentaldata set thus increasing the statistical significance
(ii) developing a multisensor-based analysis to confirmthe results obtained by the developed PF tracker whenadditional data sources are available such as electro-optical sensors indeed they can provide higheraccuracy in angular measurements and better datarate than radar sensors with a great impact on DCPAperformance
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The PhD grant of Miss Anna Elena Tirri is cofunded byEUROCONTROL through the research network HALA inthe framework of the WP-E of SESAR project
References
[1] EUROCONTROL in Proceedings of the EUROCONTROL Spec-ifications for the Use of Military Unmanned Aerial Vehicles asOperational Air Traffic Outside Segregated Airspace Version10 DocNo EUROCONTROL-SPEC-0102 Bruxelles BelgiumJuly 2007
[2] US Federal Aviation Administration (FAA) ldquoAirworthinesscertification of unmanned aircraft systemsrdquo Order 813034US Federal Aviation Administration (FAA) Washington DCUSA 2008
[3] US Federal Aviation Administration (FAA) ldquoInvestigate aNear Mid Air Collisionrdquo FAA Order 89001 vol 7 chapter 4Washington DC USA 2007
[4] G Fasano D Accardo A Moccia et al ldquoMulti-sensor-basedfully autonomous non-cooperative collision avoidance system
for unmanned air vehiclesrdquo Journal of Aerospace ComputingInformation and Communication vol 5 no 10 pp 338ndash3602008
[5] MTSI ldquoNon-cooperative detect see amp avoid (DSA) sensorstudyrdquo Tech Rep NASA ERAST 2002
[6] O Shakernia W Chen S Graham et al ldquoSense and Avoid(SAA) flight test and lessons learnedrdquo in Proceedings of the 2ndAIAA InfotechAerospace Conference and Exhibit (AIAA rsquo07)pp 2781ndash2795 Rohnert Park Calif USA May 2007
[7] D Accardo G Fasano L Forlenza A Moccia and A RispolildquoFlight test of a radar-based tracking system for UAS sense andavoidrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 49 no 2 pp 1139ndash1160 2013
[8] USFAA SpecialOperations FAAOrder 76104M January 2007[9] S J Julier and J K Uhlmann ldquoA new extension of the Kalman
filter to nonlinear systemsrdquo in Signal Processing Sensor Fusionand Target Recognition VI vol 3068 of Proceedings of SPIE pp182ndash193 Orlando Fla USA 1997
[10] N E Smith R G Cobb S J Pierce and V M Raska ldquoOptimalcollision avoidance trajectories for unmannedremotely pilotedaircraftrdquo in Proceedings of the AIAA Guidance Navigation andControl Conference (GNC 13) AIAA 2013-4619 Boston MassUSA August 2013
[11] L Lin Y Wang Y Liu C Xiong and K Zeng ldquoMarker-lessregistration based on template tracking for augmented realityrdquoMultimedia Tools and Applications vol 41 no 2 pp 235ndash2522009
[12] X Liu L Lin S Yan H Jin and W Jiang ldquoAdaptive objecttracking by learning hybrid template onlinerdquo IEEE Transactionson Circuits and Systems for Video Technology vol 21 no 11 pp1588ndash1599 2011
[13] L Lin Y Lu Y Pan and X Chen ldquoIntegrating graph partition-ing and matching for trajectory analysis in video surveillancerdquoIEEE Transactions on Image Processing vol 21 no 12 pp 4844ndash4857 2012
[14] L Xia P Li Y Guo and Z Shen ldquoResearch of maneuveringtarget tracking based on particle filterrdquo in Proceedings of the Chi-nese Automation Congress (CAC rsquo13) pp 567ndash570 ChangshaChina 2013
[15] F Gustafsson F Gunnarsson N Bergman et al ldquoParticle filtersfor positioning navigation and trackingrdquo IEEE Transactions onSignal Processing vol 50 no 2 pp 425ndash437 2002
[16] S Challa and G W Pulford ldquoJoint target tracking and classi-fication using radar and ESM sensorsrdquo IEEE Transactions onAerospace and Electronic Systems vol 37 no 3 pp 1039ndash10552001
[17] M S Grewal and A P Andrews Kalman Filtering Theory andPractice Using Matlab John Wiley amp Sons 2nd edition 2001
[18] S Haykin Kalman Filtering and Neural Networks John Wileyand Sons 2001
