Hindawi Publishing CorporationInternational Journal of Navigation and ObservationVolume 2013 Article ID 870365 12 pageshttpdxdoiorg1011552013870365

Research ArticleGNSS Reliability Testing in Signal-Degraded Scenario

A Angrisano C Gioia S Gaglione and G del Core

ldquoParthenoperdquo University of Naples Centro Direzionale di Napoli Isola C4 80143 Naples Italy

Correspondence should be addressed to C Gioia cirogioiauniparthenopeitand S Gaglione salvatoregaglioneuniparthenopeit

Received 25 October 2012 Revised 11 February 2013 Accepted 21 February 2013

Academic Editor Sandro Radicella

Copyright copy 2013 A Angrisano et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Multiconstellation satellite navigation is critical in signal-degraded environments where signals are strongly corrupted In thiscase the use of a single GNSS system does not guarantee an accurate and continuous positioning A possible approach to solvethis problem is the use of multiconstellation receivers that provide additional measurements and allows robust reliability testingin this work a GPSGLONASS combination is considered In urban scenario a modification of the classical RAIM techniqueis necessary taking into account frequent multiple blunders The FDE schemes analysed are the ldquoObservation Subset TestingrdquoldquoForward-BackwardMethodrdquo and ldquoDanishMethodrdquo they are obtained by combining different basic statistical testsThe consideredFDEmethods aremodified to optimize their behaviour in urban scenario Specifically a preliminary check is implemented to screenout bad geometries Moreover a large blunder could causemultiple test failures hence a separability index is implemented to avoidthe incorrect exclusion of blunder-free measurements Testing the RAIM algorithms of GPSGLONASS combination to verify thebenefits relative to GPS only case is a main target of this work tooThe performance of these methods is compared in terms of RMSand maximum error for the horizontal and vertical components of position and velocity

1 Introduction

GNSS (Global Navigation Satellite Systems) are world-wide all-weather navigation systems able to provide three-dimensional position velocity and time synchronization toUTC (Coordinated Universal Time) scale [1 2] The GPSsystem is the main GNSS and it is fully operational sincealmost two decades in good visibility conditions (ldquoopenskyrdquo scenario) GPS can provide a position accuracy of fewmeters for absolute positioning up to millimetre order forpostprocessed relative positioning [2]

Satellite navigation in difficult scenarios (eg urbancanyons and mountainous areas) is more critical becausemany GNSS signals are blocked or strongly degraded bynatural and artificial obstacles in these scenarios GPS onlycannot guarantee an accurate and continuous positioning dueto the lack ofmeasurements andor the presence of erroneousmeasurements A possible way to fill this gap is the use of aGNSS multiconstellation receiver considering the combined

use of GPS with other GNSS such as Galileo Beidou andGLONASS

The performance of the integrated system is increased interms of

(i) continuity directly related to satellite availability

(ii) accuracy enhanced by observation geometry im-provement and

(iii) integrity as the increased availability improves thedetection process of gross errors [3 4]

Galileo currently has only four satellites in orbit in the IOV(In-Orbit Validation) phase while Beidou is currently in thedevelopment phase The enhancement of the Russian spaceprogram has made GLONASS an ideal candidate to forma multiconstellation with GPS The combined use of thesetwo systems implies the estimation of a further unknown(in addition to navigation parameters) representing the

2 International Journal of Navigation and Observation

Table 1 GPSGLONASS differences

Parameter GPS GLONASS

Constellation

Number of SV 24 (expandable) 24Orbital planes 6 3Orbital altitude 20200 km 19100 kmOrbit inclination 55∘ 648∘

Ground track period 1 sidereal day 8 sidereal daysLayout Asymmetric Symmetric

Signal

Carrier frequencies (MHz) 157542122760

1602 + Klowast056251246 + Klowast04375

Ranging code frequencies (MHz)CA 1023L2C 1023P 1023M 1023

CA 0511P 511

Multiple access schemes CDMA FDMABroadcast ephemerides Keplerian ECEF

Reference Datum WGS84 PZ9002Time scale GPS time GLONASS time

timescale offset between the considered systems with theldquosacrificerdquo of one measurement

Integrity monitoring has a great importance in safety-critical operation like air navigation or in signal-degradedscenario where solution could be unacceptably inaccurate

Measurements in urban scenario are strongly affectedby gross errors degrading navigation solution hence aquality check on the measurements defined as RAIM isimportant The integrity of a navigation system is definedas the ability to provide timely warnings to users whenthe system should not be used [2 5] GPS and GLONASSprovide integrity information to users into the navigationmessage but this may be not timely enough for real-timeapplication [5] hence additional tools have to be used Twodifferent approaches are possible to provide integrity Thefirst employs a network of ground stations to monitor GNSSsignals and the integrity information is transmitted to theusers by a data link typical examples of this mode are GBAS(Ground Based Augmentation System) and SBAS (SatelliteBased Augmentation System) The second approach is theRAIM technique which is based on self-consistency check onredundant measurements and so it is able to detect user-levelerrors as multipath or local interference strongly degradingthe navigation solution The classical RAIM algorithms weredeveloped for aviation hence they need to be redesignedfor urban applications In this context three well-knownschemes the ldquoObservation Subset Testingrdquo the ldquoForward-Backward Methodrdquo and the ldquoDanish Methodrdquo are modifiedby implementing additional modules to screen out badgeometries and to identify the influence of a large blunder onerror-free measurements

2 GNSS

In this work GPS and GLONASS are considered becausethey are the only systems declared fully operational they aresimilar for many aspects such as the operational principle

detailed in Section 21 however they present some significantdifferences detailed in Section 22

21 GPS GLONASS Common Aspects GPS and GLONASSpositioning is based on the one-way ranging technique thetime of travel of a signal transmitted by a satellite ismeasuredand scaled by the speed of light to obtain the satellite-userdistance called pseudorange (PR) whose equation is [1 5]

120588 = 119889 + 119888120575119905119906+ 120576120588 (1)

where 120588 is the PR measurement 119889 is the geometric receiver-satellite distance 119888120575119905

119906is the receiver clock offset scaled by

the speed of light 119888 and 120576120588contains the residual errors after

atmospheric and satellite-related correctionsTrilateration uses PR measurements to compute the

navigation unknowns that are the tridimensional receivercoordinates and the receiver clock offset relative to the systemtime scale

GNSS receivers are also able to obtain Doppler measure-ments defined as the time derivative of observable phase[1 2] and related to the relative motion between the receiverand satellites Doppler observable is directly converted in apseudorange rate whose equation is [2]

=119889 +

119888120575119905119906+ 120576 (2)

where is the PR rate measurement 119889 is the time derivativeof the geometric distance receiver-satellite

119888120575119905119906is the receiver

clock drift (scaled by speed of light 119888) and 120576is the residual

errors after satellite-based corrections

22 GPS GLONASS Differences GPS and GLONASS arebased on the same operating principle but they have severaldifferences which can be classified in terms of constellationsignal and reference The differences between the two sys-tems are summarized in Table 1 and detailed in [6 7]

International Journal of Navigation and Observation 3

A comprehensive description of the aforesaid differencesamongGPS andGLONASS is provided inAngrisano 2010 [7]

For our scope the main difference is related to thedifferent time scale adopted by the systems GPS time isconnected with UTC(USNO) the UTC maintained by USNaval Observatory UTC scale is occasionally adjusted toone second to keep the scale close to the mean solar timeGPS time scale differs from UTC(USNO) of an integernumber of seconds (called leap seconds currently 16 s) afurther difference between GPS and UTC(USNO) time scale(typically less than 100 ns) due to the different master clocksused is broadcast to the users within the GPS navigationmessage GLONASS time scale is connected to UTC(RU) theUTC maintained by Russia it is corrected by leap secondsaccording to the UTC adjustments so the difference betweenthese time scales is less than 1 millisecond and is broadcast inthe GLONASS navigation message

GPS and GLONASS time scales are connected by thefollowing relation [8 9]

119905GPS = 119905GLO + 120591119903 + 120591119906 + 120591119892 (3)

where 120591119903= 119905UTC(RU)minus119905GLO is broadcast within the GLONASS

navigation message 120591119906= 119905UTC(USNO) minus 119905UTC(RU) must be

estimated and 120591119892= 119905GPS minus119905UTC(USNO) is broadcast in the GPS

navigation messageTo perform the transformation (3) 120591

119906should be known

but this information is not provided in real time An esti-mation of 120591

119906is broadcast as nonimmediate parameter in

the GLONASS almanac [10] but does not take into accountthe intersystem hardware delay bias which is dependent onspecific receiver [8] Therefore when GPS and GLONASSmeasurements are used together 120591

119906is included in the esti-

mation process as unknown

23 Estimation of Navigation Parameters In this work theadopted estimation technique is the weighted least squares(LS) which uses only a measurement model made up bysimultaneous PR and PR rate observables

Regarding PR a set of equations like (1) after lineariza-tion around a nominal state becomes

Δ120588 = 119867120588lowast Δ119909 + 120576

120588

(4)

where Δ120588 is the difference between actual and predictedmeasurements 119867

120588is the design matrix 120576

120588

is the residualerror vector and Δ119909 is the state vector containing receivercoordinates and clock offset errors

Δ119909 = [Δ119875119879

Δ (119888120575119905GPS119906

)]

119879

(5)

If GPS and GLONASS measurements are used togetheran additional unknown must be estimated as explained inSection 22 and the state vector becomes

Δ119909 = [Δ119875119879

Δ (119888120575119905GPS119906

) Δ (119888120575119905Sys)]119879

(6)

where Δ(119888120575119905Sys) is the offset between GPS and GLONASStime scales

The measurement model of PR rate observable isΔ = 119867

lowast V + 120576

(7)

where Δ is the vector containing PR rate measurementscorrected for satellite motion 119867

is the design matrix 120576

isthe residual error vector and V is the velocity state vector

V = [119881119879 119888 120575119905GPS119906

]

119879

(8)

In this case the equations are linear for the unknowns and theGPSGLONASS combined use does not imply an additionalunknown because the drift between the system time scales isnegligible

For the PRmeasurement the follow accuracy dependenton satellite elevation is assumed

1205902

PR = 1205902

URA + 1205902

Iono + 1205902

Tropo + 1205902

mp (9)

where 1205902URA is the user range accuracy (URA) related to thesatellite ephemeris and clock broadcast in theGPSnavigationmessage [2] (for GLONASS this parameter is set in orderto take into account the ephemeris inaccuracy with respectto GPS) 1205902Iono is the accuracy related to ionosphere delayafter Klobuchar model application (whose expression is in[11]) 1205902Tropo is the accuracy related to troposphere error aftercorrection model application [11] and 1205902mp is the accuracyrelated to multipath error [11]

The PR rate measurement accuracy is assumed inverselyproportional to sin(El) where El is the satellite elevation PRand PR rate weights are the inverse of their accuracies

The optimization criterion of the LS is to minimize thesum of the squared residuals defined as

119903 = 119911 minus 119867 sdot (10)

where 119911 is the measurements vector and is the state vectorestimated with the considered technique [12 13]

3 Reliability Test

Reliability refers to the consistency of the results provided bya system internal and external reliability are respectively theability to detect gross errors and the effect of an undetectedblunder on the solution [14]

The integrity of a navigation system is defined as theability to provide timely warnings to users when the systemshould not be used [2 5] Reliability monitoring is based onstatistical test of the observation residuals with the aim ofdetecting and excluding measurement errors in this workthree different RAIM FDE techniques have been developedand their performance is evaluated in terms of RMS andmaximum error for the horizontal and vertical componentsand reliable availability

Before RAIM application a check is performed to screenout bad geometries which could imply erroneous detectionsin this work the WARP (Weighted-ARP) parameter a gen-eralization of the classical ARP [5 15] is used as integritygeometry parameter and its expression is

WARP =WSlopemax sdot radic119879119892 (11)

4 International Journal of Navigation and Observation

where WSlopemax is the maximum of the weighted slope [516] which is an extension of the classical slope and takes intoaccount the measurement different accuracies and 119879

119892is the

threshold of the global test and will be discussed shortlyThe FDE schemes analysed are obtained by combining

different basic statistical tests Specifically a so-called globaltest (GT) is adopted to verify the self-consistency of themeasure set if the measurement set is declared inconsistenta local test (LT) is performed to identify and reject a blunderafter a separability check Separability refers to the abilityto separate any two measurements from one another [14]this concept is primary to avoid the incorrect exclusion ofblunder-free measurements

In the first test the decision variable 119863 is defined asthe sum of the squares of the residuals weighted by theweighting matrix119882 (consisting of the inverse of the squaredmeasurement accuracies (9) on the diagonal and of zerosoutside the diagonal)

119863 = 119903119879

119882119903 (12)

where 119863 is assumed to follow a 1205942 distribution with (119898 minus 119899)degrees of freedom or redundancy defined as the differencebetween the number ofmeasurements119898 and state dimension119899 an inconsistency in the observations is assumed if 119863exceeds the threshold 119879

119892

119879119892= 1205942

1minus119875FA (119898minus119899) (13)

where the notation 12059421minus119875FA (119898minus119899)

indicates the abscissa corre-sponding to a probability value (1 minus 119875FA) of a 120594

2 distributionof (119898 minus 119899) order 119875FA is the probability of false alarm andis fixed in accordance with application requirements 119875FAtypical value for urban navigation is 01 [17] while 119879

119892varies

with redundancyIf the GT does not pass a LT is performed analyzing

standardized residual 119908119894[18]

119908119894=

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

119903119894

radic(119862119903)119894119894

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

119894 = 1 119898 (14)

where 119862119903is the residuals variance covariance matrix

119908119894are assumed to be normally distributed each element

119908119894that exceeds the local threshold 119879

119897 corresponding to the

probability value (1 minus 119875FA2) of a normal distribution isflagged as blunder The measurement corresponding to thelargest standardized residual exceeding 119879

119897is excluded or

deweighted (depending on the method) after a separabilitycheck a large blunder could cause multiple local test failuresand therefore an erroneous measurement rejection In RAIMtechniques a parameter properly representing the separabil-ity is the correlation coefficient of119908

119894 shown in the following

120574119894119895=

(119862119903)119894119895

radic(119862119903)119894119894

sdot (119862119903)119895119895

119894 119895 = 1 119898 (15)

In the separability check if 120574119894119895exceeds a threshold (in this

case 09) the measurement suspected to be a blunder is notrejected or deweighted because it is strictly correlated toanother measurement

z H W

LSestimator

WARPcheck

Solutionimpossible

to check

Global test

Not ok

OkResiduals

Subset

Not ok

Solution unreliable

Solution reliable

Ok

Not ok andall subset checked

Redu

ndan

cyle

0

Figure 1 Subset algorithm

31 Subset Subset testing is an FDE technique that uses onlyGT [5 19 20] If a measurements set is declared inconsistentall the possible combinations of measurements are checkedto find a subset from which the supposed blunders areexcluded Only the subset that passes the GT and is declaredconsistent is used to compute the navigation solution ifmore subsets pass the GT the set with the minimum statisticvariable and the largest number of measurements is chosenIn this technique the separability check is not performedbecause standardized residuals are not analysed A completescheme of the algorithm implemented is shown in Figure 1

The Subset test is applied separately to pseudorangeand Doppler measurements and is computationally heavybecause several measurement combinations have to bechecked [20]

32 Forward-Backward Forward-Backward is an FDE tech-nique that involves the use of both global and local tests itconsists of two different steps [20ndash22] The first algorithmsection called Forward is carried out to identify and excludeerroneous measurements A measurement set is prelimi-nary tested for the integrity geometry to screen out badgeometrieswhich could imply erroneous detections After thepreliminary check the GT is carried out in order to verifymeasurements consistency If global test declares the setinconsistent the LT is performed to identify and exclude theerroneous measurement An erroneous rejection of a goodobservation is possible due to the mutual influence of the

International Journal of Navigation and Observation 5

z H W

LSestimator

WARPcheck

Solutionimpossible

to check

Global test

Not ok

Not ok

Not ok

Not ok

Ok Residuals

Local test

Ok

Ok

Solution unreliable

Separability check

rejections

Rejection reentry

LS estimator

Residuals

Global test

Solution reliable

BackwardRe

dund

ancyle

0

119870

119870 gt 1

119870 le 1

Figure 2 Forward-Backward algorithm

observations to avoid erroneous rejections the separabilitycheck is carried out the measurement flagged as possibleblunder is excluded only if it is not correlated with othermeasures Forward process is performed recursively until nomore erroneous measurements are found and the solution isdeclared reliable or unreliable

If the solution is declared reliable and 119896 measurementsare excluded (with 119896 gt 1) the Backward scheme is appliedto reintroduce observations wrongly excluded Rejectedmea-surements are iteratively implemented backward and theglobal test is performed the observation set which passes theGT is used to compute navigation solution

A complete scheme of the Forward-Backward techniqueis shown in Figure 2

33 Danish Least squares estimation is very susceptible tooutliers a possible way to solve this problem is an iterativedeweighing of erroneous measurements [20 23] The Danishmethod is an iteratively reweighted least squares algorithmused in geodetic applications for a long time this methodis used to achieve consistency between the measurementsby modifying the a priori weights In this paper the Danishmethod is used for signal degraded environments in orderto minimize the effect of blunders on the least squareadjustment This technique involves the use of the GT toverify the consistency of the measurements and the LT toidentify and deweight the outliers

A measurement set is checked for the geometry as inthe previous FDE techniques and then the GT is performedIf observations are declared not consistent by GT the LT iscarried out to identify the blunder and its related weightis reduced only if allowed by the separability check (ie ifthe measurement is not strictly correlated to the others)The variance of the suspected measurement is exponentiallyincreased (and consequently the weight is decreased) asfollows

1205902

119894119895+1

= 1205902

1198940

lowast

119890119908119894119895119879119897 if 119908

119894119895gt 119879119897

1 if 119908119894119895le 119879119897

(16)

where 1205902119894119895+1

is the variance of the 119894th observation after 119895 + 1iterations 1205902

1198940

is the a priori variance of the observation and119908119894119895is the standardized residual of the 119894th observation after 119895

iterationsIf the normalized residual of the 119894th observation does not

exceed 119879119897 its variance is maintained (the measurement is not

deweighted)The scheme of the Danish procedure is shown in

Figure 3

4 Test and Results

41 Test A static test of about 6 hours was carried out onFebruary 24 2012 The antenna was placed on the roof of the

6 International Journal of Navigation and Observation

z H W

LSestimator

WARPcheck

Solutionimpossible

to check

Global test

Residuals

Local test

Ok

Ok

Ok

Solution unreliable

Separability check

Measurementdeweight

Solution reliable

Not ok

Not ok

Not ok

Not ok

Redu

ndan

cyle

0

Figure 3 Danish algorithm

PANG (PArthenope Navigation Group) laboratory buildingCentro Direzionale of Naples (Italy) a typical example ofurban canyon (as shown in Figure 4) in this environmentmanyGNSS signals are blocked by skyscrapers or are stronglydegraded for the multipath phenomenon The only testperformed for this research was static to simplify the erroranalysis for the position (the antenna is placed in a well-known location) and for the velocity (the antenna is fixedso its velocity is zero) a kinematic test needs a referencefor error analysis more complicated to obtain and will beperformed in the future develop of this research Howeverthe static test choice does not limit the research validitybecause the operational environment is a typical signal-degraded scenario that is an urban canyon

The used receiver is a NovAtel FlexPak-G2 able to pro-vide single frequency (L1) GPSGLONASS measurementsconnected to a NovAtel antenna 702-GG

The reference solution is computed by a postprocess-ing geodetic method guaranteeing a position accuracyof mm order the coordinates of the antenna and the relativeaccuracies are shown in Table 2

42 Results Herein eight different GNSS configurations arecompared combining the two systems considered and thedifferent RAIM scheme developed

Antenna p

osition

Figure 4 Antenna position

(i) GPS only without RAIM application (briefly indi-cated as GPS no RAIM)

(ii) GPSGLONASS without RAIM application (GG noRAIM)

(iii) GPS only with Subset RAIM application (GPS Sub)(iv) GPSGLONASS with Subset RAIM application (GG

Sub)(v) GPS only with Forward-Backward RAIM application

(GPS FB)(vi) GPSGLONASS with Forward-Backward RAIM

application (GG FB)(vii) GPS only with Danish method applied (GPS Dan)(viii) GPSGLONASS with Danish method applied (GG

Dan)

Results are analyzed in terms of RMS and maximum errorsfor horizontal and vertical components in the position andvelocity domains The percentage of time mission whensolution is available is referred to as solution availability incase of RAIM application the concept of reliable availabilitydefined as the time percentage when solution is reliable isintroduced

The session is characterized by high solution availability(about 98 forGPS and 100GPSGLONASS configuration)and by very large errors (more than 1 km without RAIMapplication) the application of the developed RAIM schemesreduces the availability of the position solution In GPSstand-alone configuration the Subset test guarantees thehighest reliable availability (762) while 20 of solutionsare flagged as unreliable for Danish and Forward-Backwardschemes the reliable availability is halved with respect tothe solution availability The inclusion of GLONASS mea-surements without RAIM application improves the solutionavailability of 2 with respect to the GPS stand-alone con-figuration For the GPSGLONASS multiconstellation theSubset testing guarantees an high reliable availability (only35 of solutions are rejected by the quality control) which isincreased to 20 with respect to the GPS only configurationThe effect of the GLONASS inclusion is more evident in the

International Journal of Navigation and Observation 7

Danish

GPS no RAIM 98GG no RAIM 100

(m)

GPS Dan 49GG Dan 76

1000

500

0

minus500

minus1000

10005000minus500minus1000

(m)

Forward-Backward

GPS FB 44GPS no RAIM 98GG no RAIM 100 GG FB 74

(m)

1000

500

0

minus500

minus1000

10005000minus500minus1000

(m)

Subset

GPS no RAIM 98 GPS Sub 76GG no RAIM 100 GG Sub 97

(m)

1000

500

0

minus500

minus1000

10005000minus500minus1000

(m)

RAIM comparison

GPS Sub 76GPS FB 44GG Sub 97GG FB 74

GG Dan 76

GPS Dan 49

3002001000minus300 minus200 minus100

200

100

0

minus300

minus200

minus100

(m)

(m)

Figure 5 Horizontal position

Table 2 PANG station coordinates and accuracy

Latitude(deg min sec)

Longitude(deg min sec)

Height(m)

Standard deviation north(m)

Standard deviation east(m)

Standard deviation up(m)

40∘51101584023516310158401015840 14∘17101584003899710158401015840 906257 00006 00008 00011

Danish and Forward-Backward schemes in these cases thereliable availability reaches about 75 with an improvingof 25ndash30 with respect to the GPS only configurationsThe solution availability and the reliable availability of theposition are summarized in Table 3

Similar results are obtained in velocity domain theGLONASSmeasurements increase the reliable availability forthe three RAIM schemes relative to GPS only configurationsas in the position domain the Subset testing guaranteeshigher reliable availability with respect to the other developedschemesThe solution availability and the reliable availabilityof the velocity are summarized in Table 4

The configurations without RAIM are characterized bylarge errors in case of GPS only the maximum horizontal

error exceeds 1 km and the inclusion of GLONASS measure-ments improves the performance reducing the maximumerror to 245meter RAIM application improves all consideredconfigurations reducing both maximum and RMS errorsas shown in Figure 5 for the horizontal component in theupper figures and in the bottom left one the performanceof RAIM schemes is compared with the basic configurations(no RAIM) and in all cases the clouds relative to theRAIM solutions are significantly reduced with respect tothe baseline configurations In the bottom right of Figure 5the performances of the three developed RAIM schemes arecompared from a qualitative analysis the cloud relative tothe GPSGLONASS with forward-backward scheme is moreconcentrated with respect to the others

8 International Journal of Navigation and Observation

Danish

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

350

300

250

150

200

100

50

0

(m)

GPS Dan 49GG Dan 76

Values upto 16859

Forward-Backward

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 44GPS no RAIM 98GG no RAIM 100 GG FB 74

350

300

250

150

200

100

50

0

(m)

Values upto 16859

Subset

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 76GG no RAIM 100 GG Sub 97

350

300

250

150

200

100

50

0

(m)

Values upto 16859

RAIM comparison

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 76GPS FB 44GG Sub 97GG FB 74

GG Dan 76

GPS Dan 49

350

300

250

150

200

100

50

0

(m)

Figure 6 Horizontal position error

Table 3 Position availabilityreliable availability

No RAIMavailability

Subsetreliable availability

Danishreliable availability

Forward-Backwardreliable availability

GPS 981 762 490 436GG 100 965 758 740

In Figure 6 the horizontal position errors are plottedIn the upper figures and in the bottom left one the errorsof the three RAIM schemes are compared with the ldquonoRAIMrdquo configurations the errors of the RAIM configura-tions represented by the green and yellow dots are lowerthan the errors of the no RAIM configurations confirmingthe aforesaid qualitative analysis In the bottom right ofFigure 6 the RAIM errors are compared the Subset testingis characterized by the highest reliable availability but also bythe highest errors while the other schemes provide similarperformance Also in these cases the benefits of the inclusionof GLONASSmeasurements are clear all theGPSGLONASSconfigurations represented by the black yellow andmagenta

dots are lower with respect to the corresponding GPS onlyconfigurations The GLONASS measurements improve theredundancy increasing the RAIM efficiency

In Figure 7 the horizontal velocity errors are plotted ldquonoRAIMrdquo configurations are characterized by high error forGPS only case higher than 50ms the GLONASS inclusionreduces the errors up to 044ms As done for the positionerrors the RAIM schemes are first compared with the ldquonoRAIMrdquo configurations in the velocity domain the benefits oftheRAIMapplication are less evidentwith respect to the posi-tion domain due to the robustness of the Doppler observableIn the bottom right part of Figure 7 the horizontal velocityerrors obtained with the FDE techniques are compared as in

International Journal of Navigation and Observation 9

1

08

06

04

02

0

Danish(m

s)

Values upto 688

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

GPS Dan 56GG Dan 73

Forward-Backward1

08

06

04

02

0

(ms

)

Values upto 688

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 56GPS no RAIM 98GG no RAIM 100 GG FB 73

to 688

Subset1

08

06

04

02

0

(ms

)

Values up

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 70GG no RAIM 100 GG Sub 98

RAIM comparison1

08

06

04

02

0

(ms

)

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 70GPS FB 56GG Sub 98GG FB 73

GG Dan 73

GPS Dan 56

Figure 7 Horizontal velocity error

the position domain the Subset testing is characterized by thehighest reliable availability but also by the highest errors theother schemes provide similar performance

In Figures 8 and 9 the plots relative to the verticalcomponents of the position and velocity show the benefits ofRAIM use

The qualitative analysis provided by the previous plotsis confirmed by the results summarized in Tables 5 and 6 indetail the RAIM use improves significantly the performancein terms of RMS and maximum errors for the vertical andhorizontal components maintaining a high reliable availabil-ity in case of GG configurations The RMS horizontal errorsare halved and even better results are evident on the verticalcomponent The maximum horizontal and vertical errors forGG Subset configuration are degraded due to an erroneousmeasurements rejection in the presence of multiple blundersbetter results are obtained with the Forward-Backward andDanish methods

5 Conclusions

In signal-degraded environments such as urban canyonsGNSS navigation suffers the presence of gross errors which

strongly worsen the solution therefore in these scenariosthe use of RAIM algorithms is necessary In this workthree RAIM FDE schemes well known in literature [1718 20ndash23] are adopted Subset testing Forward-Backwardand Danish The first method is based uniquely on theGT while the others include the use of the LT too Thesemethods have been enriched adopting a preliminary checkon the satellite geometry to screen out configurations toopoor to be tested successfully and a separability test toavoid the exclusion of blunder-free measurements in caseof observations strongly correlated The main scope of thiswork is to verify the effectiveness of the RAIM schemes withthe proposed modifications in urban scenario Moreover thebenefit assessment of GLONASS inclusion is of interest too

The obtained results show the effectiveness of the adoptedalgorithms in terms of reliable availability and of RMS andmaximum errors The reliable availability is the percentageof time mission when the solution is declared reliable bythe adopted RAIM the highest value of this parameter isobtained with the Subset method which provides the largesterrors too The Forward-Backward and the Danish methodsare instead characterized by similar performances and by thesmallest errors demonstrating the validity of the separability

10 International Journal of Navigation and Observation

Danish

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

1500

100

500

0

(m)

GPS Dan 49GG Dan 76

1500

100

500

0

(m)

Forward-Backward

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 44GPS no RAIM 98GG no RAIM 100 GG FB 74

1500

100

500

0

(m)

Subset

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 76GG no RAIM 100 GG Sub 97

RAIM comparison

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 76GPS FB 44GG Sub 97GG FB 74

400

300

100

200

0

(m)

GG Dan 76

GPS Dan 49

Figure 8 Altitude

Table 4 Velocity availabilityreliable availability

No RAIMavailability

Subsetreliable availability

Danishreliable availability

Forward-backwardreliable availability

GPS 981 705 563 563GG 100 978 734 729

Table 5 Position results

RMS (m) MAX (m)H V H V

No RAIM GPS 549 856 12645 16859GG 348 654 2456 3722

Subset GPS 275 564 2990 3270GG 151 361 3216 3985

Forward-backward GPS 179 445 1597 2858GG 134 313 1597 2843

Danish GPS 232 561 1597 3431GG 160 381 1597 2815

Table 6 Velocity results

RMS (ms) MAX (ms)H V H V

No RAIM GPS 0968 1573 68750 108240GG 0042 0060 0442 0822

Subset GPS 0053 0084 0669 1251GG 0042 0067 0928 1337

Forward-Backward GPS 0047 0074 0649 1251GG 0036 0055 0367 0653

Danish GPS 0046 0073 0649 1251GG 0035 0054 0295 0642

International Journal of Navigation and Observation 11

1

08

06

04

02

0

Danish(m

s)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

GPS Dan 56GG Dan 73

Forward-Backward1

08

06

04

02

0

(ms

)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 56GPS no RAIM 98GG no RAIM 100 GG FB 73

Subset1

08

06

04

02

0

(ms

)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 70GG no RAIM 100 GG Sub 98

RAIM comparison1

08

06

04

02

0

(ms

)

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 70GPS FB 56GG Sub 98GG FB 73

GG Dan 73

GPS Dan 56

Figure 9 Vertical velocity error

check module (which cannot be applied to Subset method)The proposed algorithms have been tested on both positionand velocity domains showing comparable robustness

GPSGLONASS combination shows evident perform-ance improvements for all the considered parameters rela-tive to GPS only configurations

References

[1] B Hoffmann-Wellenhof H Lichtenegger and J CollinsGlobalPositioning System Theory and Practice Springer New YorkNY USA 1992

[2] ED Kaplan and J Hegarty ldquoFundamentals of satellite naviga-tionrdquo in Understanding GPS Principles and Applications E DKaplan Ed ArtechHouseMobile Communications Series 2ndedition 2006

[3] A Angrisano M Petovello and G Pugliano ldquoGNSSINSintegration in vehicular urban navigationrdquo in Proceedings ofthe 23rd International Technical Meeting of the Satellite Divisionof the Institute of Navigation (GNSS rsquo10) pp 1505ndash1512 TheInstitute of Navigation Portland Ore USA September 2010

[4] A Angrisano M Petovello and G Pugliano ldquoBenefits ofcombined GPSGLONASS with low-cost MEMS IMUs forvehicular urban navigationrdquo Sensors vol 12 no 4 pp 5134ndash5158 2012

[5] B Parkinson and J J Spilker Global Positioning System TheoryAnd Applications vol 1-2 American Institute of Aeronauticsand Astronautics Washington DC USA 1996

[6] C Cai Precise point positioning using dual-frequency GPS andGLONASSmeasurements [MS thesis] UCGEReport no 20291Department of Geomatics Engineering University of CalgaryCalgary Canada 2009

[7] A Angrisano GNSSINS integration methods [PhD thesis]ldquoParthenoperdquo University of Naples 2010

[8] C Cai and Y Gao ldquoA combined GPSGLONASS navigationalgorithm for use with limited satellite visibilityrdquo Journal ofNavigation vol 62 no 4 pp 671ndash685 2009

[9] A Angrisano S Gaglione G Pugliano R Robustelli RSantamaria and M Vultaggio ldquoA stochastic sigma model forGLONASS satellite pseudorangerdquo Applied Geomatics vol 3 no1 pp 49ndash57 2011

[10] ICD-GLONASS Global Navigation Satellite System GLONASSInterface Control Document version 51 Moscow Russia 2008

[11] SC-159 of the RTCAMinimum Operational Performance Stan-dards for Global Positioning SystemWide Area AugmentationSystem Airborne Equipment Document DO-229D RTCAWashington DC USA 2006

[12] E M Mikhail Observations and Least Squares Harper amp Row1976

12 International Journal of Navigation and Observation

[13] D E Wells and E J Krakiwsky The Methods of Least SquaresLecture Notes no 18 Department of Surveying EngineeringUniversity of Brunswick 1971

[14] S Hewitson and J Wang ldquoGNSS receiver autonomous integritymonitoring (RAIM) performance analysisrdquo GPS Solutions vol10 no 3 pp 155ndash170 2006

[15] G Y Chin J H Kraemer and R G Brown ldquoGPS RAIMscreening out bad geometries underworst-case bias conditionsrdquoNavigation Journal of the Institute of Navigation vol 39 no 4pp 407ndash427 1992

[16] R G Brown and G Y Chin ldquoGPS RAIM calculation ofthreshold and protection radius using chi-square methods-a geometric approachrdquo Global Positioning System Institute ofNavigation vol 5 pp 155ndash179 1997

[17] M Petovello Real-time integration of a tactical-grade IMUand GPS for high-accuracy positioning and navigation [PhDthesis] UCGE Report no 20173 Department of GeomaticsEngineering University of Calgary Calgary Canada 2003

[18] W Baarda A Testing Procedure for Use in Geodetic NetworksNetherlands Geodetic Commission Publication on GeodesyNew Series 2 5 Delft The Netherlands 1968

[19] A K Brown ldquoReceiver autonomous integrity monitoring usinga 24-satellite GPS constellationrdquo Navigation Journal of TheInstitute of Navigation vol 5 pp 21ndash33 1998 Red Book ofRAIM

[20] H Kuusniemi User-level reliability and quality monitoringin satellite-based personal navigation [PhD thesis] TampereUniversity of Technology Tampere Finland 2005

[21] H Kuusniemi A Wieser G Lachapelle and J TakalaldquoUser-level reliability monitoring in urban personal satellite-navigationrdquo IEEE Transactions on Aerospace and ElectronicSystems vol 43 no 4 pp 1305ndash1318 2007

[22] A Angrisano S Gaglione and C Gioia ldquoRAIM algorithmsfor aided GNSS in urban scenariordquo in Proceedings of theUbiquitous Positioning Indoor Navigation and Location BasedService Helsinki Finland October 2012

[23] A LeickGPS Satellite Surveying JohnWiley amp Sons HobokenNJ USA 3rd edition 2004

International Journal of

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Active and Passive Electronic Components

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RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

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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

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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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Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

2 International Journal of Navigation and Observation

Table 1 GPSGLONASS differences

Parameter GPS GLONASS

Constellation

Number of SV 24 (expandable) 24Orbital planes 6 3Orbital altitude 20200 km 19100 kmOrbit inclination 55∘ 648∘

Ground track period 1 sidereal day 8 sidereal daysLayout Asymmetric Symmetric

Signal

Carrier frequencies (MHz) 157542122760

1602 + Klowast056251246 + Klowast04375

Ranging code frequencies (MHz)CA 1023L2C 1023P 1023M 1023

CA 0511P 511

Multiple access schemes CDMA FDMABroadcast ephemerides Keplerian ECEF

Reference Datum WGS84 PZ9002Time scale GPS time GLONASS time

timescale offset between the considered systems with theldquosacrificerdquo of one measurement

Integrity monitoring has a great importance in safety-critical operation like air navigation or in signal-degradedscenario where solution could be unacceptably inaccurate

Measurements in urban scenario are strongly affectedby gross errors degrading navigation solution hence aquality check on the measurements defined as RAIM isimportant The integrity of a navigation system is definedas the ability to provide timely warnings to users whenthe system should not be used [2 5] GPS and GLONASSprovide integrity information to users into the navigationmessage but this may be not timely enough for real-timeapplication [5] hence additional tools have to be used Twodifferent approaches are possible to provide integrity Thefirst employs a network of ground stations to monitor GNSSsignals and the integrity information is transmitted to theusers by a data link typical examples of this mode are GBAS(Ground Based Augmentation System) and SBAS (SatelliteBased Augmentation System) The second approach is theRAIM technique which is based on self-consistency check onredundant measurements and so it is able to detect user-levelerrors as multipath or local interference strongly degradingthe navigation solution The classical RAIM algorithms weredeveloped for aviation hence they need to be redesignedfor urban applications In this context three well-knownschemes the ldquoObservation Subset Testingrdquo the ldquoForward-Backward Methodrdquo and the ldquoDanish Methodrdquo are modifiedby implementing additional modules to screen out badgeometries and to identify the influence of a large blunder onerror-free measurements

2 GNSS

In this work GPS and GLONASS are considered becausethey are the only systems declared fully operational they aresimilar for many aspects such as the operational principle

detailed in Section 21 however they present some significantdifferences detailed in Section 22

21 GPS GLONASS Common Aspects GPS and GLONASSpositioning is based on the one-way ranging technique thetime of travel of a signal transmitted by a satellite ismeasuredand scaled by the speed of light to obtain the satellite-userdistance called pseudorange (PR) whose equation is [1 5]

120588 = 119889 + 119888120575119905119906+ 120576120588 (1)

where 120588 is the PR measurement 119889 is the geometric receiver-satellite distance 119888120575119905

119906is the receiver clock offset scaled by

the speed of light 119888 and 120576120588contains the residual errors after

atmospheric and satellite-related correctionsTrilateration uses PR measurements to compute the

navigation unknowns that are the tridimensional receivercoordinates and the receiver clock offset relative to the systemtime scale

GNSS receivers are also able to obtain Doppler measure-ments defined as the time derivative of observable phase[1 2] and related to the relative motion between the receiverand satellites Doppler observable is directly converted in apseudorange rate whose equation is [2]

=119889 +

119888120575119905119906+ 120576 (2)

where is the PR rate measurement 119889 is the time derivativeof the geometric distance receiver-satellite

119888120575119905119906is the receiver

clock drift (scaled by speed of light 119888) and 120576is the residual

errors after satellite-based corrections

22 GPS GLONASS Differences GPS and GLONASS arebased on the same operating principle but they have severaldifferences which can be classified in terms of constellationsignal and reference The differences between the two sys-tems are summarized in Table 1 and detailed in [6 7]

International Journal of Navigation and Observation 3

A comprehensive description of the aforesaid differencesamongGPS andGLONASS is provided inAngrisano 2010 [7]

For our scope the main difference is related to thedifferent time scale adopted by the systems GPS time isconnected with UTC(USNO) the UTC maintained by USNaval Observatory UTC scale is occasionally adjusted toone second to keep the scale close to the mean solar timeGPS time scale differs from UTC(USNO) of an integernumber of seconds (called leap seconds currently 16 s) afurther difference between GPS and UTC(USNO) time scale(typically less than 100 ns) due to the different master clocksused is broadcast to the users within the GPS navigationmessage GLONASS time scale is connected to UTC(RU) theUTC maintained by Russia it is corrected by leap secondsaccording to the UTC adjustments so the difference betweenthese time scales is less than 1 millisecond and is broadcast inthe GLONASS navigation message

GPS and GLONASS time scales are connected by thefollowing relation [8 9]

119905GPS = 119905GLO + 120591119903 + 120591119906 + 120591119892 (3)

where 120591119903= 119905UTC(RU)minus119905GLO is broadcast within the GLONASS

navigation message 120591119906= 119905UTC(USNO) minus 119905UTC(RU) must be

estimated and 120591119892= 119905GPS minus119905UTC(USNO) is broadcast in the GPS

navigation messageTo perform the transformation (3) 120591

119906should be known

but this information is not provided in real time An esti-mation of 120591

119906is broadcast as nonimmediate parameter in

the GLONASS almanac [10] but does not take into accountthe intersystem hardware delay bias which is dependent onspecific receiver [8] Therefore when GPS and GLONASSmeasurements are used together 120591

119906is included in the esti-

mation process as unknown

23 Estimation of Navigation Parameters In this work theadopted estimation technique is the weighted least squares(LS) which uses only a measurement model made up bysimultaneous PR and PR rate observables

Regarding PR a set of equations like (1) after lineariza-tion around a nominal state becomes

Δ120588 = 119867120588lowast Δ119909 + 120576

120588

(4)

where Δ120588 is the difference between actual and predictedmeasurements 119867

120588is the design matrix 120576

120588

is the residualerror vector and Δ119909 is the state vector containing receivercoordinates and clock offset errors

Δ119909 = [Δ119875119879

Δ (119888120575119905GPS119906

)]

119879

(5)

If GPS and GLONASS measurements are used togetheran additional unknown must be estimated as explained inSection 22 and the state vector becomes

Δ119909 = [Δ119875119879

Δ (119888120575119905GPS119906

) Δ (119888120575119905Sys)]119879

(6)

where Δ(119888120575119905Sys) is the offset between GPS and GLONASStime scales

The measurement model of PR rate observable isΔ = 119867

lowast V + 120576

(7)

where Δ is the vector containing PR rate measurementscorrected for satellite motion 119867

is the design matrix 120576

isthe residual error vector and V is the velocity state vector

V = [119881119879 119888 120575119905GPS119906

]

119879

(8)

In this case the equations are linear for the unknowns and theGPSGLONASS combined use does not imply an additionalunknown because the drift between the system time scales isnegligible

For the PRmeasurement the follow accuracy dependenton satellite elevation is assumed

1205902

PR = 1205902

URA + 1205902

Iono + 1205902

Tropo + 1205902

mp (9)

where 1205902URA is the user range accuracy (URA) related to thesatellite ephemeris and clock broadcast in theGPSnavigationmessage [2] (for GLONASS this parameter is set in orderto take into account the ephemeris inaccuracy with respectto GPS) 1205902Iono is the accuracy related to ionosphere delayafter Klobuchar model application (whose expression is in[11]) 1205902Tropo is the accuracy related to troposphere error aftercorrection model application [11] and 1205902mp is the accuracyrelated to multipath error [11]

The PR rate measurement accuracy is assumed inverselyproportional to sin(El) where El is the satellite elevation PRand PR rate weights are the inverse of their accuracies