[19] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Transactions of the ASME Series D Journal of BasicEngineering vol 82 no 1 pp 35ndash45 1960
[20] S Arulampalam and B Ristic ldquoComparison of the particle filterwith range-parameterised and modified polar EKFs for angle-only trackingrdquo in Signal and Data Processing of Small Targetsvol 4048 of Proceedings of SPIE pp 288ndash299 Orlando FlaUSA April 2000
[21] X Lin T Kirubarajan Y Bar-Shalom and S Maskell ldquoCom-parison of EKF pseudomeasurement and particle filters fora bearing-only target tracking problemrdquo in Signal and Data
12 The Scientific World Journal
Processing of Small Targets vol 4728 of Proceedings of SPIE pp240ndash250 April 2002
[22] M S Arulampalam S Maskell N Gordon and T Clapp ldquoAtutorial on particle filters for online nonlinearnon-GaussianBayesian trackingrdquo IEEE Transactions on Signal Processing vol50 no 2 pp 174ndash188 2002
[23] A Doucet N de Freitas and N Gordon ldquoAn introduction tosequential Monte Carlo methodsrdquo in Sequential Monte CarloMethods in Practice Statistics for Engineering and InformationScience pp 3ndash14 Springer New York NY USA 2001
[24] B Liu andCHao ldquoSequential bearings-only-tracking initiationwith particle filteringmethodrdquoThe ScientificWorld Journal vol2013 Article ID 489121 7 pages 2013
[25] R Karlsson and F Gustafsson ldquoRecursive Bayesian estimationbearings-only applicationsrdquo IEE Proceedings Radar Sonar andNavigation vol 152 no 5 pp 305ndash313 2005
[26] N Gordon ldquoHybrid bootstrap filter for target tracking inclutterrdquo in Proceedings of the American Control Conference vol1 pp 628ndash632 June 1995
[27] S Mcginnity and G W Irwin ldquoMultiple model bootstrapfilter for maneuvering target trackingrdquo IEEE Transactions onAerospace and Electronic Systems vol 36 no 3 pp 1006ndash10122000
[28] M R Morelande and S Challa ldquoManoeuvring target trackingin clutter using particle filtersrdquo IEEE Transactions on Aerospaceand Electronic Systems vol 41 no 1 pp 252ndash270 2005
[29] D Lerro and Y Bar-Shalom ldquoTracking with de-biased consis-tent converted measurements versus EKFrdquo IEEE TransactionsonAerospace and Electronic Systems vol 29 no 3 pp 1015ndash10221993
[30] G Fasano L Forlenza D Accardo A Moccia and A RispolildquoIntegrated obstacle detection system based on radar andoptical sensorsrdquo inProceedings of the AIAA Infotech at Aerospace(AIAA rsquo10) Atlanta Ga USA April 2010
[31] S S Blackman and R F Popoli Design and Analysis of ModernTracking Systems Artech House Norwood Mass USA 1999
[32] G Fasano D Accardo A Moccia and A Rispoli ldquoAn inno-vative procedure for calibration of strapdown electro-opticalsensors onboard unmanned air vehiclesrdquo Sensors vol 10 no 1pp 639ndash654 2010
[33] B Ristic S Arulampalam and N Gordon Beyond the KalmanFilter Particle Filter for Tracking Applications Artech HouseNew York NY USA 2004
[34] A Haug and L Williams ldquoA spherical constant velocity modelfor target tracking in three dimensionsrdquo in IEEE AerospaceConference pp 1ndash15 Big Sky Mont USA March 2012
[35] X R Li and V P Jilkov ldquoA survey of maneuvering target track-ing dynamic modelsrdquo in Proceedings of the SPIE Conference onsignal and Data Processing of Small Targets vol 39 pp 1333ndash1364 Orlando Fla USA April 2000
[36] G Fasano A Moccia D Accardo and A Rispoli ldquoDevelop-ment and test of an integrated sensor system for autonomouscollision avoidancerdquo in Proceedings of the 26th Congress ofInternational Council of the Aeronautical Sciences (ICAS rsquo08) pp3625ndash3634 Anchorage Alaska USA September 2008
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
The Scientific World Journal 11
6 Conclusion and Future Works