The optimization criterion of the LS is to minimize thesum of the squared residuals defined as

119903 = 119911 minus 119867 sdot (10)

where 119911 is the measurements vector and is the state vectorestimated with the considered technique [12 13]

3 Reliability Test

Reliability refers to the consistency of the results provided bya system internal and external reliability are respectively theability to detect gross errors and the effect of an undetectedblunder on the solution [14]

The integrity of a navigation system is defined as theability to provide timely warnings to users when the systemshould not be used [2 5] Reliability monitoring is based onstatistical test of the observation residuals with the aim ofdetecting and excluding measurement errors in this workthree different RAIM FDE techniques have been developedand their performance is evaluated in terms of RMS andmaximum error for the horizontal and vertical componentsand reliable availability

Before RAIM application a check is performed to screenout bad geometries which could imply erroneous detectionsin this work the WARP (Weighted-ARP) parameter a gen-eralization of the classical ARP [5 15] is used as integritygeometry parameter and its expression is

WARP =WSlopemax sdot radic119879119892 (11)

4 International Journal of Navigation and Observation

where WSlopemax is the maximum of the weighted slope [516] which is an extension of the classical slope and takes intoaccount the measurement different accuracies and 119879

119892is the

threshold of the global test and will be discussed shortlyThe FDE schemes analysed are obtained by combining

different basic statistical tests Specifically a so-called globaltest (GT) is adopted to verify the self-consistency of themeasure set if the measurement set is declared inconsistenta local test (LT) is performed to identify and reject a blunderafter a separability check Separability refers to the abilityto separate any two measurements from one another [14]this concept is primary to avoid the incorrect exclusion ofblunder-free measurements

In the first test the decision variable 119863 is defined asthe sum of the squares of the residuals weighted by theweighting matrix119882 (consisting of the inverse of the squaredmeasurement accuracies (9) on the diagonal and of zerosoutside the diagonal)

119863 = 119903119879

119882119903 (12)

where 119863 is assumed to follow a 1205942 distribution with (119898 minus 119899)degrees of freedom or redundancy defined as the differencebetween the number ofmeasurements119898 and state dimension119899 an inconsistency in the observations is assumed if 119863exceeds the threshold 119879

119892

119879119892= 1205942

1minus119875FA (119898minus119899) (13)

where the notation 12059421minus119875FA (119898minus119899)

indicates the abscissa corre-sponding to a probability value (1 minus 119875FA) of a 120594

2 distributionof (119898 minus 119899) order 119875FA is the probability of false alarm andis fixed in accordance with application requirements 119875FAtypical value for urban navigation is 01 [17] while 119879

119892varies

with redundancyIf the GT does not pass a LT is performed analyzing

standardized residual 119908119894[18]

119908119894=

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

119903119894

radic(119862119903)119894119894

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

119894 = 1 119898 (14)

where 119862119903is the residuals variance covariance matrix

119908119894are assumed to be normally distributed each element

119908119894that exceeds the local threshold 119879

119897 corresponding to the

probability value (1 minus 119875FA2) of a normal distribution isflagged as blunder The measurement corresponding to thelargest standardized residual exceeding 119879

119897is excluded or

deweighted (depending on the method) after a separabilitycheck a large blunder could cause multiple local test failuresand therefore an erroneous measurement rejection In RAIMtechniques a parameter properly representing the separabil-ity is the correlation coefficient of119908

119894 shown in the following

120574119894119895=

(119862119903)119894119895

radic(119862119903)119894119894

sdot (119862119903)119895119895

119894 119895 = 1 119898 (15)

In the separability check if 120574119894119895exceeds a threshold (in this

case 09) the measurement suspected to be a blunder is notrejected or deweighted because it is strictly correlated toanother measurement

z H W

LSestimator

WARPcheck

Solutionimpossible

to check

Global test

Not ok

OkResiduals

Subset

Not ok

Solution unreliable

Solution reliable

Ok

Not ok andall subset checked

Redu

ndan

cyle

0

Figure 1 Subset algorithm

31 Subset Subset testing is an FDE technique that uses onlyGT [5 19 20] If a measurements set is declared inconsistentall the possible combinations of measurements are checkedto find a subset from which the supposed blunders areexcluded Only the subset that passes the GT and is declaredconsistent is used to compute the navigation solution ifmore subsets pass the GT the set with the minimum statisticvariable and the largest number of measurements is chosenIn this technique the separability check is not performedbecause standardized residuals are not analysed A completescheme of the algorithm implemented is shown in Figure 1

The Subset test is applied separately to pseudorangeand Doppler measurements and is computationally heavybecause several measurement combinations have to bechecked [20]

32 Forward-Backward Forward-Backward is an FDE tech-nique that involves the use of both global and local tests itconsists of two different steps [20ndash22] The first algorithmsection called Forward is carried out to identify and excludeerroneous measurements A measurement set is prelimi-nary tested for the integrity geometry to screen out badgeometrieswhich could imply erroneous detections After thepreliminary check the GT is carried out in order to verifymeasurements consistency If global test declares the setinconsistent the LT is performed to identify and exclude theerroneous measurement An erroneous rejection of a goodobservation is possible due to the mutual influence of the

International Journal of Navigation and Observation 5

z H W

LSestimator

WARPcheck

Solutionimpossible

to check

Global test

Not ok

Not ok

Not ok

Not ok

Ok Residuals

Local test

Ok

Ok

Solution unreliable

Separability check

rejections

Rejection reentry

LS estimator

Residuals

Global test

Solution reliable

BackwardRe

dund

ancyle

0

119870

119870 gt 1

119870 le 1

Figure 2 Forward-Backward algorithm

observations to avoid erroneous rejections the separabilitycheck is carried out the measurement flagged as possibleblunder is excluded only if it is not correlated with othermeasures Forward process is performed recursively until nomore erroneous measurements are found and the solution isdeclared reliable or unreliable

If the solution is declared reliable and 119896 measurementsare excluded (with 119896 gt 1) the Backward scheme is appliedto reintroduce observations wrongly excluded Rejectedmea-surements are iteratively implemented backward and theglobal test is performed the observation set which passes theGT is used to compute navigation solution

A complete scheme of the Forward-Backward techniqueis shown in Figure 2

33 Danish Least squares estimation is very susceptible tooutliers a possible way to solve this problem is an iterativedeweighing of erroneous measurements [20 23] The Danishmethod is an iteratively reweighted least squares algorithmused in geodetic applications for a long time this methodis used to achieve consistency between the measurementsby modifying the a priori weights In this paper the Danishmethod is used for signal degraded environments in orderto minimize the effect of blunders on the least squareadjustment This technique involves the use of the GT toverify the consistency of the measurements and the LT toidentify and deweight the outliers

A measurement set is checked for the geometry as inthe previous FDE techniques and then the GT is performedIf observations are declared not consistent by GT the LT iscarried out to identify the blunder and its related weightis reduced only if allowed by the separability check (ie ifthe measurement is not strictly correlated to the others)The variance of the suspected measurement is exponentiallyincreased (and consequently the weight is decreased) asfollows

1205902

119894119895+1

= 1205902

1198940

lowast

119890119908119894119895119879119897 if 119908

119894119895gt 119879119897

1 if 119908119894119895le 119879119897

(16)

where 1205902119894119895+1

is the variance of the 119894th observation after 119895 + 1iterations 1205902

1198940

is the a priori variance of the observation and119908119894119895is the standardized residual of the 119894th observation after 119895

iterationsIf the normalized residual of the 119894th observation does not

exceed 119879119897 its variance is maintained (the measurement is not

deweighted)The scheme of the Danish procedure is shown in

Figure 3

4 Test and Results

41 Test A static test of about 6 hours was carried out onFebruary 24 2012 The antenna was placed on the roof of the

6 International Journal of Navigation and Observation

z H W

LSestimator

WARPcheck

Solutionimpossible

to check

Global test

Residuals

Local test

Ok

Ok

Ok

Solution unreliable

Separability check

Measurementdeweight

Solution reliable

Not ok

Not ok

Not ok

Not ok

Redu

ndan

cyle

0

Figure 3 Danish algorithm

PANG (PArthenope Navigation Group) laboratory buildingCentro Direzionale of Naples (Italy) a typical example ofurban canyon (as shown in Figure 4) in this environmentmanyGNSS signals are blocked by skyscrapers or are stronglydegraded for the multipath phenomenon The only testperformed for this research was static to simplify the erroranalysis for the position (the antenna is placed in a well-known location) and for the velocity (the antenna is fixedso its velocity is zero) a kinematic test needs a referencefor error analysis more complicated to obtain and will beperformed in the future develop of this research Howeverthe static test choice does not limit the research validitybecause the operational environment is a typical signal-degraded scenario that is an urban canyon

The used receiver is a NovAtel FlexPak-G2 able to pro-vide single frequency (L1) GPSGLONASS measurementsconnected to a NovAtel antenna 702-GG

The reference solution is computed by a postprocess-ing geodetic method guaranteeing a position accuracyof mm order the coordinates of the antenna and the relativeaccuracies are shown in Table 2

42 Results Herein eight different GNSS configurations arecompared combining the two systems considered and thedifferent RAIM scheme developed

Antenna p

osition

Figure 4 Antenna position

(i) GPS only without RAIM application (briefly indi-cated as GPS no RAIM)

(ii) GPSGLONASS without RAIM application (GG noRAIM)

(iii) GPS only with Subset RAIM application (GPS Sub)(iv) GPSGLONASS with Subset RAIM application (GG

Sub)(v) GPS only with Forward-Backward RAIM application

(GPS FB)(vi) GPSGLONASS with Forward-Backward RAIM

application (GG FB)(vii) GPS only with Danish method applied (GPS Dan)(viii) GPSGLONASS with Danish method applied (GG

Dan)

Results are analyzed in terms of RMS and maximum errorsfor horizontal and vertical components in the position andvelocity domains The percentage of time mission whensolution is available is referred to as solution availability incase of RAIM application the concept of reliable availabilitydefined as the time percentage when solution is reliable isintroduced

The session is characterized by high solution availability(about 98 forGPS and 100GPSGLONASS configuration)and by very large errors (more than 1 km without RAIMapplication) the application of the developed RAIM schemesreduces the availability of the position solution In GPSstand-alone configuration the Subset test guarantees thehighest reliable availability (762) while 20 of solutionsare flagged as unreliable for Danish and Forward-Backwardschemes the reliable availability is halved with respect tothe solution availability The inclusion of GLONASS mea-surements without RAIM application improves the solutionavailability of 2 with respect to the GPS stand-alone con-figuration For the GPSGLONASS multiconstellation theSubset testing guarantees an high reliable availability (only35 of solutions are rejected by the quality control) which isincreased to 20 with respect to the GPS only configurationThe effect of the GLONASS inclusion is more evident in the

International Journal of Navigation and Observation 7

Danish

GPS no RAIM 98GG no RAIM 100

(m)

GPS Dan 49GG Dan 76

1000

500

0

minus500

minus1000

10005000minus500minus1000

(m)

Forward-Backward

GPS FB 44GPS no RAIM 98GG no RAIM 100 GG FB 74

(m)

1000

500

0

minus500

minus1000

10005000minus500minus1000

(m)

Subset

GPS no RAIM 98 GPS Sub 76GG no RAIM 100 GG Sub 97

(m)

1000

500

0

minus500

minus1000

10005000minus500minus1000

(m)

RAIM comparison

GPS Sub 76GPS FB 44GG Sub 97GG FB 74

GG Dan 76

GPS Dan 49

3002001000minus300 minus200 minus100

200

100

0

minus300

minus200

minus100

(m)

(m)

Figure 5 Horizontal position

Table 2 PANG station coordinates and accuracy

Latitude(deg min sec)

Longitude(deg min sec)

Height(m)

Standard deviation north(m)

Standard deviation east(m)

Standard deviation up(m)

40∘51101584023516310158401015840 14∘17101584003899710158401015840 906257 00006 00008 00011

Danish and Forward-Backward schemes in these cases thereliable availability reaches about 75 with an improvingof 25ndash30 with respect to the GPS only configurationsThe solution availability and the reliable availability of theposition are summarized in Table 3

Similar results are obtained in velocity domain theGLONASSmeasurements increase the reliable availability forthe three RAIM schemes relative to GPS only configurationsas in the position domain the Subset testing guaranteeshigher reliable availability with respect to the other developedschemesThe solution availability and the reliable availabilityof the velocity are summarized in Table 4

The configurations without RAIM are characterized bylarge errors in case of GPS only the maximum horizontal

error exceeds 1 km and the inclusion of GLONASS measure-ments improves the performance reducing the maximumerror to 245meter RAIM application improves all consideredconfigurations reducing both maximum and RMS errorsas shown in Figure 5 for the horizontal component in theupper figures and in the bottom left one the performanceof RAIM schemes is compared with the basic configurations(no RAIM) and in all cases the clouds relative to theRAIM solutions are significantly reduced with respect tothe baseline configurations In the bottom right of Figure 5the performances of the three developed RAIM schemes arecompared from a qualitative analysis the cloud relative tothe GPSGLONASS with forward-backward scheme is moreconcentrated with respect to the others

8 International Journal of Navigation and Observation

Danish

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

350

300

250

150

200

100

50

0

(m)

GPS Dan 49GG Dan 76

Values upto 16859

Forward-Backward

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 44GPS no RAIM 98GG no RAIM 100 GG FB 74

350

300

250

150

200

100

50

0

(m)

Values upto 16859

Subset

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 76GG no RAIM 100 GG Sub 97

350

300

250

150

200

100

50

0

(m)

Values upto 16859

RAIM comparison

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 76GPS FB 44GG Sub 97GG FB 74

GG Dan 76

GPS Dan 49

350

300

250

150

200

100

50

0

(m)

Figure 6 Horizontal position error

Table 3 Position availabilityreliable availability

No RAIMavailability

Subsetreliable availability

Danishreliable availability

Forward-Backwardreliable availability

GPS 981 762 490 436GG 100 965 758 740

In Figure 6 the horizontal position errors are plottedIn the upper figures and in the bottom left one the errorsof the three RAIM schemes are compared with the ldquonoRAIMrdquo configurations the errors of the RAIM configura-tions represented by the green and yellow dots are lowerthan the errors of the no RAIM configurations confirmingthe aforesaid qualitative analysis In the bottom right ofFigure 6 the RAIM errors are compared the Subset testingis characterized by the highest reliable availability but also bythe highest errors while the other schemes provide similarperformance Also in these cases the benefits of the inclusionof GLONASSmeasurements are clear all theGPSGLONASSconfigurations represented by the black yellow andmagenta

dots are lower with respect to the corresponding GPS onlyconfigurations The GLONASS measurements improve theredundancy increasing the RAIM efficiency

In Figure 7 the horizontal velocity errors are plotted ldquonoRAIMrdquo configurations are characterized by high error forGPS only case higher than 50ms the GLONASS inclusionreduces the errors up to 044ms As done for the positionerrors the RAIM schemes are first compared with the ldquonoRAIMrdquo configurations in the velocity domain the benefits oftheRAIMapplication are less evidentwith respect to the posi-tion domain due to the robustness of the Doppler observableIn the bottom right part of Figure 7 the horizontal velocityerrors obtained with the FDE techniques are compared as in

International Journal of Navigation and Observation 9

1

08

06

04

02

0

Danish(m

s)

Values upto 688

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

GPS Dan 56GG Dan 73

Forward-Backward1

08

06

04

02

0

(ms

)

Values upto 688

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 56GPS no RAIM 98GG no RAIM 100 GG FB 73

to 688

Subset1

08

06

04

02

0

(ms

)

Values up

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 70GG no RAIM 100 GG Sub 98

RAIM comparison1

08

06

04

02

0

(ms

)

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 70GPS FB 56GG Sub 98GG FB 73

GG Dan 73

GPS Dan 56

Figure 7 Horizontal velocity error

the position domain the Subset testing is characterized by thehighest reliable availability but also by the highest errors theother schemes provide similar performance

In Figures 8 and 9 the plots relative to the verticalcomponents of the position and velocity show the benefits ofRAIM use

The qualitative analysis provided by the previous plotsis confirmed by the results summarized in Tables 5 and 6 indetail the RAIM use improves significantly the performancein terms of RMS and maximum errors for the vertical andhorizontal components maintaining a high reliable availabil-ity in case of GG configurations The RMS horizontal errorsare halved and even better results are evident on the verticalcomponent The maximum horizontal and vertical errors forGG Subset configuration are degraded due to an erroneousmeasurements rejection in the presence of multiple blundersbetter results are obtained with the Forward-Backward andDanish methods

5 Conclusions

In signal-degraded environments such as urban canyonsGNSS navigation suffers the presence of gross errors which

strongly worsen the solution therefore in these scenariosthe use of RAIM algorithms is necessary In this workthree RAIM FDE schemes well known in literature [1718 20ndash23] are adopted Subset testing Forward-Backwardand Danish The first method is based uniquely on theGT while the others include the use of the LT too Thesemethods have been enriched adopting a preliminary checkon the satellite geometry to screen out configurations toopoor to be tested successfully and a separability test toavoid the exclusion of blunder-free measurements in caseof observations strongly correlated The main scope of thiswork is to verify the effectiveness of the RAIM schemes withthe proposed modifications in urban scenario Moreover thebenefit assessment of GLONASS inclusion is of interest too

The obtained results show the effectiveness of the adoptedalgorithms in terms of reliable availability and of RMS andmaximum errors The reliable availability is the percentageof time mission when the solution is declared reliable bythe adopted RAIM the highest value of this parameter isobtained with the Subset method which provides the largesterrors too The Forward-Backward and the Danish methodsare instead characterized by similar performances and by thesmallest errors demonstrating the validity of the separability

10 International Journal of Navigation and Observation

Danish

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

1500

100

500

0

(m)

GPS Dan 49GG Dan 76

1500

100

500

0

(m)

Forward-Backward

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 44GPS no RAIM 98GG no RAIM 100 GG FB 74

1500

100

500

0

(m)

Subset

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 76GG no RAIM 100 GG Sub 97

RAIM comparison

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 76GPS FB 44GG Sub 97GG FB 74

400

300

100

200

0

(m)

GG Dan 76

GPS Dan 49

Figure 8 Altitude

Table 4 Velocity availabilityreliable availability

No RAIMavailability

Subsetreliable availability

Danishreliable availability

Forward-backwardreliable availability

GPS 981 705 563 563GG 100 978 734 729

Table 5 Position results

RMS (m) MAX (m)H V H V

No RAIM GPS 549 856 12645 16859GG 348 654 2456 3722

Subset GPS 275 564 2990 3270GG 151 361 3216 3985

Forward-backward GPS 179 445 1597 2858GG 134 313 1597 2843

Danish GPS 232 561 1597 3431GG 160 381 1597 2815

Table 6 Velocity results

RMS (ms) MAX (ms)H V H V

No RAIM GPS 0968 1573 68750 108240GG 0042 0060 0442 0822

Subset GPS 0053 0084 0669 1251GG 0042 0067 0928 1337

Forward-Backward GPS 0047 0074 0649 1251GG 0036 0055 0367 0653

Danish GPS 0046 0073 0649 1251GG 0035 0054 0295 0642

International Journal of Navigation and Observation 11

1

08

06

04

02

0

Danish(m

s)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

GPS Dan 56GG Dan 73

Forward-Backward1

08

06

04

02

0

(ms

)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 56GPS no RAIM 98GG no RAIM 100 GG FB 73

Subset1

08

06

04

02

0

(ms

)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 70GG no RAIM 100 GG Sub 98

RAIM comparison1

08

06

04

02

0

(ms

)

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 70GPS FB 56GG Sub 98GG FB 73

GG Dan 73

GPS Dan 56

Figure 9 Vertical velocity error

check module (which cannot be applied to Subset method)The proposed algorithms have been tested on both positionand velocity domains showing comparable robustness

GPSGLONASS combination shows evident perform-ance improvements for all the considered parameters rela-tive to GPS only configurations

References

[1] B Hoffmann-Wellenhof H Lichtenegger and J CollinsGlobalPositioning System Theory and Practice Springer New YorkNY USA 1992

[2] ED Kaplan and J Hegarty ldquoFundamentals of satellite naviga-tionrdquo in Understanding GPS Principles and Applications E DKaplan Ed ArtechHouseMobile Communications Series 2ndedition 2006

[3] A Angrisano M Petovello and G Pugliano ldquoGNSSINSintegration in vehicular urban navigationrdquo in Proceedings ofthe 23rd International Technical Meeting of the Satellite Divisionof the Institute of Navigation (GNSS rsquo10) pp 1505ndash1512 TheInstitute of Navigation Portland Ore USA September 2010

[4] A Angrisano M Petovello and G Pugliano ldquoBenefits ofcombined GPSGLONASS with low-cost MEMS IMUs forvehicular urban navigationrdquo Sensors vol 12 no 4 pp 5134ndash5158 2012

[5] B Parkinson and J J Spilker Global Positioning System TheoryAnd Applications vol 1-2 American Institute of Aeronauticsand Astronautics Washington DC USA 1996

[6] C Cai Precise point positioning using dual-frequency GPS andGLONASSmeasurements [MS thesis] UCGEReport no 20291Department of Geomatics Engineering University of CalgaryCalgary Canada 2009

[7] A Angrisano GNSSINS integration methods [PhD thesis]ldquoParthenoperdquo University of Naples 2010

[8] C Cai and Y Gao ldquoA combined GPSGLONASS navigationalgorithm for use with limited satellite visibilityrdquo Journal ofNavigation vol 62 no 4 pp 671ndash685 2009

[9] A Angrisano S Gaglione G Pugliano R Robustelli RSantamaria and M Vultaggio ldquoA stochastic sigma model forGLONASS satellite pseudorangerdquo Applied Geomatics vol 3 no1 pp 49ndash57 2011

[10] ICD-GLONASS Global Navigation Satellite System GLONASSInterface Control Document version 51 Moscow Russia 2008

[11] SC-159 of the RTCAMinimum Operational Performance Stan-dards for Global Positioning SystemWide Area AugmentationSystem Airborne Equipment Document DO-229D RTCAWashington DC USA 2006

[12] E M Mikhail Observations and Least Squares Harper amp Row1976

12 International Journal of Navigation and Observation

[13] D E Wells and E J Krakiwsky The Methods of Least SquaresLecture Notes no 18 Department of Surveying EngineeringUniversity of Brunswick 1971

[14] S Hewitson and J Wang ldquoGNSS receiver autonomous integritymonitoring (RAIM) performance analysisrdquo GPS Solutions vol10 no 3 pp 155ndash170 2006

[15] G Y Chin J H Kraemer and R G Brown ldquoGPS RAIMscreening out bad geometries underworst-case bias conditionsrdquoNavigation Journal of the Institute of Navigation vol 39 no 4pp 407ndash427 1992

[16] R G Brown and G Y Chin ldquoGPS RAIM calculation ofthreshold and protection radius using chi-square methods-a geometric approachrdquo Global Positioning System Institute ofNavigation vol 5 pp 155ndash179 1997

[17] M Petovello Real-time integration of a tactical-grade IMUand GPS for high-accuracy positioning and navigation [PhDthesis] UCGE Report no 20173 Department of GeomaticsEngineering University of Calgary Calgary Canada 2003

[18] W Baarda A Testing Procedure for Use in Geodetic NetworksNetherlands Geodetic Commission Publication on GeodesyNew Series 2 5 Delft The Netherlands 1968

[19] A K Brown ldquoReceiver autonomous integrity monitoring usinga 24-satellite GPS constellationrdquo Navigation Journal of TheInstitute of Navigation vol 5 pp 21ndash33 1998 Red Book ofRAIM

[20] H Kuusniemi User-level reliability and quality monitoringin satellite-based personal navigation [PhD thesis] TampereUniversity of Technology Tampere Finland 2005

[21] H Kuusniemi A Wieser G Lachapelle and J TakalaldquoUser-level reliability monitoring in urban personal satellite-navigationrdquo IEEE Transactions on Aerospace and ElectronicSystems vol 43 no 4 pp 1305ndash1318 2007

[22] A Angrisano S Gaglione and C Gioia ldquoRAIM algorithmsfor aided GNSS in urban scenariordquo in Proceedings of theUbiquitous Positioning Indoor Navigation and Location BasedService Helsinki Finland October 2012

[23] A LeickGPS Satellite Surveying JohnWiley amp Sons HobokenNJ USA 3rd edition 2004

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Electrical and Computer Engineering

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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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Navigation and Observation

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DistributedSensor Networks

International Journal of

International Journal of Navigation and Observation 3

A comprehensive description of the aforesaid differencesamongGPS andGLONASS is provided inAngrisano 2010 [7]

For our scope the main difference is related to thedifferent time scale adopted by the systems GPS time isconnected with UTC(USNO) the UTC maintained by USNaval Observatory UTC scale is occasionally adjusted toone second to keep the scale close to the mean solar timeGPS time scale differs from UTC(USNO) of an integernumber of seconds (called leap seconds currently 16 s) afurther difference between GPS and UTC(USNO) time scale(typically less than 100 ns) due to the different master clocksused is broadcast to the users within the GPS navigationmessage GLONASS time scale is connected to UTC(RU) theUTC maintained by Russia it is corrected by leap secondsaccording to the UTC adjustments so the difference betweenthese time scales is less than 1 millisecond and is broadcast inthe GLONASS navigation message

GPS and GLONASS time scales are connected by thefollowing relation [8 9]

119905GPS = 119905GLO + 120591119903 + 120591119906 + 120591119892 (3)

where 120591119903= 119905UTC(RU)minus119905GLO is broadcast within the GLONASS

navigation message 120591119906= 119905UTC(USNO) minus 119905UTC(RU) must be

estimated and 120591119892= 119905GPS minus119905UTC(USNO) is broadcast in the GPS

navigation messageTo perform the transformation (3) 120591

119906should be known

but this information is not provided in real time An esti-mation of 120591

119906is broadcast as nonimmediate parameter in

the GLONASS almanac [10] but does not take into accountthe intersystem hardware delay bias which is dependent onspecific receiver [8] Therefore when GPS and GLONASSmeasurements are used together 120591

119906is included in the esti-

mation process as unknown

23 Estimation of Navigation Parameters In this work theadopted estimation technique is the weighted least squares(LS) which uses only a measurement model made up bysimultaneous PR and PR rate observables

Regarding PR a set of equations like (1) after lineariza-tion around a nominal state becomes

Δ120588 = 119867120588lowast Δ119909 + 120576

120588

(4)

where Δ120588 is the difference between actual and predictedmeasurements 119867

120588is the design matrix 120576

120588

is the residualerror vector and Δ119909 is the state vector containing receivercoordinates and clock offset errors

Δ119909 = [Δ119875119879

Δ (119888120575119905GPS119906

)]

119879

(5)

If GPS and GLONASS measurements are used togetheran additional unknown must be estimated as explained inSection 22 and the state vector becomes

Δ119909 = [Δ119875119879

Δ (119888120575119905GPS119906

) Δ (119888120575119905Sys)]119879

(6)

where Δ(119888120575119905Sys) is the offset between GPS and GLONASStime scales

The measurement model of PR rate observable isΔ = 119867

lowast V + 120576

(7)

where Δ is the vector containing PR rate measurementscorrected for satellite motion 119867

is the design matrix 120576

isthe residual error vector and V is the velocity state vector

V = [119881119879 119888 120575119905GPS119906

]

119879

(8)

In this case the equations are linear for the unknowns and theGPSGLONASS combined use does not imply an additionalunknown because the drift between the system time scales isnegligible

For the PRmeasurement the follow accuracy dependenton satellite elevation is assumed

1205902

PR = 1205902

URA + 1205902

Iono + 1205902

Tropo + 1205902

mp (9)

where 1205902URA is the user range accuracy (URA) related to thesatellite ephemeris and clock broadcast in theGPSnavigationmessage [2] (for GLONASS this parameter is set in orderto take into account the ephemeris inaccuracy with respectto GPS) 1205902Iono is the accuracy related to ionosphere delayafter Klobuchar model application (whose expression is in[11]) 1205902Tropo is the accuracy related to troposphere error aftercorrection model application [11] and 1205902mp is the accuracyrelated to multipath error [11]

The PR rate measurement accuracy is assumed inverselyproportional to sin(El) where El is the satellite elevation PRand PR rate weights are the inverse of their accuracies

The optimization criterion of the LS is to minimize thesum of the squared residuals defined as

119903 = 119911 minus 119867 sdot (10)

where 119911 is the measurements vector and is the state vectorestimated with the considered technique [12 13]

3 Reliability Test

Reliability refers to the consistency of the results provided bya system internal and external reliability are respectively theability to detect gross errors and the effect of an undetectedblunder on the solution [14]

The integrity of a navigation system is defined as theability to provide timely warnings to users when the systemshould not be used [2 5] Reliability monitoring is based onstatistical test of the observation residuals with the aim ofdetecting and excluding measurement errors in this workthree different RAIM FDE techniques have been developedand their performance is evaluated in terms of RMS andmaximum error for the horizontal and vertical componentsand reliable availability

Before RAIM application a check is performed to screenout bad geometries which could imply erroneous detectionsin this work the WARP (Weighted-ARP) parameter a gen-eralization of the classical ARP [5 15] is used as integritygeometry parameter and its expression is

WARP =WSlopemax sdot radic119879119892 (11)

4 International Journal of Navigation and Observation

where WSlopemax is the maximum of the weighted slope [516] which is an extension of the classical slope and takes intoaccount the measurement different accuracies and 119879

119892is the

threshold of the global test and will be discussed shortlyThe FDE schemes analysed are obtained by combining

different basic statistical tests Specifically a so-called globaltest (GT) is adopted to verify the self-consistency of themeasure set if the measurement set is declared inconsistenta local test (LT) is performed to identify and reject a blunderafter a separability check Separability refers to the abilityto separate any two measurements from one another [14]this concept is primary to avoid the incorrect exclusion ofblunder-free measurements

In the first test the decision variable 119863 is defined asthe sum of the squares of the residuals weighted by theweighting matrix119882 (consisting of the inverse of the squaredmeasurement accuracies (9) on the diagonal and of zerosoutside the diagonal)

119863 = 119903119879

119882119903 (12)

where 119863 is assumed to follow a 1205942 distribution with (119898 minus 119899)degrees of freedom or redundancy defined as the differencebetween the number ofmeasurements119898 and state dimension119899 an inconsistency in the observations is assumed if 119863exceeds the threshold 119879

119892

119879119892= 1205942

1minus119875FA (119898minus119899) (13)

where the notation 12059421minus119875FA (119898minus119899)

indicates the abscissa corre-sponding to a probability value (1 minus 119875FA) of a 120594

2 distributionof (119898 minus 119899) order 119875FA is the probability of false alarm andis fixed in accordance with application requirements 119875FAtypical value for urban navigation is 01 [17] while 119879

119892varies

with redundancyIf the GT does not pass a LT is performed analyzing

standardized residual 119908119894[18]

119908119894=

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

119903119894

radic(119862119903)119894119894

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

119894 = 1 119898 (14)

where 119862119903is the residuals variance covariance matrix

119908119894are assumed to be normally distributed each element

119908119894that exceeds the local threshold 119879

119897 corresponding to the

probability value (1 minus 119875FA2) of a normal distribution isflagged as blunder The measurement corresponding to thelargest standardized residual exceeding 119879

119897is excluded or

deweighted (depending on the method) after a separabilitycheck a large blunder could cause multiple local test failuresand therefore an erroneous measurement rejection In RAIMtechniques a parameter properly representing the separabil-ity is the correlation coefficient of119908

119894 shown in the following

120574119894119895=

(119862119903)119894119895

radic(119862119903)119894119894

sdot (119862119903)119895119895

119894 119895 = 1 119898 (15)

In the separability check if 120574119894119895exceeds a threshold (in this

case 09) the measurement suspected to be a blunder is notrejected or deweighted because it is strictly correlated toanother measurement

z H W

LSestimator

WARPcheck

Solutionimpossible

to check

Global test

Not ok

OkResiduals

Subset

Not ok

Solution unreliable

Solution reliable

Ok

Not ok andall subset checked

Redu

ndan

cyle

0

Figure 1 Subset algorithm

31 Subset Subset testing is an FDE technique that uses onlyGT [5 19 20] If a measurements set is declared inconsistentall the possible combinations of measurements are checkedto find a subset from which the supposed blunders areexcluded Only the subset that passes the GT and is declaredconsistent is used to compute the navigation solution ifmore subsets pass the GT the set with the minimum statisticvariable and the largest number of measurements is chosenIn this technique the separability check is not performedbecause standardized residuals are not analysed A completescheme of the algorithm implemented is shown in Figure 1

The Subset test is applied separately to pseudorangeand Doppler measurements and is computationally heavybecause several measurement combinations have to bechecked [20]

32 Forward-Backward Forward-Backward is an FDE tech-nique that involves the use of both global and local tests itconsists of two different steps [20ndash22] The first algorithmsection called Forward is carried out to identify and excludeerroneous measurements A measurement set is prelimi-nary tested for the integrity geometry to screen out badgeometrieswhich could imply erroneous detections After thepreliminary check the GT is carried out in order to verifymeasurements consistency If global test declares the setinconsistent the LT is performed to identify and exclude theerroneous measurement An erroneous rejection of a goodobservation is possible due to the mutual influence of the

International Journal of Navigation and Observation 5

z H W

LSestimator

WARPcheck

Solutionimpossible

to check

Global test

Not ok

Not ok

Not ok

Not ok

Ok Residuals

Local test

Ok

Ok

Solution unreliable

Separability check

rejections

Rejection reentry

LS estimator

Residuals

Global test

Solution reliable

BackwardRe

dund

ancyle

0

119870

119870 gt 1

119870 le 1

Figure 2 Forward-Backward algorithm

observations to avoid erroneous rejections the separabilitycheck is carried out the measurement flagged as possibleblunder is excluded only if it is not correlated with othermeasures Forward process is performed recursively until nomore erroneous measurements are found and the solution isdeclared reliable or unreliable

If the solution is declared reliable and 119896 measurementsare excluded (with 119896 gt 1) the Backward scheme is appliedto reintroduce observations wrongly excluded Rejectedmea-surements are iteratively implemented backward and theglobal test is performed the observation set which passes theGT is used to compute navigation solution

A complete scheme of the Forward-Backward techniqueis shown in Figure 2

33 Danish Least squares estimation is very susceptible tooutliers a possible way to solve this problem is an iterativedeweighing of erroneous measurements [20 23] The Danishmethod is an iteratively reweighted least squares algorithmused in geodetic applications for a long time this methodis used to achieve consistency between the measurementsby modifying the a priori weights In this paper the Danishmethod is used for signal degraded environments in orderto minimize the effect of blunders on the least squareadjustment This technique involves the use of the GT toverify the consistency of the measurements and the LT toidentify and deweight the outliers

A measurement set is checked for the geometry as inthe previous FDE techniques and then the GT is performedIf observations are declared not consistent by GT the LT iscarried out to identify the blunder and its related weightis reduced only if allowed by the separability check (ie ifthe measurement is not strictly correlated to the others)The variance of the suspected measurement is exponentiallyincreased (and consequently the weight is decreased) asfollows

1205902

119894119895+1

= 1205902

1198940

lowast

119890119908119894119895119879119897 if 119908

119894119895gt 119879119897

1 if 119908119894119895le 119879119897

(16)

where 1205902119894119895+1

is the variance of the 119894th observation after 119895 + 1iterations 1205902

1198940

is the a priori variance of the observation and119908119894119895is the standardized residual of the 119894th observation after 119895

iterationsIf the normalized residual of the 119894th observation does not

exceed 119879119897 its variance is maintained (the measurement is not

deweighted)The scheme of the Danish procedure is shown in

Figure 3

4 Test and Results

41 Test A static test of about 6 hours was carried out onFebruary 24 2012 The antenna was placed on the roof of the

6 International Journal of Navigation and Observation

z H W

LSestimator

WARPcheck

Solutionimpossible

to check

Global test

Residuals

Local test

Ok

Ok

Ok

Solution unreliable

Separability check

Measurementdeweight

Solution reliable

Not ok

Not ok

Not ok

Not ok

Redu

ndan

cyle

0

Figure 3 Danish algorithm

PANG (PArthenope Navigation Group) laboratory buildingCentro Direzionale of Naples (Italy) a typical example ofurban canyon (as shown in Figure 4) in this environmentmanyGNSS signals are blocked by skyscrapers or are stronglydegraded for the multipath phenomenon The only testperformed for this research was static to simplify the erroranalysis for the position (the antenna is placed in a well-known location) and for the velocity (the antenna is fixedso its velocity is zero) a kinematic test needs a referencefor error analysis more complicated to obtain and will beperformed in the future develop of this research Howeverthe static test choice does not limit the research validitybecause the operational environment is a typical signal-degraded scenario that is an urban canyon

The used receiver is a NovAtel FlexPak-G2 able to pro-vide single frequency (L1) GPSGLONASS measurementsconnected to a NovAtel antenna 702-GG

The reference solution is computed by a postprocess-ing geodetic method guaranteeing a position accuracyof mm order the coordinates of the antenna and the relativeaccuracies are shown in Table 2

42 Results Herein eight different GNSS configurations arecompared combining the two systems considered and thedifferent RAIM scheme developed

Antenna p

osition

Figure 4 Antenna position

(i) GPS only without RAIM application (briefly indi-cated as GPS no RAIM)

(ii) GPSGLONASS without RAIM application (GG noRAIM)

(iii) GPS only with Subset RAIM application (GPS Sub)(iv) GPSGLONASS with Subset RAIM application (GG

Sub)(v) GPS only with Forward-Backward RAIM application

(GPS FB)(vi) GPSGLONASS with Forward-Backward RAIM

application (GG FB)(vii) GPS only with Danish method applied (GPS Dan)(viii) GPSGLONASS with Danish method applied (GG

Dan)

Results are analyzed in terms of RMS and maximum errorsfor horizontal and vertical components in the position andvelocity domains The percentage of time mission whensolution is available is referred to as solution availability incase of RAIM application the concept of reliable availabilitydefined as the time percentage when solution is reliable isintroduced

The session is characterized by high solution availability(about 98 forGPS and 100GPSGLONASS configuration)and by very large errors (more than 1 km without RAIMapplication) the application of the developed RAIM schemesreduces the availability of the position solution In GPSstand-alone configuration the Subset test guarantees thehighest reliable availability (762) while 20 of solutionsare flagged as unreliable for Danish and Forward-Backwardschemes the reliable availability is halved with respect tothe solution availability The inclusion of GLONASS mea-surements without RAIM application improves the solutionavailability of 2 with respect to the GPS stand-alone con-figuration For the GPSGLONASS multiconstellation theSubset testing guarantees an high reliable availability (only35 of solutions are rejected by the quality control) which isincreased to 20 with respect to the GPS only configurationThe effect of the GLONASS inclusion is more evident in the

International Journal of Navigation and Observation 7

Danish

GPS no RAIM 98GG no RAIM 100

(m)

GPS Dan 49GG Dan 76

1000

500

0

minus500

minus1000

10005000minus500minus1000

(m)

Forward-Backward

GPS FB 44GPS no RAIM 98GG no RAIM 100 GG FB 74

(m)

1000

500

0

minus500

minus1000

10005000minus500minus1000

(m)

Subset

GPS no RAIM 98 GPS Sub 76GG no RAIM 100 GG Sub 97

(m)

1000

500

0

minus500

minus1000

10005000minus500minus1000

(m)

RAIM comparison

GPS Sub 76GPS FB 44GG Sub 97GG FB 74

GG Dan 76

GPS Dan 49

3002001000minus300 minus200 minus100

200

100

0

minus300

minus200

minus100

(m)

(m)

Figure 5 Horizontal position

Table 2 PANG station coordinates and accuracy

Latitude(deg min sec)

Longitude(deg min sec)

Height(m)

Standard deviation north(m)

Standard deviation east(m)

Standard deviation up(m)

40∘51101584023516310158401015840 14∘17101584003899710158401015840 906257 00006 00008 00011

Danish and Forward-Backward schemes in these cases thereliable availability reaches about 75 with an improvingof 25ndash30 with respect to the GPS only configurationsThe solution availability and the reliable availability of theposition are summarized in Table 3

Similar results are obtained in velocity domain theGLONASSmeasurements increase the reliable availability forthe three RAIM schemes relative to GPS only configurationsas in the position domain the Subset testing guaranteeshigher reliable availability with respect to the other developedschemesThe solution availability and the reliable availabilityof the velocity are summarized in Table 4

The configurations without RAIM are characterized bylarge errors in case of GPS only the maximum horizontal

error exceeds 1 km and the inclusion of GLONASS measure-ments improves the performance reducing the maximumerror to 245meter RAIM application improves all consideredconfigurations reducing both maximum and RMS errorsas shown in Figure 5 for the horizontal component in theupper figures and in the bottom left one the performanceof RAIM schemes is compared with the basic configurations(no RAIM) and in all cases the clouds relative to theRAIM solutions are significantly reduced with respect tothe baseline configurations In the bottom right of Figure 5the performances of the three developed RAIM schemes arecompared from a qualitative analysis the cloud relative tothe GPSGLONASS with forward-backward scheme is moreconcentrated with respect to the others

8 International Journal of Navigation and Observation

Danish

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

350

300

250

150

200

100

50

0

(m)

GPS Dan 49GG Dan 76

Values upto 16859

Forward-Backward

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 44GPS no RAIM 98GG no RAIM 100 GG FB 74

350

300

250

150

200

100

50

0

(m)

Values upto 16859

Subset

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 76GG no RAIM 100 GG Sub 97

350

300

250

150

200

100

50

0

(m)

Values upto 16859

RAIM comparison

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 76GPS FB 44GG Sub 97GG FB 74

GG Dan 76

GPS Dan 49

350

300

250

150

200

100

50

0

(m)

Figure 6 Horizontal position error

Table 3 Position availabilityreliable availability

No RAIMavailability

Subsetreliable availability

Danishreliable availability

Forward-Backwardreliable availability

GPS 981 762 490 436GG 100 965 758 740

In Figure 6 the horizontal position errors are plottedIn the upper figures and in the bottom left one the errorsof the three RAIM schemes are compared with the ldquonoRAIMrdquo configurations the errors of the RAIM configura-tions represented by the green and yellow dots are lowerthan the errors of the no RAIM configurations confirmingthe aforesaid qualitative analysis In the bottom right ofFigure 6 the RAIM errors are compared the Subset testingis characterized by the highest reliable availability but also bythe highest errors while the other schemes provide similarperformance Also in these cases the benefits of the inclusionof GLONASSmeasurements are clear all theGPSGLONASSconfigurations represented by the black yellow andmagenta

dots are lower with respect to the corresponding GPS onlyconfigurations The GLONASS measurements improve theredundancy increasing the RAIM efficiency