This paper focused on algorithm and test results fromobstacle tracking software based on particle filter and aimedat demonstrating UAS autonomous collision detection capa-bility in terms of reliable estimation of Distance at ClosestPoint of Approach The algorithm performance has beeninitially evaluated in radar-only configuration since the maininterest was addressed to the analysis of the potential impactof nonlinear filters on tracking capabilities with respect toassessed EKF first in a single sensor framework
The software has been tested in off-line simulations basedon real data recorded during a flight test campaign and aquasi-frontal encounter between the own aircraft and theintruder has been presented as test case The results pointedout that the developed algorithm is able to detect and trackthe obstacle trajectory with accuracy comparable to the EKFIn particular some advantages were highlighted in the directdetermination of Distance at Closest Point of Approach witha potential reduction of the delay for collision detectionThis result permits planning additional future investigationactivities such as
(i) performing the comparison on a larger experimentaldata set thus increasing the statistical significance
(ii) developing a multisensor-based analysis to confirmthe results obtained by the developed PF tracker whenadditional data sources are available such as electro-optical sensors indeed they can provide higheraccuracy in angular measurements and better datarate than radar sensors with a great impact on DCPAperformance
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The PhD grant of Miss Anna Elena Tirri is cofunded byEUROCONTROL through the research network HALA inthe framework of the WP-E of SESAR project
References
[1] EUROCONTROL in Proceedings of the EUROCONTROL Spec-ifications for the Use of Military Unmanned Aerial Vehicles asOperational Air Traffic Outside Segregated Airspace Version10 DocNo EUROCONTROL-SPEC-0102 Bruxelles BelgiumJuly 2007
[2] US Federal Aviation Administration (FAA) ldquoAirworthinesscertification of unmanned aircraft systemsrdquo Order 813034US Federal Aviation Administration (FAA) Washington DCUSA 2008
[3] US Federal Aviation Administration (FAA) ldquoInvestigate aNear Mid Air Collisionrdquo FAA Order 89001 vol 7 chapter 4Washington DC USA 2007
[4] G Fasano D Accardo A Moccia et al ldquoMulti-sensor-basedfully autonomous non-cooperative collision avoidance system
for unmanned air vehiclesrdquo Journal of Aerospace ComputingInformation and Communication vol 5 no 10 pp 338ndash3602008
[5] MTSI ldquoNon-cooperative detect see amp avoid (DSA) sensorstudyrdquo Tech Rep NASA ERAST 2002
[6] O Shakernia W Chen S Graham et al ldquoSense and Avoid(SAA) flight test and lessons learnedrdquo in Proceedings of the 2ndAIAA InfotechAerospace Conference and Exhibit (AIAA rsquo07)pp 2781ndash2795 Rohnert Park Calif USA May 2007
[7] D Accardo G Fasano L Forlenza A Moccia and A RispolildquoFlight test of a radar-based tracking system for UAS sense andavoidrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 49 no 2 pp 1139ndash1160 2013
[8] USFAA SpecialOperations FAAOrder 76104M January 2007[9] S J Julier and J K Uhlmann ldquoA new extension of the Kalman
filter to nonlinear systemsrdquo in Signal Processing Sensor Fusionand Target Recognition VI vol 3068 of Proceedings of SPIE pp182ndash193 Orlando Fla USA 1997
[10] N E Smith R G Cobb S J Pierce and V M Raska ldquoOptimalcollision avoidance trajectories for unmannedremotely pilotedaircraftrdquo in Proceedings of the AIAA Guidance Navigation andControl Conference (GNC 13) AIAA 2013-4619 Boston MassUSA August 2013
[11] L Lin Y Wang Y Liu C Xiong and K Zeng ldquoMarker-lessregistration based on template tracking for augmented realityrdquoMultimedia Tools and Applications vol 41 no 2 pp 235ndash2522009
[12] X Liu L Lin S Yan H Jin and W Jiang ldquoAdaptive objecttracking by learning hybrid template onlinerdquo IEEE Transactionson Circuits and Systems for Video Technology vol 21 no 11 pp1588ndash1599 2011
[13] L Lin Y Lu Y Pan and X Chen ldquoIntegrating graph partition-ing and matching for trajectory analysis in video surveillancerdquoIEEE Transactions on Image Processing vol 21 no 12 pp 4844ndash4857 2012
[14] L Xia P Li Y Guo and Z Shen ldquoResearch of maneuveringtarget tracking based on particle filterrdquo in Proceedings of the Chi-nese Automation Congress (CAC rsquo13) pp 567ndash570 ChangshaChina 2013
[15] F Gustafsson F Gunnarsson N Bergman et al ldquoParticle filtersfor positioning navigation and trackingrdquo IEEE Transactions onSignal Processing vol 50 no 2 pp 425ndash437 2002
[16] S Challa and G W Pulford ldquoJoint target tracking and classi-fication using radar and ESM sensorsrdquo IEEE Transactions onAerospace and Electronic Systems vol 37 no 3 pp 1039ndash10552001
[17] M S Grewal and A P Andrews Kalman Filtering Theory andPractice Using Matlab John Wiley amp Sons 2nd edition 2001
[18] S Haykin Kalman Filtering and Neural Networks John Wileyand Sons 2001
[19] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Transactions of the ASME Series D Journal of BasicEngineering vol 82 no 1 pp 35ndash45 1960
[20] S Arulampalam and B Ristic ldquoComparison of the particle filterwith range-parameterised and modified polar EKFs for angle-only trackingrdquo in Signal and Data Processing of Small Targetsvol 4048 of Proceedings of SPIE pp 288ndash299 Orlando FlaUSA April 2000
[21] X Lin T Kirubarajan Y Bar-Shalom and S Maskell ldquoCom-parison of EKF pseudomeasurement and particle filters fora bearing-only target tracking problemrdquo in Signal and Data
12 The Scientific World Journal
Processing of Small Targets vol 4728 of Proceedings of SPIE pp240ndash250 April 2002
[22] M S Arulampalam S Maskell N Gordon and T Clapp ldquoAtutorial on particle filters for online nonlinearnon-GaussianBayesian trackingrdquo IEEE Transactions on Signal Processing vol50 no 2 pp 174ndash188 2002
[23] A Doucet N de Freitas and N Gordon ldquoAn introduction tosequential Monte Carlo methodsrdquo in Sequential Monte CarloMethods in Practice Statistics for Engineering and InformationScience pp 3ndash14 Springer New York NY USA 2001
[24] B Liu andCHao ldquoSequential bearings-only-tracking initiationwith particle filteringmethodrdquoThe ScientificWorld Journal vol2013 Article ID 489121 7 pages 2013
[25] R Karlsson and F Gustafsson ldquoRecursive Bayesian estimationbearings-only applicationsrdquo IEE Proceedings Radar Sonar andNavigation vol 152 no 5 pp 305ndash313 2005
[26] N Gordon ldquoHybrid bootstrap filter for target tracking inclutterrdquo in Proceedings of the American Control Conference vol1 pp 628ndash632 June 1995
[27] S Mcginnity and G W Irwin ldquoMultiple model bootstrapfilter for maneuvering target trackingrdquo IEEE Transactions onAerospace and Electronic Systems vol 36 no 3 pp 1006ndash10122000
[28] M R Morelande and S Challa ldquoManoeuvring target trackingin clutter using particle filtersrdquo IEEE Transactions on Aerospaceand Electronic Systems vol 41 no 1 pp 252ndash270 2005
[29] D Lerro and Y Bar-Shalom ldquoTracking with de-biased consis-tent converted measurements versus EKFrdquo IEEE TransactionsonAerospace and Electronic Systems vol 29 no 3 pp 1015ndash10221993
[30] G Fasano L Forlenza D Accardo A Moccia and A RispolildquoIntegrated obstacle detection system based on radar andoptical sensorsrdquo inProceedings of the AIAA Infotech at Aerospace(AIAA rsquo10) Atlanta Ga USA April 2010
[31] S S Blackman and R F Popoli Design and Analysis of ModernTracking Systems Artech House Norwood Mass USA 1999
[32] G Fasano D Accardo A Moccia and A Rispoli ldquoAn inno-vative procedure for calibration of strapdown electro-opticalsensors onboard unmanned air vehiclesrdquo Sensors vol 10 no 1pp 639ndash654 2010
[33] B Ristic S Arulampalam and N Gordon Beyond the KalmanFilter Particle Filter for Tracking Applications Artech HouseNew York NY USA 2004