In Figure 7 the horizontal velocity errors are plotted ldquonoRAIMrdquo configurations are characterized by high error forGPS only case higher than 50ms the GLONASS inclusionreduces the errors up to 044ms As done for the positionerrors the RAIM schemes are first compared with the ldquonoRAIMrdquo configurations in the velocity domain the benefits oftheRAIMapplication are less evidentwith respect to the posi-tion domain due to the robustness of the Doppler observableIn the bottom right part of Figure 7 the horizontal velocityerrors obtained with the FDE techniques are compared as in

International Journal of Navigation and Observation 9

1

08

06

04

02

0

Danish(m

s)

Values upto 688

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

GPS Dan 56GG Dan 73

Forward-Backward1

08

06

04

02

0

(ms

)

Values upto 688

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 56GPS no RAIM 98GG no RAIM 100 GG FB 73

to 688

Subset1

08

06

04

02

0

(ms

)

Values up

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 70GG no RAIM 100 GG Sub 98

RAIM comparison1

08

06

04

02

0

(ms

)

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 70GPS FB 56GG Sub 98GG FB 73

GG Dan 73

GPS Dan 56

Figure 7 Horizontal velocity error

the position domain the Subset testing is characterized by thehighest reliable availability but also by the highest errors theother schemes provide similar performance

In Figures 8 and 9 the plots relative to the verticalcomponents of the position and velocity show the benefits ofRAIM use

The qualitative analysis provided by the previous plotsis confirmed by the results summarized in Tables 5 and 6 indetail the RAIM use improves significantly the performancein terms of RMS and maximum errors for the vertical andhorizontal components maintaining a high reliable availabil-ity in case of GG configurations The RMS horizontal errorsare halved and even better results are evident on the verticalcomponent The maximum horizontal and vertical errors forGG Subset configuration are degraded due to an erroneousmeasurements rejection in the presence of multiple blundersbetter results are obtained with the Forward-Backward andDanish methods

5 Conclusions

In signal-degraded environments such as urban canyonsGNSS navigation suffers the presence of gross errors which

strongly worsen the solution therefore in these scenariosthe use of RAIM algorithms is necessary In this workthree RAIM FDE schemes well known in literature [1718 20ndash23] are adopted Subset testing Forward-Backwardand Danish The first method is based uniquely on theGT while the others include the use of the LT too Thesemethods have been enriched adopting a preliminary checkon the satellite geometry to screen out configurations toopoor to be tested successfully and a separability test toavoid the exclusion of blunder-free measurements in caseof observations strongly correlated The main scope of thiswork is to verify the effectiveness of the RAIM schemes withthe proposed modifications in urban scenario Moreover thebenefit assessment of GLONASS inclusion is of interest too

The obtained results show the effectiveness of the adoptedalgorithms in terms of reliable availability and of RMS andmaximum errors The reliable availability is the percentageof time mission when the solution is declared reliable bythe adopted RAIM the highest value of this parameter isobtained with the Subset method which provides the largesterrors too The Forward-Backward and the Danish methodsare instead characterized by similar performances and by thesmallest errors demonstrating the validity of the separability

10 International Journal of Navigation and Observation

Danish

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

1500

100

500

0

(m)

GPS Dan 49GG Dan 76

1500

100

500

0

(m)

Forward-Backward

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 44GPS no RAIM 98GG no RAIM 100 GG FB 74

1500

100

500

0

(m)

Subset

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 76GG no RAIM 100 GG Sub 97

RAIM comparison

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 76GPS FB 44GG Sub 97GG FB 74

400

300

100

200

0

(m)

GG Dan 76

GPS Dan 49

Figure 8 Altitude

Table 4 Velocity availabilityreliable availability

No RAIMavailability

Subsetreliable availability

Danishreliable availability

Forward-backwardreliable availability

GPS 981 705 563 563GG 100 978 734 729

Table 5 Position results

RMS (m) MAX (m)H V H V

No RAIM GPS 549 856 12645 16859GG 348 654 2456 3722

Subset GPS 275 564 2990 3270GG 151 361 3216 3985

Forward-backward GPS 179 445 1597 2858GG 134 313 1597 2843

Danish GPS 232 561 1597 3431GG 160 381 1597 2815

Table 6 Velocity results

RMS (ms) MAX (ms)H V H V

No RAIM GPS 0968 1573 68750 108240GG 0042 0060 0442 0822

Subset GPS 0053 0084 0669 1251GG 0042 0067 0928 1337

Forward-Backward GPS 0047 0074 0649 1251GG 0036 0055 0367 0653

Danish GPS 0046 0073 0649 1251GG 0035 0054 0295 0642

International Journal of Navigation and Observation 11

1

08

06

04

02

0

Danish(m

s)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

GPS Dan 56GG Dan 73

Forward-Backward1

08

06

04

02

0

(ms

)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 56GPS no RAIM 98GG no RAIM 100 GG FB 73

Subset1

08

06

04

02

0

(ms

)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 70GG no RAIM 100 GG Sub 98

RAIM comparison1

08

06

04

02

0

(ms

)

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 70GPS FB 56GG Sub 98GG FB 73

GG Dan 73

GPS Dan 56

Figure 9 Vertical velocity error

check module (which cannot be applied to Subset method)The proposed algorithms have been tested on both positionand velocity domains showing comparable robustness

GPSGLONASS combination shows evident perform-ance improvements for all the considered parameters rela-tive to GPS only configurations

References

[1] B Hoffmann-Wellenhof H Lichtenegger and J CollinsGlobalPositioning System Theory and Practice Springer New YorkNY USA 1992

[2] ED Kaplan and J Hegarty ldquoFundamentals of satellite naviga-tionrdquo in Understanding GPS Principles and Applications E DKaplan Ed ArtechHouseMobile Communications Series 2ndedition 2006

[3] A Angrisano M Petovello and G Pugliano ldquoGNSSINSintegration in vehicular urban navigationrdquo in Proceedings ofthe 23rd International Technical Meeting of the Satellite Divisionof the Institute of Navigation (GNSS rsquo10) pp 1505ndash1512 TheInstitute of Navigation Portland Ore USA September 2010

[4] A Angrisano M Petovello and G Pugliano ldquoBenefits ofcombined GPSGLONASS with low-cost MEMS IMUs forvehicular urban navigationrdquo Sensors vol 12 no 4 pp 5134ndash5158 2012

[5] B Parkinson and J J Spilker Global Positioning System TheoryAnd Applications vol 1-2 American Institute of Aeronauticsand Astronautics Washington DC USA 1996

[6] C Cai Precise point positioning using dual-frequency GPS andGLONASSmeasurements [MS thesis] UCGEReport no 20291Department of Geomatics Engineering University of CalgaryCalgary Canada 2009

[7] A Angrisano GNSSINS integration methods [PhD thesis]ldquoParthenoperdquo University of Naples 2010

[8] C Cai and Y Gao ldquoA combined GPSGLONASS navigationalgorithm for use with limited satellite visibilityrdquo Journal ofNavigation vol 62 no 4 pp 671ndash685 2009

[9] A Angrisano S Gaglione G Pugliano R Robustelli RSantamaria and M Vultaggio ldquoA stochastic sigma model forGLONASS satellite pseudorangerdquo Applied Geomatics vol 3 no1 pp 49ndash57 2011

[10] ICD-GLONASS Global Navigation Satellite System GLONASSInterface Control Document version 51 Moscow Russia 2008

[11] SC-159 of the RTCAMinimum Operational Performance Stan-dards for Global Positioning SystemWide Area AugmentationSystem Airborne Equipment Document DO-229D RTCAWashington DC USA 2006

[12] E M Mikhail Observations and Least Squares Harper amp Row1976

12 International Journal of Navigation and Observation

[13] D E Wells and E J Krakiwsky The Methods of Least SquaresLecture Notes no 18 Department of Surveying EngineeringUniversity of Brunswick 1971

[14] S Hewitson and J Wang ldquoGNSS receiver autonomous integritymonitoring (RAIM) performance analysisrdquo GPS Solutions vol10 no 3 pp 155ndash170 2006

[15] G Y Chin J H Kraemer and R G Brown ldquoGPS RAIMscreening out bad geometries underworst-case bias conditionsrdquoNavigation Journal of the Institute of Navigation vol 39 no 4pp 407ndash427 1992

[16] R G Brown and G Y Chin ldquoGPS RAIM calculation ofthreshold and protection radius using chi-square methods-a geometric approachrdquo Global Positioning System Institute ofNavigation vol 5 pp 155ndash179 1997

[17] M Petovello Real-time integration of a tactical-grade IMUand GPS for high-accuracy positioning and navigation [PhDthesis] UCGE Report no 20173 Department of GeomaticsEngineering University of Calgary Calgary Canada 2003

[18] W Baarda A Testing Procedure for Use in Geodetic NetworksNetherlands Geodetic Commission Publication on GeodesyNew Series 2 5 Delft The Netherlands 1968

[19] A K Brown ldquoReceiver autonomous integrity monitoring usinga 24-satellite GPS constellationrdquo Navigation Journal of TheInstitute of Navigation vol 5 pp 21ndash33 1998 Red Book ofRAIM

[20] H Kuusniemi User-level reliability and quality monitoringin satellite-based personal navigation [PhD thesis] TampereUniversity of Technology Tampere Finland 2005

[21] H Kuusniemi A Wieser G Lachapelle and J TakalaldquoUser-level reliability monitoring in urban personal satellite-navigationrdquo IEEE Transactions on Aerospace and ElectronicSystems vol 43 no 4 pp 1305ndash1318 2007

[22] A Angrisano S Gaglione and C Gioia ldquoRAIM algorithmsfor aided GNSS in urban scenariordquo in Proceedings of theUbiquitous Positioning Indoor Navigation and Location BasedService Helsinki Finland October 2012

[23] A LeickGPS Satellite Surveying JohnWiley amp Sons HobokenNJ USA 3rd edition 2004

International Journal of

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Active and Passive Electronic Components

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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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

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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

4 International Journal of Navigation and Observation

where WSlopemax is the maximum of the weighted slope [516] which is an extension of the classical slope and takes intoaccount the measurement different accuracies and 119879

119892is the

threshold of the global test and will be discussed shortlyThe FDE schemes analysed are obtained by combining

different basic statistical tests Specifically a so-called globaltest (GT) is adopted to verify the self-consistency of themeasure set if the measurement set is declared inconsistenta local test (LT) is performed to identify and reject a blunderafter a separability check Separability refers to the abilityto separate any two measurements from one another [14]this concept is primary to avoid the incorrect exclusion ofblunder-free measurements

In the first test the decision variable 119863 is defined asthe sum of the squares of the residuals weighted by theweighting matrix119882 (consisting of the inverse of the squaredmeasurement accuracies (9) on the diagonal and of zerosoutside the diagonal)

119863 = 119903119879

119882119903 (12)

where 119863 is assumed to follow a 1205942 distribution with (119898 minus 119899)degrees of freedom or redundancy defined as the differencebetween the number ofmeasurements119898 and state dimension119899 an inconsistency in the observations is assumed if 119863exceeds the threshold 119879

119892

119879119892= 1205942

1minus119875FA (119898minus119899) (13)

where the notation 12059421minus119875FA (119898minus119899)

indicates the abscissa corre-sponding to a probability value (1 minus 119875FA) of a 120594

2 distributionof (119898 minus 119899) order 119875FA is the probability of false alarm andis fixed in accordance with application requirements 119875FAtypical value for urban navigation is 01 [17] while 119879

119892varies

with redundancyIf the GT does not pass a LT is performed analyzing

standardized residual 119908119894[18]

119908119894=

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

119903119894

radic(119862119903)119894119894

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

119894 = 1 119898 (14)

where 119862119903is the residuals variance covariance matrix

119908119894are assumed to be normally distributed each element

119908119894that exceeds the local threshold 119879

119897 corresponding to the

probability value (1 minus 119875FA2) of a normal distribution isflagged as blunder The measurement corresponding to thelargest standardized residual exceeding 119879

119897is excluded or

deweighted (depending on the method) after a separabilitycheck a large blunder could cause multiple local test failuresand therefore an erroneous measurement rejection In RAIMtechniques a parameter properly representing the separabil-ity is the correlation coefficient of119908

119894 shown in the following

120574119894119895=

(119862119903)119894119895

radic(119862119903)119894119894

sdot (119862119903)119895119895

119894 119895 = 1 119898 (15)

In the separability check if 120574119894119895exceeds a threshold (in this

case 09) the measurement suspected to be a blunder is notrejected or deweighted because it is strictly correlated toanother measurement

z H W

LSestimator

WARPcheck

Solutionimpossible

to check

Global test

Not ok

OkResiduals

Subset

Not ok

Solution unreliable

Solution reliable

Ok

Not ok andall subset checked

Redu

ndan

cyle

0

Figure 1 Subset algorithm

31 Subset Subset testing is an FDE technique that uses onlyGT [5 19 20] If a measurements set is declared inconsistentall the possible combinations of measurements are checkedto find a subset from which the supposed blunders areexcluded Only the subset that passes the GT and is declaredconsistent is used to compute the navigation solution ifmore subsets pass the GT the set with the minimum statisticvariable and the largest number of measurements is chosenIn this technique the separability check is not performedbecause standardized residuals are not analysed A completescheme of the algorithm implemented is shown in Figure 1

The Subset test is applied separately to pseudorangeand Doppler measurements and is computationally heavybecause several measurement combinations have to bechecked [20]

32 Forward-Backward Forward-Backward is an FDE tech-nique that involves the use of both global and local tests itconsists of two different steps [20ndash22] The first algorithmsection called Forward is carried out to identify and excludeerroneous measurements A measurement set is prelimi-nary tested for the integrity geometry to screen out badgeometrieswhich could imply erroneous detections After thepreliminary check the GT is carried out in order to verifymeasurements consistency If global test declares the setinconsistent the LT is performed to identify and exclude theerroneous measurement An erroneous rejection of a goodobservation is possible due to the mutual influence of the

International Journal of Navigation and Observation 5

z H W

LSestimator

WARPcheck

Solutionimpossible

to check

Global test

Not ok

Not ok

Not ok

Not ok

Ok Residuals

Local test

Ok

Ok

Solution unreliable

Separability check

rejections

Rejection reentry

LS estimator

Residuals

Global test

Solution reliable

BackwardRe

dund

ancyle

0

119870

119870 gt 1

119870 le 1

Figure 2 Forward-Backward algorithm

observations to avoid erroneous rejections the separabilitycheck is carried out the measurement flagged as possibleblunder is excluded only if it is not correlated with othermeasures Forward process is performed recursively until nomore erroneous measurements are found and the solution isdeclared reliable or unreliable

If the solution is declared reliable and 119896 measurementsare excluded (with 119896 gt 1) the Backward scheme is appliedto reintroduce observations wrongly excluded Rejectedmea-surements are iteratively implemented backward and theglobal test is performed the observation set which passes theGT is used to compute navigation solution

A complete scheme of the Forward-Backward techniqueis shown in Figure 2

33 Danish Least squares estimation is very susceptible tooutliers a possible way to solve this problem is an iterativedeweighing of erroneous measurements [20 23] The Danishmethod is an iteratively reweighted least squares algorithmused in geodetic applications for a long time this methodis used to achieve consistency between the measurementsby modifying the a priori weights In this paper the Danishmethod is used for signal degraded environments in orderto minimize the effect of blunders on the least squareadjustment This technique involves the use of the GT toverify the consistency of the measurements and the LT toidentify and deweight the outliers

A measurement set is checked for the geometry as inthe previous FDE techniques and then the GT is performedIf observations are declared not consistent by GT the LT iscarried out to identify the blunder and its related weightis reduced only if allowed by the separability check (ie ifthe measurement is not strictly correlated to the others)The variance of the suspected measurement is exponentiallyincreased (and consequently the weight is decreased) asfollows

1205902

119894119895+1

= 1205902

1198940

lowast

119890119908119894119895119879119897 if 119908

119894119895gt 119879119897

1 if 119908119894119895le 119879119897

(16)

where 1205902119894119895+1

is the variance of the 119894th observation after 119895 + 1iterations 1205902

1198940

is the a priori variance of the observation and119908119894119895is the standardized residual of the 119894th observation after 119895

iterationsIf the normalized residual of the 119894th observation does not

exceed 119879119897 its variance is maintained (the measurement is not

deweighted)The scheme of the Danish procedure is shown in

Figure 3

4 Test and Results

41 Test A static test of about 6 hours was carried out onFebruary 24 2012 The antenna was placed on the roof of the

6 International Journal of Navigation and Observation

z H W

LSestimator

WARPcheck

Solutionimpossible

to check

Global test

Residuals

Local test

Ok

Ok

Ok

Solution unreliable

Separability check

Measurementdeweight

Solution reliable

Not ok

Not ok

Not ok

Not ok

Redu

ndan

cyle

0

Figure 3 Danish algorithm

PANG (PArthenope Navigation Group) laboratory buildingCentro Direzionale of Naples (Italy) a typical example ofurban canyon (as shown in Figure 4) in this environmentmanyGNSS signals are blocked by skyscrapers or are stronglydegraded for the multipath phenomenon The only testperformed for this research was static to simplify the erroranalysis for the position (the antenna is placed in a well-known location) and for the velocity (the antenna is fixedso its velocity is zero) a kinematic test needs a referencefor error analysis more complicated to obtain and will beperformed in the future develop of this research Howeverthe static test choice does not limit the research validitybecause the operational environment is a typical signal-degraded scenario that is an urban canyon

The used receiver is a NovAtel FlexPak-G2 able to pro-vide single frequency (L1) GPSGLONASS measurementsconnected to a NovAtel antenna 702-GG

The reference solution is computed by a postprocess-ing geodetic method guaranteeing a position accuracyof mm order the coordinates of the antenna and the relativeaccuracies are shown in Table 2

42 Results Herein eight different GNSS configurations arecompared combining the two systems considered and thedifferent RAIM scheme developed

Antenna p

osition

Figure 4 Antenna position

(i) GPS only without RAIM application (briefly indi-cated as GPS no RAIM)

(ii) GPSGLONASS without RAIM application (GG noRAIM)

(iii) GPS only with Subset RAIM application (GPS Sub)(iv) GPSGLONASS with Subset RAIM application (GG

Sub)(v) GPS only with Forward-Backward RAIM application

(GPS FB)(vi) GPSGLONASS with Forward-Backward RAIM

application (GG FB)(vii) GPS only with Danish method applied (GPS Dan)(viii) GPSGLONASS with Danish method applied (GG

Dan)

Results are analyzed in terms of RMS and maximum errorsfor horizontal and vertical components in the position andvelocity domains The percentage of time mission whensolution is available is referred to as solution availability incase of RAIM application the concept of reliable availabilitydefined as the time percentage when solution is reliable isintroduced

The session is characterized by high solution availability(about 98 forGPS and 100GPSGLONASS configuration)and by very large errors (more than 1 km without RAIMapplication) the application of the developed RAIM schemesreduces the availability of the position solution In GPSstand-alone configuration the Subset test guarantees thehighest reliable availability (762) while 20 of solutionsare flagged as unreliable for Danish and Forward-Backwardschemes the reliable availability is halved with respect tothe solution availability The inclusion of GLONASS mea-surements without RAIM application improves the solutionavailability of 2 with respect to the GPS stand-alone con-figuration For the GPSGLONASS multiconstellation theSubset testing guarantees an high reliable availability (only35 of solutions are rejected by the quality control) which isincreased to 20 with respect to the GPS only configurationThe effect of the GLONASS inclusion is more evident in the

International Journal of Navigation and Observation 7

Danish

GPS no RAIM 98GG no RAIM 100

(m)

GPS Dan 49GG Dan 76

1000

500

0

minus500

minus1000

10005000minus500minus1000

(m)

Forward-Backward

GPS FB 44GPS no RAIM 98GG no RAIM 100 GG FB 74

(m)

1000

500

0

minus500

minus1000

10005000minus500minus1000

(m)

Subset

GPS no RAIM 98 GPS Sub 76GG no RAIM 100 GG Sub 97

(m)

1000

500

0

minus500

minus1000

10005000minus500minus1000

(m)

RAIM comparison

GPS Sub 76GPS FB 44GG Sub 97GG FB 74

GG Dan 76

GPS Dan 49

3002001000minus300 minus200 minus100

200

100

0

minus300

minus200

minus100

(m)

(m)

Figure 5 Horizontal position

Table 2 PANG station coordinates and accuracy

Latitude(deg min sec)

Longitude(deg min sec)

Height(m)

Standard deviation north(m)

Standard deviation east(m)

Standard deviation up(m)

40∘51101584023516310158401015840 14∘17101584003899710158401015840 906257 00006 00008 00011

Danish and Forward-Backward schemes in these cases thereliable availability reaches about 75 with an improvingof 25ndash30 with respect to the GPS only configurationsThe solution availability and the reliable availability of theposition are summarized in Table 3

Similar results are obtained in velocity domain theGLONASSmeasurements increase the reliable availability forthe three RAIM schemes relative to GPS only configurationsas in the position domain the Subset testing guaranteeshigher reliable availability with respect to the other developedschemesThe solution availability and the reliable availabilityof the velocity are summarized in Table 4

The configurations without RAIM are characterized bylarge errors in case of GPS only the maximum horizontal

error exceeds 1 km and the inclusion of GLONASS measure-ments improves the performance reducing the maximumerror to 245meter RAIM application improves all consideredconfigurations reducing both maximum and RMS errorsas shown in Figure 5 for the horizontal component in theupper figures and in the bottom left one the performanceof RAIM schemes is compared with the basic configurations(no RAIM) and in all cases the clouds relative to theRAIM solutions are significantly reduced with respect tothe baseline configurations In the bottom right of Figure 5the performances of the three developed RAIM schemes arecompared from a qualitative analysis the cloud relative tothe GPSGLONASS with forward-backward scheme is moreconcentrated with respect to the others

8 International Journal of Navigation and Observation

Danish

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

350

300

250

150

200

100

50

0

(m)

GPS Dan 49GG Dan 76

Values upto 16859

Forward-Backward

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 44GPS no RAIM 98GG no RAIM 100 GG FB 74

350

300

250

150

200

100

50

0

(m)

Values upto 16859

Subset

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 76GG no RAIM 100 GG Sub 97

350

300

250

150

200

100

50

0

(m)

Values upto 16859

RAIM comparison

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 76GPS FB 44GG Sub 97GG FB 74

GG Dan 76

GPS Dan 49

350

300

250

150

200

100

50

0

(m)

Figure 6 Horizontal position error

Table 3 Position availabilityreliable availability

No RAIMavailability

Subsetreliable availability

Danishreliable availability

Forward-Backwardreliable availability

GPS 981 762 490 436GG 100 965 758 740

In Figure 6 the horizontal position errors are plottedIn the upper figures and in the bottom left one the errorsof the three RAIM schemes are compared with the ldquonoRAIMrdquo configurations the errors of the RAIM configura-tions represented by the green and yellow dots are lowerthan the errors of the no RAIM configurations confirmingthe aforesaid qualitative analysis In the bottom right ofFigure 6 the RAIM errors are compared the Subset testingis characterized by the highest reliable availability but also bythe highest errors while the other schemes provide similarperformance Also in these cases the benefits of the inclusionof GLONASSmeasurements are clear all theGPSGLONASSconfigurations represented by the black yellow andmagenta

dots are lower with respect to the corresponding GPS onlyconfigurations The GLONASS measurements improve theredundancy increasing the RAIM efficiency

In Figure 7 the horizontal velocity errors are plotted ldquonoRAIMrdquo configurations are characterized by high error forGPS only case higher than 50ms the GLONASS inclusionreduces the errors up to 044ms As done for the positionerrors the RAIM schemes are first compared with the ldquonoRAIMrdquo configurations in the velocity domain the benefits oftheRAIMapplication are less evidentwith respect to the posi-tion domain due to the robustness of the Doppler observableIn the bottom right part of Figure 7 the horizontal velocityerrors obtained with the FDE techniques are compared as in

International Journal of Navigation and Observation 9

1

08

06

04

02

0

Danish(m

s)

Values upto 688

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

GPS Dan 56GG Dan 73

Forward-Backward1

08

06

04

02

0

(ms

)

Values upto 688

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 56GPS no RAIM 98GG no RAIM 100 GG FB 73

to 688

Subset1

08

06

04

02

0

(ms

)

Values up

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 70GG no RAIM 100 GG Sub 98

RAIM comparison1

08

06

04

02

0

(ms

)

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 70GPS FB 56GG Sub 98GG FB 73

GG Dan 73

GPS Dan 56

Figure 7 Horizontal velocity error

the position domain the Subset testing is characterized by thehighest reliable availability but also by the highest errors theother schemes provide similar performance

In Figures 8 and 9 the plots relative to the verticalcomponents of the position and velocity show the benefits ofRAIM use

The qualitative analysis provided by the previous plotsis confirmed by the results summarized in Tables 5 and 6 indetail the RAIM use improves significantly the performancein terms of RMS and maximum errors for the vertical andhorizontal components maintaining a high reliable availabil-ity in case of GG configurations The RMS horizontal errorsare halved and even better results are evident on the verticalcomponent The maximum horizontal and vertical errors forGG Subset configuration are degraded due to an erroneousmeasurements rejection in the presence of multiple blundersbetter results are obtained with the Forward-Backward andDanish methods

5 Conclusions

In signal-degraded environments such as urban canyonsGNSS navigation suffers the presence of gross errors which

strongly worsen the solution therefore in these scenariosthe use of RAIM algorithms is necessary In this workthree RAIM FDE schemes well known in literature [1718 20ndash23] are adopted Subset testing Forward-Backwardand Danish The first method is based uniquely on theGT while the others include the use of the LT too Thesemethods have been enriched adopting a preliminary checkon the satellite geometry to screen out configurations toopoor to be tested successfully and a separability test toavoid the exclusion of blunder-free measurements in caseof observations strongly correlated The main scope of thiswork is to verify the effectiveness of the RAIM schemes withthe proposed modifications in urban scenario Moreover thebenefit assessment of GLONASS inclusion is of interest too

The obtained results show the effectiveness of the adoptedalgorithms in terms of reliable availability and of RMS andmaximum errors The reliable availability is the percentageof time mission when the solution is declared reliable bythe adopted RAIM the highest value of this parameter isobtained with the Subset method which provides the largesterrors too The Forward-Backward and the Danish methodsare instead characterized by similar performances and by thesmallest errors demonstrating the validity of the separability

10 International Journal of Navigation and Observation

Danish

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

1500

100

500

0

(m)

GPS Dan 49GG Dan 76

1500

100

500

0

(m)

Forward-Backward

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 44GPS no RAIM 98GG no RAIM 100 GG FB 74

1500

100

500

0

(m)

Subset

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 76GG no RAIM 100 GG Sub 97

RAIM comparison

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 76GPS FB 44GG Sub 97GG FB 74

400

300

100

200

0

(m)

GG Dan 76

GPS Dan 49

Figure 8 Altitude

Table 4 Velocity availabilityreliable availability

No RAIMavailability

Subsetreliable availability

Danishreliable availability

Forward-backwardreliable availability

GPS 981 705 563 563GG 100 978 734 729

Table 5 Position results

RMS (m) MAX (m)H V H V

No RAIM GPS 549 856 12645 16859GG 348 654 2456 3722

Subset GPS 275 564 2990 3270GG 151 361 3216 3985

Forward-backward GPS 179 445 1597 2858GG 134 313 1597 2843

Danish GPS 232 561 1597 3431GG 160 381 1597 2815

Table 6 Velocity results

RMS (ms) MAX (ms)H V H V

No RAIM GPS 0968 1573 68750 108240GG 0042 0060 0442 0822

Subset GPS 0053 0084 0669 1251GG 0042 0067 0928 1337

Forward-Backward GPS 0047 0074 0649 1251GG 0036 0055 0367 0653

Danish GPS 0046 0073 0649 1251GG 0035 0054 0295 0642

International Journal of Navigation and Observation 11

1

08

06

04

02

0

Danish(m

s)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

GPS Dan 56GG Dan 73

Forward-Backward1

08

06

04

02

0

(ms

)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 56GPS no RAIM 98GG no RAIM 100 GG FB 73

Subset1

08

06

04

02

0

(ms

)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 70GG no RAIM 100 GG Sub 98

RAIM comparison1

08

06

04

02

0

(ms

)

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 70GPS FB 56GG Sub 98GG FB 73

GG Dan 73

GPS Dan 56

Figure 9 Vertical velocity error

check module (which cannot be applied to Subset method)The proposed algorithms have been tested on both positionand velocity domains showing comparable robustness

GPSGLONASS combination shows evident perform-ance improvements for all the considered parameters rela-tive to GPS only configurations

References

[1] B Hoffmann-Wellenhof H Lichtenegger and J CollinsGlobalPositioning System Theory and Practice Springer New YorkNY USA 1992

[2] ED Kaplan and J Hegarty ldquoFundamentals of satellite naviga-tionrdquo in Understanding GPS Principles and Applications E DKaplan Ed ArtechHouseMobile Communications Series 2ndedition 2006

[3] A Angrisano M Petovello and G Pugliano ldquoGNSSINSintegration in vehicular urban navigationrdquo in Proceedings ofthe 23rd International Technical Meeting of the Satellite Divisionof the Institute of Navigation (GNSS rsquo10) pp 1505ndash1512 TheInstitute of Navigation Portland Ore USA September 2010

[4] A Angrisano M Petovello and G Pugliano ldquoBenefits ofcombined GPSGLONASS with low-cost MEMS IMUs forvehicular urban navigationrdquo Sensors vol 12 no 4 pp 5134ndash5158 2012

[5] B Parkinson and J J Spilker Global Positioning System TheoryAnd Applications vol 1-2 American Institute of Aeronauticsand Astronautics Washington DC USA 1996

[6] C Cai Precise point positioning using dual-frequency GPS andGLONASSmeasurements [MS thesis] UCGEReport no 20291Department of Geomatics Engineering University of CalgaryCalgary Canada 2009

[7] A Angrisano GNSSINS integration methods [PhD thesis]ldquoParthenoperdquo University of Naples 2010

[8] C Cai and Y Gao ldquoA combined GPSGLONASS navigationalgorithm for use with limited satellite visibilityrdquo Journal ofNavigation vol 62 no 4 pp 671ndash685 2009

[9] A Angrisano S Gaglione G Pugliano R Robustelli RSantamaria and M Vultaggio ldquoA stochastic sigma model forGLONASS satellite pseudorangerdquo Applied Geomatics vol 3 no1 pp 49ndash57 2011

[10] ICD-GLONASS Global Navigation Satellite System GLONASSInterface Control Document version 51 Moscow Russia 2008

[11] SC-159 of the RTCAMinimum Operational Performance Stan-dards for Global Positioning SystemWide Area AugmentationSystem Airborne Equipment Document DO-229D RTCAWashington DC USA 2006

[12] E M Mikhail Observations and Least Squares Harper amp Row1976

12 International Journal of Navigation and Observation

[13] D E Wells and E J Krakiwsky The Methods of Least SquaresLecture Notes no 18 Department of Surveying EngineeringUniversity of Brunswick 1971

[14] S Hewitson and J Wang ldquoGNSS receiver autonomous integritymonitoring (RAIM) performance analysisrdquo GPS Solutions vol10 no 3 pp 155ndash170 2006

[15] G Y Chin J H Kraemer and R G Brown ldquoGPS RAIMscreening out bad geometries underworst-case bias conditionsrdquoNavigation Journal of the Institute of Navigation vol 39 no 4pp 407ndash427 1992

[16] R G Brown and G Y Chin ldquoGPS RAIM calculation ofthreshold and protection radius using chi-square methods-a geometric approachrdquo Global Positioning System Institute ofNavigation vol 5 pp 155ndash179 1997

[17] M Petovello Real-time integration of a tactical-grade IMUand GPS for high-accuracy positioning and navigation [PhDthesis] UCGE Report no 20173 Department of GeomaticsEngineering University of Calgary Calgary Canada 2003

[18] W Baarda A Testing Procedure for Use in Geodetic NetworksNetherlands Geodetic Commission Publication on GeodesyNew Series 2 5 Delft The Netherlands 1968

[19] A K Brown ldquoReceiver autonomous integrity monitoring usinga 24-satellite GPS constellationrdquo Navigation Journal of TheInstitute of Navigation vol 5 pp 21ndash33 1998 Red Book ofRAIM

[20] H Kuusniemi User-level reliability and quality monitoringin satellite-based personal navigation [PhD thesis] TampereUniversity of Technology Tampere Finland 2005

[21] H Kuusniemi A Wieser G Lachapelle and J TakalaldquoUser-level reliability monitoring in urban personal satellite-navigationrdquo IEEE Transactions on Aerospace and ElectronicSystems vol 43 no 4 pp 1305ndash1318 2007

[22] A Angrisano S Gaglione and C Gioia ldquoRAIM algorithmsfor aided GNSS in urban scenariordquo in Proceedings of theUbiquitous Positioning Indoor Navigation and Location BasedService Helsinki Finland October 2012

[23] A LeickGPS Satellite Surveying JohnWiley amp Sons HobokenNJ USA 3rd edition 2004

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

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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 Navigation and Observation 5

z H W

LSestimator

WARPcheck

Solutionimpossible

to check

Global test

Not ok

Not ok

Not ok

Not ok

Ok Residuals

Local test

Ok

Ok

Solution unreliable

Separability check

rejections

Rejection reentry

LS estimator

Residuals

Global test

Solution reliable

BackwardRe

dund

ancyle

0

119870

119870 gt 1

119870 le 1

Figure 2 Forward-Backward algorithm

observations to avoid erroneous rejections the separabilitycheck is carried out the measurement flagged as possibleblunder is excluded only if it is not correlated with othermeasures Forward process is performed recursively until nomore erroneous measurements are found and the solution isdeclared reliable or unreliable

If the solution is declared reliable and 119896 measurementsare excluded (with 119896 gt 1) the Backward scheme is appliedto reintroduce observations wrongly excluded Rejectedmea-surements are iteratively implemented backward and theglobal test is performed the observation set which passes theGT is used to compute navigation solution

A complete scheme of the Forward-Backward techniqueis shown in Figure 2

33 Danish Least squares estimation is very susceptible tooutliers a possible way to solve this problem is an iterativedeweighing of erroneous measurements [20 23] The Danishmethod is an iteratively reweighted least squares algorithmused in geodetic applications for a long time this methodis used to achieve consistency between the measurementsby modifying the a priori weights In this paper the Danishmethod is used for signal degraded environments in orderto minimize the effect of blunders on the least squareadjustment This technique involves the use of the GT toverify the consistency of the measurements and the LT toidentify and deweight the outliers

A measurement set is checked for the geometry as inthe previous FDE techniques and then the GT is performedIf observations are declared not consistent by GT the LT iscarried out to identify the blunder and its related weightis reduced only if allowed by the separability check (ie ifthe measurement is not strictly correlated to the others)The variance of the suspected measurement is exponentiallyincreased (and consequently the weight is decreased) asfollows

1205902

119894119895+1

= 1205902

1198940

lowast

119890119908119894119895119879119897 if 119908

119894119895gt 119879119897

1 if 119908119894119895le 119879119897

(16)

where 1205902119894119895+1

is the variance of the 119894th observation after 119895 + 1iterations 1205902

1198940

is the a priori variance of the observation and119908119894119895is the standardized residual of the 119894th observation after 119895

iterationsIf the normalized residual of the 119894th observation does not

exceed 119879119897 its variance is maintained (the measurement is not

deweighted)The scheme of the Danish procedure is shown in

Figure 3

4 Test and Results

41 Test A static test of about 6 hours was carried out onFebruary 24 2012 The antenna was placed on the roof of the

6 International Journal of Navigation and Observation

z H W

LSestimator

WARPcheck

Solutionimpossible

to check

Global test

Residuals

Local test

Ok

Ok

Ok

Solution unreliable

Separability check

Measurementdeweight

Solution reliable

Not ok

Not ok

Not ok

Not ok

Redu

ndan

cyle

0

Figure 3 Danish algorithm

PANG (PArthenope Navigation Group) laboratory buildingCentro Direzionale of Naples (Italy) a typical example ofurban canyon (as shown in Figure 4) in this environmentmanyGNSS signals are blocked by skyscrapers or are stronglydegraded for the multipath phenomenon The only testperformed for this research was static to simplify the erroranalysis for the position (the antenna is placed in a well-known location) and for the velocity (the antenna is fixedso its velocity is zero) a kinematic test needs a referencefor error analysis more complicated to obtain and will beperformed in the future develop of this research Howeverthe static test choice does not limit the research validitybecause the operational environment is a typical signal-degraded scenario that is an urban canyon

The used receiver is a NovAtel FlexPak-G2 able to pro-vide single frequency (L1) GPSGLONASS measurementsconnected to a NovAtel antenna 702-GG

The reference solution is computed by a postprocess-ing geodetic method guaranteeing a position accuracyof mm order the coordinates of the antenna and the relativeaccuracies are shown in Table 2

42 Results Herein eight different GNSS configurations arecompared combining the two systems considered and thedifferent RAIM scheme developed

Antenna p

osition

Figure 4 Antenna position

(i) GPS only without RAIM application (briefly indi-cated as GPS no RAIM)

(ii) GPSGLONASS without RAIM application (GG noRAIM)

(iii) GPS only with Subset RAIM application (GPS Sub)(iv) GPSGLONASS with Subset RAIM application (GG

Sub)(v) GPS only with Forward-Backward RAIM application

(GPS FB)(vi) GPSGLONASS with Forward-Backward RAIM

application (GG FB)(vii) GPS only with Danish method applied (GPS Dan)(viii) GPSGLONASS with Danish method applied (GG

Dan)

Results are analyzed in terms of RMS and maximum errorsfor horizontal and vertical components in the position andvelocity domains The percentage of time mission whensolution is available is referred to as solution availability incase of RAIM application the concept of reliable availabilitydefined as the time percentage when solution is reliable isintroduced

The session is characterized by high solution availability(about 98 forGPS and 100GPSGLONASS configuration)and by very large errors (more than 1 km without RAIMapplication) the application of the developed RAIM schemesreduces the availability of the position solution In GPSstand-alone configuration the Subset test guarantees thehighest reliable availability (762) while 20 of solutionsare flagged as unreliable for Danish and Forward-Backwardschemes the reliable availability is halved with respect tothe solution availability The inclusion of GLONASS mea-surements without RAIM application improves the solutionavailability of 2 with respect to the GPS stand-alone con-figuration For the GPSGLONASS multiconstellation theSubset testing guarantees an high reliable availability (only35 of solutions are rejected by the quality control) which isincreased to 20 with respect to the GPS only configurationThe effect of the GLONASS inclusion is more evident in the

International Journal of Navigation and Observation 7

Danish

GPS no RAIM 98GG no RAIM 100

(m)

GPS Dan 49GG Dan 76

1000

500

0

minus500

minus1000

10005000minus500minus1000

(m)

Forward-Backward

GPS FB 44GPS no RAIM 98GG no RAIM 100 GG FB 74

(m)

1000

500

0

minus500

minus1000

10005000minus500minus1000

(m)

Subset

GPS no RAIM 98 GPS Sub 76GG no RAIM 100 GG Sub 97

(m)

1000

500

0

minus500

minus1000

10005000minus500minus1000

(m)

RAIM comparison

GPS Sub 76GPS FB 44GG Sub 97GG FB 74

GG Dan 76

GPS Dan 49

3002001000minus300 minus200 minus100

200

100

0

minus300

minus200

minus100

(m)

(m)

Figure 5 Horizontal position

Table 2 PANG station coordinates and accuracy

Latitude(deg min sec)

Longitude(deg min sec)

Height(m)

Standard deviation north(m)

Standard deviation east(m)

Standard deviation up(m)

40∘51101584023516310158401015840 14∘17101584003899710158401015840 906257 00006 00008 00011

Danish and Forward-Backward schemes in these cases thereliable availability reaches about 75 with an improvingof 25ndash30 with respect to the GPS only configurationsThe solution availability and the reliable availability of theposition are summarized in Table 3

Similar results are obtained in velocity domain theGLONASSmeasurements increase the reliable availability forthe three RAIM schemes relative to GPS only configurationsas in the position domain the Subset testing guaranteeshigher reliable availability with respect to the other developedschemesThe solution availability and the reliable availabilityof the velocity are summarized in Table 4

The configurations without RAIM are characterized bylarge errors in case of GPS only the maximum horizontal

error exceeds 1 km and the inclusion of GLONASS measure-ments improves the performance reducing the maximumerror to 245meter RAIM application improves all consideredconfigurations reducing both maximum and RMS errorsas shown in Figure 5 for the horizontal component in theupper figures and in the bottom left one the performanceof RAIM schemes is compared with the basic configurations(no RAIM) and in all cases the clouds relative to theRAIM solutions are significantly reduced with respect tothe baseline configurations In the bottom right of Figure 5the performances of the three developed RAIM schemes arecompared from a qualitative analysis the cloud relative tothe GPSGLONASS with forward-backward scheme is moreconcentrated with respect to the others

8 International Journal of Navigation and Observation

Danish

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

350

300

250

150

200

100

50

0

(m)

GPS Dan 49GG Dan 76

Values upto 16859

Forward-Backward

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 44GPS no RAIM 98GG no RAIM 100 GG FB 74

350

300

250

150

200

100

50

0

(m)

Values upto 16859

Subset

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 76GG no RAIM 100 GG Sub 97

350

300

250

150

200

100

50

0

(m)

Values upto 16859

RAIM comparison

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 76GPS FB 44GG Sub 97GG FB 74

GG Dan 76

GPS Dan 49

350

300

250

150

200

100

50

0

(m)

Figure 6 Horizontal position error

Table 3 Position availabilityreliable availability

No RAIMavailability

Subsetreliable availability

Danishreliable availability

Forward-Backwardreliable availability

GPS 981 762 490 436GG 100 965 758 740

In Figure 6 the horizontal position errors are plottedIn the upper figures and in the bottom left one the errorsof the three RAIM schemes are compared with the ldquonoRAIMrdquo configurations the errors of the RAIM configura-tions represented by the green and yellow dots are lowerthan the errors of the no RAIM configurations confirmingthe aforesaid qualitative analysis In the bottom right ofFigure 6 the RAIM errors are compared the Subset testingis characterized by the highest reliable availability but also bythe highest errors while the other schemes provide similarperformance Also in these cases the benefits of the inclusionof GLONASSmeasurements are clear all theGPSGLONASSconfigurations represented by the black yellow andmagenta

dots are lower with respect to the corresponding GPS onlyconfigurations The GLONASS measurements improve theredundancy increasing the RAIM efficiency