[34] A Haug and L Williams ldquoA spherical constant velocity modelfor target tracking in three dimensionsrdquo in IEEE AerospaceConference pp 1ndash15 Big Sky Mont USA March 2012
[35] X R Li and V P Jilkov ldquoA survey of maneuvering target track-ing dynamic modelsrdquo in Proceedings of the SPIE Conference onsignal and Data Processing of Small Targets vol 39 pp 1333ndash1364 Orlando Fla USA April 2000
[36] G Fasano A Moccia D Accardo and A Rispoli ldquoDevelop-ment and test of an integrated sensor system for autonomouscollision avoidancerdquo in Proceedings of the 26th Congress ofInternational Council of the Aeronautical Sciences (ICAS rsquo08) pp3625ndash3634 Anchorage Alaska USA September 2008
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
12 The Scientific World Journal
Processing of Small Targets vol 4728 of Proceedings of SPIE pp240ndash250 April 2002
[22] M S Arulampalam S Maskell N Gordon and T Clapp ldquoAtutorial on particle filters for online nonlinearnon-GaussianBayesian trackingrdquo IEEE Transactions on Signal Processing vol50 no 2 pp 174ndash188 2002
[23] A Doucet N de Freitas and N Gordon ldquoAn introduction tosequential Monte Carlo methodsrdquo in Sequential Monte CarloMethods in Practice Statistics for Engineering and InformationScience pp 3ndash14 Springer New York NY USA 2001
[24] B Liu andCHao ldquoSequential bearings-only-tracking initiationwith particle filteringmethodrdquoThe ScientificWorld Journal vol2013 Article ID 489121 7 pages 2013
[25] R Karlsson and F Gustafsson ldquoRecursive Bayesian estimationbearings-only applicationsrdquo IEE Proceedings Radar Sonar andNavigation vol 152 no 5 pp 305ndash313 2005
[26] N Gordon ldquoHybrid bootstrap filter for target tracking inclutterrdquo in Proceedings of the American Control Conference vol1 pp 628ndash632 June 1995
[27] S Mcginnity and G W Irwin ldquoMultiple model bootstrapfilter for maneuvering target trackingrdquo IEEE Transactions onAerospace and Electronic Systems vol 36 no 3 pp 1006ndash10122000
[28] M R Morelande and S Challa ldquoManoeuvring target trackingin clutter using particle filtersrdquo IEEE Transactions on Aerospaceand Electronic Systems vol 41 no 1 pp 252ndash270 2005
[29] D Lerro and Y Bar-Shalom ldquoTracking with de-biased consis-tent converted measurements versus EKFrdquo IEEE TransactionsonAerospace and Electronic Systems vol 29 no 3 pp 1015ndash10221993
[30] G Fasano L Forlenza D Accardo A Moccia and A RispolildquoIntegrated obstacle detection system based on radar andoptical sensorsrdquo inProceedings of the AIAA Infotech at Aerospace(AIAA rsquo10) Atlanta Ga USA April 2010
[31] S S Blackman and R F Popoli Design and Analysis of ModernTracking Systems Artech House Norwood Mass USA 1999
[32] G Fasano D Accardo A Moccia and A Rispoli ldquoAn inno-vative procedure for calibration of strapdown electro-opticalsensors onboard unmanned air vehiclesrdquo Sensors vol 10 no 1pp 639ndash654 2010
[33] B Ristic S Arulampalam and N Gordon Beyond the KalmanFilter Particle Filter for Tracking Applications Artech HouseNew York NY USA 2004
[34] A Haug and L Williams ldquoA spherical constant velocity modelfor target tracking in three dimensionsrdquo in IEEE AerospaceConference pp 1ndash15 Big Sky Mont USA March 2012
[35] X R Li and V P Jilkov ldquoA survey of maneuvering target track-ing dynamic modelsrdquo in Proceedings of the SPIE Conference onsignal and Data Processing of Small Targets vol 39 pp 1333ndash1364 Orlando Fla USA April 2000
[36] G Fasano A Moccia D Accardo and A Rispoli ldquoDevelop-ment and test of an integrated sensor system for autonomouscollision avoidancerdquo in Proceedings of the 26th Congress ofInternational Council of the Aeronautical Sciences (ICAS rsquo08) pp3625ndash3634 Anchorage Alaska USA September 2008
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of