In Figure 7 the horizontal velocity errors are plotted ldquonoRAIMrdquo configurations are characterized by high error forGPS only case higher than 50ms the GLONASS inclusionreduces the errors up to 044ms As done for the positionerrors the RAIM schemes are first compared with the ldquonoRAIMrdquo configurations in the velocity domain the benefits oftheRAIMapplication are less evidentwith respect to the posi-tion domain due to the robustness of the Doppler observableIn the bottom right part of Figure 7 the horizontal velocityerrors obtained with the FDE techniques are compared as in

International Journal of Navigation and Observation 9

1

08

06

04

02

0

Danish(m

s)

Values upto 688

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

GPS Dan 56GG Dan 73

Forward-Backward1

08

06

04

02

0

(ms

)

Values upto 688

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 56GPS no RAIM 98GG no RAIM 100 GG FB 73

to 688

Subset1

08

06

04

02

0

(ms

)

Values up

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 70GG no RAIM 100 GG Sub 98

RAIM comparison1

08

06

04

02

0

(ms

)

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 70GPS FB 56GG Sub 98GG FB 73

GG Dan 73

GPS Dan 56

Figure 7 Horizontal velocity error

the position domain the Subset testing is characterized by thehighest reliable availability but also by the highest errors theother schemes provide similar performance

In Figures 8 and 9 the plots relative to the verticalcomponents of the position and velocity show the benefits ofRAIM use

The qualitative analysis provided by the previous plotsis confirmed by the results summarized in Tables 5 and 6 indetail the RAIM use improves significantly the performancein terms of RMS and maximum errors for the vertical andhorizontal components maintaining a high reliable availabil-ity in case of GG configurations The RMS horizontal errorsare halved and even better results are evident on the verticalcomponent The maximum horizontal and vertical errors forGG Subset configuration are degraded due to an erroneousmeasurements rejection in the presence of multiple blundersbetter results are obtained with the Forward-Backward andDanish methods

5 Conclusions

In signal-degraded environments such as urban canyonsGNSS navigation suffers the presence of gross errors which

strongly worsen the solution therefore in these scenariosthe use of RAIM algorithms is necessary In this workthree RAIM FDE schemes well known in literature [1718 20ndash23] are adopted Subset testing Forward-Backwardand Danish The first method is based uniquely on theGT while the others include the use of the LT too Thesemethods have been enriched adopting a preliminary checkon the satellite geometry to screen out configurations toopoor to be tested successfully and a separability test toavoid the exclusion of blunder-free measurements in caseof observations strongly correlated The main scope of thiswork is to verify the effectiveness of the RAIM schemes withthe proposed modifications in urban scenario Moreover thebenefit assessment of GLONASS inclusion is of interest too

The obtained results show the effectiveness of the adoptedalgorithms in terms of reliable availability and of RMS andmaximum errors The reliable availability is the percentageof time mission when the solution is declared reliable bythe adopted RAIM the highest value of this parameter isobtained with the Subset method which provides the largesterrors too The Forward-Backward and the Danish methodsare instead characterized by similar performances and by thesmallest errors demonstrating the validity of the separability

10 International Journal of Navigation and Observation

Danish

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

1500

100

500

0

(m)

GPS Dan 49GG Dan 76

1500

100

500

0

(m)

Forward-Backward

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 44GPS no RAIM 98GG no RAIM 100 GG FB 74

1500

100

500

0

(m)

Subset

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 76GG no RAIM 100 GG Sub 97

RAIM comparison

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 76GPS FB 44GG Sub 97GG FB 74

400

300

100

200

0

(m)

GG Dan 76

GPS Dan 49

Figure 8 Altitude

Table 4 Velocity availabilityreliable availability

No RAIMavailability

Subsetreliable availability

Danishreliable availability

Forward-backwardreliable availability

GPS 981 705 563 563GG 100 978 734 729

Table 5 Position results

RMS (m) MAX (m)H V H V

No RAIM GPS 549 856 12645 16859GG 348 654 2456 3722

Subset GPS 275 564 2990 3270GG 151 361 3216 3985

Forward-backward GPS 179 445 1597 2858GG 134 313 1597 2843

Danish GPS 232 561 1597 3431GG 160 381 1597 2815

Table 6 Velocity results

RMS (ms) MAX (ms)H V H V

No RAIM GPS 0968 1573 68750 108240GG 0042 0060 0442 0822

Subset GPS 0053 0084 0669 1251GG 0042 0067 0928 1337

Forward-Backward GPS 0047 0074 0649 1251GG 0036 0055 0367 0653

Danish GPS 0046 0073 0649 1251GG 0035 0054 0295 0642

International Journal of Navigation and Observation 11

1

08

06

04

02

0

Danish(m

s)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

GPS Dan 56GG Dan 73

Forward-Backward1

08

06

04

02

0

(ms

)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 56GPS no RAIM 98GG no RAIM 100 GG FB 73

Subset1

08

06

04

02

0

(ms

)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 70GG no RAIM 100 GG Sub 98

RAIM comparison1

08

06

04

02

0

(ms

)

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 70GPS FB 56GG Sub 98GG FB 73

GG Dan 73

GPS Dan 56

Figure 9 Vertical velocity error

check module (which cannot be applied to Subset method)The proposed algorithms have been tested on both positionand velocity domains showing comparable robustness

GPSGLONASS combination shows evident perform-ance improvements for all the considered parameters rela-tive to GPS only configurations

References

[1] B Hoffmann-Wellenhof H Lichtenegger and J CollinsGlobalPositioning System Theory and Practice Springer New YorkNY USA 1992

[2] ED Kaplan and J Hegarty ldquoFundamentals of satellite naviga-tionrdquo in Understanding GPS Principles and Applications E DKaplan Ed ArtechHouseMobile Communications Series 2ndedition 2006

[3] A Angrisano M Petovello and G Pugliano ldquoGNSSINSintegration in vehicular urban navigationrdquo in Proceedings ofthe 23rd International Technical Meeting of the Satellite Divisionof the Institute of Navigation (GNSS rsquo10) pp 1505ndash1512 TheInstitute of Navigation Portland Ore USA September 2010

[4] A Angrisano M Petovello and G Pugliano ldquoBenefits ofcombined GPSGLONASS with low-cost MEMS IMUs forvehicular urban navigationrdquo Sensors vol 12 no 4 pp 5134ndash5158 2012

[5] B Parkinson and J J Spilker Global Positioning System TheoryAnd Applications vol 1-2 American Institute of Aeronauticsand Astronautics Washington DC USA 1996

[6] C Cai Precise point positioning using dual-frequency GPS andGLONASSmeasurements [MS thesis] UCGEReport no 20291Department of Geomatics Engineering University of CalgaryCalgary Canada 2009

[7] A Angrisano GNSSINS integration methods [PhD thesis]ldquoParthenoperdquo University of Naples 2010

[8] C Cai and Y Gao ldquoA combined GPSGLONASS navigationalgorithm for use with limited satellite visibilityrdquo Journal ofNavigation vol 62 no 4 pp 671ndash685 2009

[9] A Angrisano S Gaglione G Pugliano R Robustelli RSantamaria and M Vultaggio ldquoA stochastic sigma model forGLONASS satellite pseudorangerdquo Applied Geomatics vol 3 no1 pp 49ndash57 2011

[10] ICD-GLONASS Global Navigation Satellite System GLONASSInterface Control Document version 51 Moscow Russia 2008

[11] SC-159 of the RTCAMinimum Operational Performance Stan-dards for Global Positioning SystemWide Area AugmentationSystem Airborne Equipment Document DO-229D RTCAWashington DC USA 2006

[12] E M Mikhail Observations and Least Squares Harper amp Row1976

12 International Journal of Navigation and Observation

[13] D E Wells and E J Krakiwsky The Methods of Least SquaresLecture Notes no 18 Department of Surveying EngineeringUniversity of Brunswick 1971

[14] S Hewitson and J Wang ldquoGNSS receiver autonomous integritymonitoring (RAIM) performance analysisrdquo GPS Solutions vol10 no 3 pp 155ndash170 2006

[15] G Y Chin J H Kraemer and R G Brown ldquoGPS RAIMscreening out bad geometries underworst-case bias conditionsrdquoNavigation Journal of the Institute of Navigation vol 39 no 4pp 407ndash427 1992

[16] R G Brown and G Y Chin ldquoGPS RAIM calculation ofthreshold and protection radius using chi-square methods-a geometric approachrdquo Global Positioning System Institute ofNavigation vol 5 pp 155ndash179 1997

[17] M Petovello Real-time integration of a tactical-grade IMUand GPS for high-accuracy positioning and navigation [PhDthesis] UCGE Report no 20173 Department of GeomaticsEngineering University of Calgary Calgary Canada 2003

[18] W Baarda A Testing Procedure for Use in Geodetic NetworksNetherlands Geodetic Commission Publication on GeodesyNew Series 2 5 Delft The Netherlands 1968

[19] A K Brown ldquoReceiver autonomous integrity monitoring usinga 24-satellite GPS constellationrdquo Navigation Journal of TheInstitute of Navigation vol 5 pp 21ndash33 1998 Red Book ofRAIM

[20] H Kuusniemi User-level reliability and quality monitoringin satellite-based personal navigation [PhD thesis] TampereUniversity of Technology Tampere Finland 2005

[21] H Kuusniemi A Wieser G Lachapelle and J TakalaldquoUser-level reliability monitoring in urban personal satellite-navigationrdquo IEEE Transactions on Aerospace and ElectronicSystems vol 43 no 4 pp 1305ndash1318 2007

[22] A Angrisano S Gaglione and C Gioia ldquoRAIM algorithmsfor aided GNSS in urban scenariordquo in Proceedings of theUbiquitous Positioning Indoor Navigation and Location BasedService Helsinki Finland October 2012

[23] A LeickGPS Satellite Surveying JohnWiley amp Sons HobokenNJ USA 3rd edition 2004

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

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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

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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

6 International Journal of Navigation and Observation

z H W

LSestimator

WARPcheck

Solutionimpossible

to check

Global test

Residuals

Local test

Ok

Ok

Ok

Solution unreliable

Separability check

Measurementdeweight

Solution reliable

Not ok

Not ok

Not ok

Not ok

Redu

ndan

cyle

0

Figure 3 Danish algorithm

PANG (PArthenope Navigation Group) laboratory buildingCentro Direzionale of Naples (Italy) a typical example ofurban canyon (as shown in Figure 4) in this environmentmanyGNSS signals are blocked by skyscrapers or are stronglydegraded for the multipath phenomenon The only testperformed for this research was static to simplify the erroranalysis for the position (the antenna is placed in a well-known location) and for the velocity (the antenna is fixedso its velocity is zero) a kinematic test needs a referencefor error analysis more complicated to obtain and will beperformed in the future develop of this research Howeverthe static test choice does not limit the research validitybecause the operational environment is a typical signal-degraded scenario that is an urban canyon

The used receiver is a NovAtel FlexPak-G2 able to pro-vide single frequency (L1) GPSGLONASS measurementsconnected to a NovAtel antenna 702-GG

The reference solution is computed by a postprocess-ing geodetic method guaranteeing a position accuracyof mm order the coordinates of the antenna and the relativeaccuracies are shown in Table 2

42 Results Herein eight different GNSS configurations arecompared combining the two systems considered and thedifferent RAIM scheme developed

Antenna p

osition

Figure 4 Antenna position

(i) GPS only without RAIM application (briefly indi-cated as GPS no RAIM)

(ii) GPSGLONASS without RAIM application (GG noRAIM)

(iii) GPS only with Subset RAIM application (GPS Sub)(iv) GPSGLONASS with Subset RAIM application (GG

Sub)(v) GPS only with Forward-Backward RAIM application

(GPS FB)(vi) GPSGLONASS with Forward-Backward RAIM

application (GG FB)(vii) GPS only with Danish method applied (GPS Dan)(viii) GPSGLONASS with Danish method applied (GG

Dan)

Results are analyzed in terms of RMS and maximum errorsfor horizontal and vertical components in the position andvelocity domains The percentage of time mission whensolution is available is referred to as solution availability incase of RAIM application the concept of reliable availabilitydefined as the time percentage when solution is reliable isintroduced

The session is characterized by high solution availability(about 98 forGPS and 100GPSGLONASS configuration)and by very large errors (more than 1 km without RAIMapplication) the application of the developed RAIM schemesreduces the availability of the position solution In GPSstand-alone configuration the Subset test guarantees thehighest reliable availability (762) while 20 of solutionsare flagged as unreliable for Danish and Forward-Backwardschemes the reliable availability is halved with respect tothe solution availability The inclusion of GLONASS mea-surements without RAIM application improves the solutionavailability of 2 with respect to the GPS stand-alone con-figuration For the GPSGLONASS multiconstellation theSubset testing guarantees an high reliable availability (only35 of solutions are rejected by the quality control) which isincreased to 20 with respect to the GPS only configurationThe effect of the GLONASS inclusion is more evident in the

International Journal of Navigation and Observation 7

Danish

GPS no RAIM 98GG no RAIM 100

(m)

GPS Dan 49GG Dan 76

1000

500

0

minus500

minus1000

10005000minus500minus1000

(m)

Forward-Backward

GPS FB 44GPS no RAIM 98GG no RAIM 100 GG FB 74

(m)

1000

500

0

minus500

minus1000

10005000minus500minus1000

(m)

Subset

GPS no RAIM 98 GPS Sub 76GG no RAIM 100 GG Sub 97

(m)

1000

500

0

minus500

minus1000

10005000minus500minus1000

(m)

RAIM comparison

GPS Sub 76GPS FB 44GG Sub 97GG FB 74

GG Dan 76

GPS Dan 49

3002001000minus300 minus200 minus100

200

100

0

minus300

minus200

minus100

(m)

(m)

Figure 5 Horizontal position

Table 2 PANG station coordinates and accuracy

Latitude(deg min sec)

Longitude(deg min sec)

Height(m)

Standard deviation north(m)

Standard deviation east(m)

Standard deviation up(m)

40∘51101584023516310158401015840 14∘17101584003899710158401015840 906257 00006 00008 00011

Danish and Forward-Backward schemes in these cases thereliable availability reaches about 75 with an improvingof 25ndash30 with respect to the GPS only configurationsThe solution availability and the reliable availability of theposition are summarized in Table 3

Similar results are obtained in velocity domain theGLONASSmeasurements increase the reliable availability forthe three RAIM schemes relative to GPS only configurationsas in the position domain the Subset testing guaranteeshigher reliable availability with respect to the other developedschemesThe solution availability and the reliable availabilityof the velocity are summarized in Table 4

The configurations without RAIM are characterized bylarge errors in case of GPS only the maximum horizontal

error exceeds 1 km and the inclusion of GLONASS measure-ments improves the performance reducing the maximumerror to 245meter RAIM application improves all consideredconfigurations reducing both maximum and RMS errorsas shown in Figure 5 for the horizontal component in theupper figures and in the bottom left one the performanceof RAIM schemes is compared with the basic configurations(no RAIM) and in all cases the clouds relative to theRAIM solutions are significantly reduced with respect tothe baseline configurations In the bottom right of Figure 5the performances of the three developed RAIM schemes arecompared from a qualitative analysis the cloud relative tothe GPSGLONASS with forward-backward scheme is moreconcentrated with respect to the others

8 International Journal of Navigation and Observation

Danish

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

350

300

250

150

200

100

50

0

(m)

GPS Dan 49GG Dan 76

Values upto 16859

Forward-Backward

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 44GPS no RAIM 98GG no RAIM 100 GG FB 74

350

300

250

150

200

100

50

0

(m)

Values upto 16859

Subset

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 76GG no RAIM 100 GG Sub 97

350

300

250

150

200

100

50

0

(m)

Values upto 16859

RAIM comparison

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 76GPS FB 44GG Sub 97GG FB 74

GG Dan 76

GPS Dan 49

350

300

250

150

200

100

50

0

(m)

Figure 6 Horizontal position error

Table 3 Position availabilityreliable availability

No RAIMavailability

Subsetreliable availability

Danishreliable availability

Forward-Backwardreliable availability

GPS 981 762 490 436GG 100 965 758 740

In Figure 6 the horizontal position errors are plottedIn the upper figures and in the bottom left one the errorsof the three RAIM schemes are compared with the ldquonoRAIMrdquo configurations the errors of the RAIM configura-tions represented by the green and yellow dots are lowerthan the errors of the no RAIM configurations confirmingthe aforesaid qualitative analysis In the bottom right ofFigure 6 the RAIM errors are compared the Subset testingis characterized by the highest reliable availability but also bythe highest errors while the other schemes provide similarperformance Also in these cases the benefits of the inclusionof GLONASSmeasurements are clear all theGPSGLONASSconfigurations represented by the black yellow andmagenta

dots are lower with respect to the corresponding GPS onlyconfigurations The GLONASS measurements improve theredundancy increasing the RAIM efficiency

In Figure 7 the horizontal velocity errors are plotted ldquonoRAIMrdquo configurations are characterized by high error forGPS only case higher than 50ms the GLONASS inclusionreduces the errors up to 044ms As done for the positionerrors the RAIM schemes are first compared with the ldquonoRAIMrdquo configurations in the velocity domain the benefits oftheRAIMapplication are less evidentwith respect to the posi-tion domain due to the robustness of the Doppler observableIn the bottom right part of Figure 7 the horizontal velocityerrors obtained with the FDE techniques are compared as in

International Journal of Navigation and Observation 9

1

08

06

04

02

0

Danish(m

s)

Values upto 688

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

GPS Dan 56GG Dan 73

Forward-Backward1

08

06

04

02

0

(ms

)

Values upto 688

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 56GPS no RAIM 98GG no RAIM 100 GG FB 73

to 688

Subset1

08

06

04

02

0

(ms

)

Values up

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 70GG no RAIM 100 GG Sub 98

RAIM comparison1

08

06

04

02

0

(ms

)

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 70GPS FB 56GG Sub 98GG FB 73

GG Dan 73

GPS Dan 56

Figure 7 Horizontal velocity error

the position domain the Subset testing is characterized by thehighest reliable availability but also by the highest errors theother schemes provide similar performance

In Figures 8 and 9 the plots relative to the verticalcomponents of the position and velocity show the benefits ofRAIM use

The qualitative analysis provided by the previous plotsis confirmed by the results summarized in Tables 5 and 6 indetail the RAIM use improves significantly the performancein terms of RMS and maximum errors for the vertical andhorizontal components maintaining a high reliable availabil-ity in case of GG configurations The RMS horizontal errorsare halved and even better results are evident on the verticalcomponent The maximum horizontal and vertical errors forGG Subset configuration are degraded due to an erroneousmeasurements rejection in the presence of multiple blundersbetter results are obtained with the Forward-Backward andDanish methods

5 Conclusions

In signal-degraded environments such as urban canyonsGNSS navigation suffers the presence of gross errors which

strongly worsen the solution therefore in these scenariosthe use of RAIM algorithms is necessary In this workthree RAIM FDE schemes well known in literature [1718 20ndash23] are adopted Subset testing Forward-Backwardand Danish The first method is based uniquely on theGT while the others include the use of the LT too Thesemethods have been enriched adopting a preliminary checkon the satellite geometry to screen out configurations toopoor to be tested successfully and a separability test toavoid the exclusion of blunder-free measurements in caseof observations strongly correlated The main scope of thiswork is to verify the effectiveness of the RAIM schemes withthe proposed modifications in urban scenario Moreover thebenefit assessment of GLONASS inclusion is of interest too

The obtained results show the effectiveness of the adoptedalgorithms in terms of reliable availability and of RMS andmaximum errors The reliable availability is the percentageof time mission when the solution is declared reliable bythe adopted RAIM the highest value of this parameter isobtained with the Subset method which provides the largesterrors too The Forward-Backward and the Danish methodsare instead characterized by similar performances and by thesmallest errors demonstrating the validity of the separability

10 International Journal of Navigation and Observation

Danish

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

1500

100

500

0

(m)

GPS Dan 49GG Dan 76

1500

100

500

0

(m)

Forward-Backward

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 44GPS no RAIM 98GG no RAIM 100 GG FB 74

1500

100

500

0

(m)

Subset

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 76GG no RAIM 100 GG Sub 97

RAIM comparison

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 76GPS FB 44GG Sub 97GG FB 74

400

300

100

200

0

(m)

GG Dan 76

GPS Dan 49

Figure 8 Altitude

Table 4 Velocity availabilityreliable availability

No RAIMavailability

Subsetreliable availability

Danishreliable availability

Forward-backwardreliable availability

GPS 981 705 563 563GG 100 978 734 729

Table 5 Position results

RMS (m) MAX (m)H V H V

No RAIM GPS 549 856 12645 16859GG 348 654 2456 3722

Subset GPS 275 564 2990 3270GG 151 361 3216 3985

Forward-backward GPS 179 445 1597 2858GG 134 313 1597 2843

Danish GPS 232 561 1597 3431GG 160 381 1597 2815

Table 6 Velocity results

RMS (ms) MAX (ms)H V H V

No RAIM GPS 0968 1573 68750 108240GG 0042 0060 0442 0822

Subset GPS 0053 0084 0669 1251GG 0042 0067 0928 1337

Forward-Backward GPS 0047 0074 0649 1251GG 0036 0055 0367 0653

Danish GPS 0046 0073 0649 1251GG 0035 0054 0295 0642

International Journal of Navigation and Observation 11

1

08

06

04

02

0

Danish(m

s)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

GPS Dan 56GG Dan 73

Forward-Backward1

08

06

04

02

0

(ms

)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 56GPS no RAIM 98GG no RAIM 100 GG FB 73

Subset1

08

06

04

02

0

(ms

)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 70GG no RAIM 100 GG Sub 98

RAIM comparison1

08

06

04

02

0

(ms

)

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 70GPS FB 56GG Sub 98GG FB 73

GG Dan 73

GPS Dan 56

Figure 9 Vertical velocity error

check module (which cannot be applied to Subset method)The proposed algorithms have been tested on both positionand velocity domains showing comparable robustness

GPSGLONASS combination shows evident perform-ance improvements for all the considered parameters rela-tive to GPS only configurations

References

[1] B Hoffmann-Wellenhof H Lichtenegger and J CollinsGlobalPositioning System Theory and Practice Springer New YorkNY USA 1992

[2] ED Kaplan and J Hegarty ldquoFundamentals of satellite naviga-tionrdquo in Understanding GPS Principles and Applications E DKaplan Ed ArtechHouseMobile Communications Series 2ndedition 2006

[3] A Angrisano M Petovello and G Pugliano ldquoGNSSINSintegration in vehicular urban navigationrdquo in Proceedings ofthe 23rd International Technical Meeting of the Satellite Divisionof the Institute of Navigation (GNSS rsquo10) pp 1505ndash1512 TheInstitute of Navigation Portland Ore USA September 2010

[4] A Angrisano M Petovello and G Pugliano ldquoBenefits ofcombined GPSGLONASS with low-cost MEMS IMUs forvehicular urban navigationrdquo Sensors vol 12 no 4 pp 5134ndash5158 2012

[5] B Parkinson and J J Spilker Global Positioning System TheoryAnd Applications vol 1-2 American Institute of Aeronauticsand Astronautics Washington DC USA 1996

[6] C Cai Precise point positioning using dual-frequency GPS andGLONASSmeasurements [MS thesis] UCGEReport no 20291Department of Geomatics Engineering University of CalgaryCalgary Canada 2009

[7] A Angrisano GNSSINS integration methods [PhD thesis]ldquoParthenoperdquo University of Naples 2010

[8] C Cai and Y Gao ldquoA combined GPSGLONASS navigationalgorithm for use with limited satellite visibilityrdquo Journal ofNavigation vol 62 no 4 pp 671ndash685 2009

[9] A Angrisano S Gaglione G Pugliano R Robustelli RSantamaria and M Vultaggio ldquoA stochastic sigma model forGLONASS satellite pseudorangerdquo Applied Geomatics vol 3 no1 pp 49ndash57 2011

[10] ICD-GLONASS Global Navigation Satellite System GLONASSInterface Control Document version 51 Moscow Russia 2008

[11] SC-159 of the RTCAMinimum Operational Performance Stan-dards for Global Positioning SystemWide Area AugmentationSystem Airborne Equipment Document DO-229D RTCAWashington DC USA 2006

[12] E M Mikhail Observations and Least Squares Harper amp Row1976

12 International Journal of Navigation and Observation

[13] D E Wells and E J Krakiwsky The Methods of Least SquaresLecture Notes no 18 Department of Surveying EngineeringUniversity of Brunswick 1971

[14] S Hewitson and J Wang ldquoGNSS receiver autonomous integritymonitoring (RAIM) performance analysisrdquo GPS Solutions vol10 no 3 pp 155ndash170 2006

[15] G Y Chin J H Kraemer and R G Brown ldquoGPS RAIMscreening out bad geometries underworst-case bias conditionsrdquoNavigation Journal of the Institute of Navigation vol 39 no 4pp 407ndash427 1992

[16] R G Brown and G Y Chin ldquoGPS RAIM calculation ofthreshold and protection radius using chi-square methods-a geometric approachrdquo Global Positioning System Institute ofNavigation vol 5 pp 155ndash179 1997

[17] M Petovello Real-time integration of a tactical-grade IMUand GPS for high-accuracy positioning and navigation [PhDthesis] UCGE Report no 20173 Department of GeomaticsEngineering University of Calgary Calgary Canada 2003

[18] W Baarda A Testing Procedure for Use in Geodetic NetworksNetherlands Geodetic Commission Publication on GeodesyNew Series 2 5 Delft The Netherlands 1968

[19] A K Brown ldquoReceiver autonomous integrity monitoring usinga 24-satellite GPS constellationrdquo Navigation Journal of TheInstitute of Navigation vol 5 pp 21ndash33 1998 Red Book ofRAIM

[20] H Kuusniemi User-level reliability and quality monitoringin satellite-based personal navigation [PhD thesis] TampereUniversity of Technology Tampere Finland 2005

[21] H Kuusniemi A Wieser G Lachapelle and J TakalaldquoUser-level reliability monitoring in urban personal satellite-navigationrdquo IEEE Transactions on Aerospace and ElectronicSystems vol 43 no 4 pp 1305ndash1318 2007

[22] A Angrisano S Gaglione and C Gioia ldquoRAIM algorithmsfor aided GNSS in urban scenariordquo in Proceedings of theUbiquitous Positioning Indoor Navigation and Location BasedService Helsinki Finland October 2012

[23] A LeickGPS Satellite Surveying JohnWiley amp Sons HobokenNJ USA 3rd edition 2004

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 Navigation and Observation 7

Danish

GPS no RAIM 98GG no RAIM 100

(m)

GPS Dan 49GG Dan 76

1000

500

0

minus500

minus1000

10005000minus500minus1000

(m)

Forward-Backward

GPS FB 44GPS no RAIM 98GG no RAIM 100 GG FB 74

(m)

1000

500

0

minus500

minus1000

10005000minus500minus1000

(m)

Subset

GPS no RAIM 98 GPS Sub 76GG no RAIM 100 GG Sub 97

(m)

1000

500

0

minus500

minus1000

10005000minus500minus1000

(m)

RAIM comparison

GPS Sub 76GPS FB 44GG Sub 97GG FB 74

GG Dan 76

GPS Dan 49

3002001000minus300 minus200 minus100

200

100

0

minus300

minus200

minus100

(m)

(m)

Figure 5 Horizontal position

Table 2 PANG station coordinates and accuracy

Latitude(deg min sec)

Longitude(deg min sec)

Height(m)

Standard deviation north(m)

Standard deviation east(m)

Standard deviation up(m)

40∘51101584023516310158401015840 14∘17101584003899710158401015840 906257 00006 00008 00011

Danish and Forward-Backward schemes in these cases thereliable availability reaches about 75 with an improvingof 25ndash30 with respect to the GPS only configurationsThe solution availability and the reliable availability of theposition are summarized in Table 3

Similar results are obtained in velocity domain theGLONASSmeasurements increase the reliable availability forthe three RAIM schemes relative to GPS only configurationsas in the position domain the Subset testing guaranteeshigher reliable availability with respect to the other developedschemesThe solution availability and the reliable availabilityof the velocity are summarized in Table 4

The configurations without RAIM are characterized bylarge errors in case of GPS only the maximum horizontal

error exceeds 1 km and the inclusion of GLONASS measure-ments improves the performance reducing the maximumerror to 245meter RAIM application improves all consideredconfigurations reducing both maximum and RMS errorsas shown in Figure 5 for the horizontal component in theupper figures and in the bottom left one the performanceof RAIM schemes is compared with the basic configurations(no RAIM) and in all cases the clouds relative to theRAIM solutions are significantly reduced with respect tothe baseline configurations In the bottom right of Figure 5the performances of the three developed RAIM schemes arecompared from a qualitative analysis the cloud relative tothe GPSGLONASS with forward-backward scheme is moreconcentrated with respect to the others

8 International Journal of Navigation and Observation

Danish

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

350

300

250

150

200

100

50

0

(m)

GPS Dan 49GG Dan 76

Values upto 16859

Forward-Backward

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 44GPS no RAIM 98GG no RAIM 100 GG FB 74

350

300

250

150

200

100

50

0

(m)

Values upto 16859

Subset

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 76GG no RAIM 100 GG Sub 97

350

300

250

150

200

100

50

0

(m)

Values upto 16859

RAIM comparison

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 76GPS FB 44GG Sub 97GG FB 74

GG Dan 76

GPS Dan 49

350

300

250

150

200

100

50

0

(m)

Figure 6 Horizontal position error

Table 3 Position availabilityreliable availability

No RAIMavailability

Subsetreliable availability

Danishreliable availability

Forward-Backwardreliable availability

GPS 981 762 490 436GG 100 965 758 740

In Figure 6 the horizontal position errors are plottedIn the upper figures and in the bottom left one the errorsof the three RAIM schemes are compared with the ldquonoRAIMrdquo configurations the errors of the RAIM configura-tions represented by the green and yellow dots are lowerthan the errors of the no RAIM configurations confirmingthe aforesaid qualitative analysis In the bottom right ofFigure 6 the RAIM errors are compared the Subset testingis characterized by the highest reliable availability but also bythe highest errors while the other schemes provide similarperformance Also in these cases the benefits of the inclusionof GLONASSmeasurements are clear all theGPSGLONASSconfigurations represented by the black yellow andmagenta

dots are lower with respect to the corresponding GPS onlyconfigurations The GLONASS measurements improve theredundancy increasing the RAIM efficiency

In Figure 7 the horizontal velocity errors are plotted ldquonoRAIMrdquo configurations are characterized by high error forGPS only case higher than 50ms the GLONASS inclusionreduces the errors up to 044ms As done for the positionerrors the RAIM schemes are first compared with the ldquonoRAIMrdquo configurations in the velocity domain the benefits oftheRAIMapplication are less evidentwith respect to the posi-tion domain due to the robustness of the Doppler observableIn the bottom right part of Figure 7 the horizontal velocityerrors obtained with the FDE techniques are compared as in

International Journal of Navigation and Observation 9

1

08

06

04

02

0

Danish(m

s)

Values upto 688

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

GPS Dan 56GG Dan 73

Forward-Backward1

08

06

04

02

0

(ms

)

Values upto 688

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 56GPS no RAIM 98GG no RAIM 100 GG FB 73

to 688

Subset1

08

06

04

02

0

(ms

)

Values up

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 70GG no RAIM 100 GG Sub 98

RAIM comparison1

08

06

04

02

0

(ms

)

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 70GPS FB 56GG Sub 98GG FB 73

GG Dan 73

GPS Dan 56

Figure 7 Horizontal velocity error

the position domain the Subset testing is characterized by thehighest reliable availability but also by the highest errors theother schemes provide similar performance

In Figures 8 and 9 the plots relative to the verticalcomponents of the position and velocity show the benefits ofRAIM use

The qualitative analysis provided by the previous plotsis confirmed by the results summarized in Tables 5 and 6 indetail the RAIM use improves significantly the performancein terms of RMS and maximum errors for the vertical andhorizontal components maintaining a high reliable availabil-ity in case of GG configurations The RMS horizontal errorsare halved and even better results are evident on the verticalcomponent The maximum horizontal and vertical errors forGG Subset configuration are degraded due to an erroneousmeasurements rejection in the presence of multiple blundersbetter results are obtained with the Forward-Backward andDanish methods

5 Conclusions

In signal-degraded environments such as urban canyonsGNSS navigation suffers the presence of gross errors which

strongly worsen the solution therefore in these scenariosthe use of RAIM algorithms is necessary In this workthree RAIM FDE schemes well known in literature [1718 20ndash23] are adopted Subset testing Forward-Backwardand Danish The first method is based uniquely on theGT while the others include the use of the LT too Thesemethods have been enriched adopting a preliminary checkon the satellite geometry to screen out configurations toopoor to be tested successfully and a separability test toavoid the exclusion of blunder-free measurements in caseof observations strongly correlated The main scope of thiswork is to verify the effectiveness of the RAIM schemes withthe proposed modifications in urban scenario Moreover thebenefit assessment of GLONASS inclusion is of interest too

The obtained results show the effectiveness of the adoptedalgorithms in terms of reliable availability and of RMS andmaximum errors The reliable availability is the percentageof time mission when the solution is declared reliable bythe adopted RAIM the highest value of this parameter isobtained with the Subset method which provides the largesterrors too The Forward-Backward and the Danish methodsare instead characterized by similar performances and by thesmallest errors demonstrating the validity of the separability

10 International Journal of Navigation and Observation

Danish

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

1500

100

500

0

(m)

GPS Dan 49GG Dan 76

1500

100

500

0

(m)

Forward-Backward

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 44GPS no RAIM 98GG no RAIM 100 GG FB 74

1500

100

500

0

(m)

Subset

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 76GG no RAIM 100 GG Sub 97

RAIM comparison

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 76GPS FB 44GG Sub 97GG FB 74

400

300

100

200

0

(m)

GG Dan 76

GPS Dan 49

Figure 8 Altitude

Table 4 Velocity availabilityreliable availability

No RAIMavailability

Subsetreliable availability

Danishreliable availability

Forward-backwardreliable availability

GPS 981 705 563 563GG 100 978 734 729

Table 5 Position results

RMS (m) MAX (m)H V H V

No RAIM GPS 549 856 12645 16859GG 348 654 2456 3722

Subset GPS 275 564 2990 3270GG 151 361 3216 3985

Forward-backward GPS 179 445 1597 2858GG 134 313 1597 2843

Danish GPS 232 561 1597 3431GG 160 381 1597 2815

Table 6 Velocity results

RMS (ms) MAX (ms)H V H V

No RAIM GPS 0968 1573 68750 108240GG 0042 0060 0442 0822

Subset GPS 0053 0084 0669 1251GG 0042 0067 0928 1337

Forward-Backward GPS 0047 0074 0649 1251GG 0036 0055 0367 0653

Danish GPS 0046 0073 0649 1251GG 0035 0054 0295 0642

International Journal of Navigation and Observation 11

1

08

06

04

02

0

Danish(m

s)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

GPS Dan 56GG Dan 73

Forward-Backward1

08

06

04

02

0

(ms

)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 56GPS no RAIM 98GG no RAIM 100 GG FB 73

Subset1

08

06

04

02

0

(ms

)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 70GG no RAIM 100 GG Sub 98

RAIM comparison1

08

06

04

02

0

(ms

)

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 70GPS FB 56GG Sub 98GG FB 73

GG Dan 73

GPS Dan 56

Figure 9 Vertical velocity error

check module (which cannot be applied to Subset method)The proposed algorithms have been tested on both positionand velocity domains showing comparable robustness

GPSGLONASS combination shows evident perform-ance improvements for all the considered parameters rela-tive to GPS only configurations

References

[1] B Hoffmann-Wellenhof H Lichtenegger and J CollinsGlobalPositioning System Theory and Practice Springer New YorkNY USA 1992

[2] ED Kaplan and J Hegarty ldquoFundamentals of satellite naviga-tionrdquo in Understanding GPS Principles and Applications E DKaplan Ed ArtechHouseMobile Communications Series 2ndedition 2006

[3] A Angrisano M Petovello and G Pugliano ldquoGNSSINSintegration in vehicular urban navigationrdquo in Proceedings ofthe 23rd International Technical Meeting of the Satellite Divisionof the Institute of Navigation (GNSS rsquo10) pp 1505ndash1512 TheInstitute of Navigation Portland Ore USA September 2010

[4] A Angrisano M Petovello and G Pugliano ldquoBenefits ofcombined GPSGLONASS with low-cost MEMS IMUs forvehicular urban navigationrdquo Sensors vol 12 no 4 pp 5134ndash5158 2012

[5] B Parkinson and J J Spilker Global Positioning System TheoryAnd Applications vol 1-2 American Institute of Aeronauticsand Astronautics Washington DC USA 1996

[6] C Cai Precise point positioning using dual-frequency GPS andGLONASSmeasurements [MS thesis] UCGEReport no 20291Department of Geomatics Engineering University of CalgaryCalgary Canada 2009

[7] A Angrisano GNSSINS integration methods [PhD thesis]ldquoParthenoperdquo University of Naples 2010

[8] C Cai and Y Gao ldquoA combined GPSGLONASS navigationalgorithm for use with limited satellite visibilityrdquo Journal ofNavigation vol 62 no 4 pp 671ndash685 2009

[9] A Angrisano S Gaglione G Pugliano R Robustelli RSantamaria and M Vultaggio ldquoA stochastic sigma model forGLONASS satellite pseudorangerdquo Applied Geomatics vol 3 no1 pp 49ndash57 2011

[10] ICD-GLONASS Global Navigation Satellite System GLONASSInterface Control Document version 51 Moscow Russia 2008

[11] SC-159 of the RTCAMinimum Operational Performance Stan-dards for Global Positioning SystemWide Area AugmentationSystem Airborne Equipment Document DO-229D RTCAWashington DC USA 2006

[12] E M Mikhail Observations and Least Squares Harper amp Row1976

12 International Journal of Navigation and Observation

[13] D E Wells and E J Krakiwsky The Methods of Least SquaresLecture Notes no 18 Department of Surveying EngineeringUniversity of Brunswick 1971

[14] S Hewitson and J Wang ldquoGNSS receiver autonomous integritymonitoring (RAIM) performance analysisrdquo GPS Solutions vol10 no 3 pp 155ndash170 2006

[15] G Y Chin J H Kraemer and R G Brown ldquoGPS RAIMscreening out bad geometries underworst-case bias conditionsrdquoNavigation Journal of the Institute of Navigation vol 39 no 4pp 407ndash427 1992

[16] R G Brown and G Y Chin ldquoGPS RAIM calculation ofthreshold and protection radius using chi-square methods-a geometric approachrdquo Global Positioning System Institute ofNavigation vol 5 pp 155ndash179 1997

[17] M Petovello Real-time integration of a tactical-grade IMUand GPS for high-accuracy positioning and navigation [PhDthesis] UCGE Report no 20173 Department of GeomaticsEngineering University of Calgary Calgary Canada 2003

[18] W Baarda A Testing Procedure for Use in Geodetic NetworksNetherlands Geodetic Commission Publication on GeodesyNew Series 2 5 Delft The Netherlands 1968

[19] A K Brown ldquoReceiver autonomous integrity monitoring usinga 24-satellite GPS constellationrdquo Navigation Journal of TheInstitute of Navigation vol 5 pp 21ndash33 1998 Red Book ofRAIM

[20] H Kuusniemi User-level reliability and quality monitoringin satellite-based personal navigation [PhD thesis] TampereUniversity of Technology Tampere Finland 2005

[21] H Kuusniemi A Wieser G Lachapelle and J TakalaldquoUser-level reliability monitoring in urban personal satellite-navigationrdquo IEEE Transactions on Aerospace and ElectronicSystems vol 43 no 4 pp 1305ndash1318 2007

[22] A Angrisano S Gaglione and C Gioia ldquoRAIM algorithmsfor aided GNSS in urban scenariordquo in Proceedings of theUbiquitous Positioning Indoor Navigation and Location BasedService Helsinki Finland October 2012

[23] A LeickGPS Satellite Surveying JohnWiley amp Sons HobokenNJ USA 3rd edition 2004

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 International Journal of Navigation and Observation

Danish

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

350

300

250

150

200

100

50

0

(m)

GPS Dan 49GG Dan 76

Values upto 16859

Forward-Backward

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 44GPS no RAIM 98GG no RAIM 100 GG FB 74

350

300

250

150

200

100

50

0

(m)

Values upto 16859

Subset

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 76GG no RAIM 100 GG Sub 97

350

300

250

150

200

100

50

0

(m)

Values upto 16859

RAIM comparison

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 76GPS FB 44GG Sub 97GG FB 74

GG Dan 76

GPS Dan 49

350

300

250

150

200

100

50

0

(m)

Figure 6 Horizontal position error

Table 3 Position availabilityreliable availability

No RAIMavailability

Subsetreliable availability

Danishreliable availability

Forward-Backwardreliable availability

GPS 981 762 490 436GG 100 965 758 740

In Figure 6 the horizontal position errors are plottedIn the upper figures and in the bottom left one the errorsof the three RAIM schemes are compared with the ldquonoRAIMrdquo configurations the errors of the RAIM configura-tions represented by the green and yellow dots are lowerthan the errors of the no RAIM configurations confirmingthe aforesaid qualitative analysis In the bottom right ofFigure 6 the RAIM errors are compared the Subset testingis characterized by the highest reliable availability but also bythe highest errors while the other schemes provide similarperformance Also in these cases the benefits of the inclusionof GLONASSmeasurements are clear all theGPSGLONASSconfigurations represented by the black yellow andmagenta

dots are lower with respect to the corresponding GPS onlyconfigurations The GLONASS measurements improve theredundancy increasing the RAIM efficiency

In Figure 7 the horizontal velocity errors are plotted ldquonoRAIMrdquo configurations are characterized by high error forGPS only case higher than 50ms the GLONASS inclusionreduces the errors up to 044ms As done for the positionerrors the RAIM schemes are first compared with the ldquonoRAIMrdquo configurations in the velocity domain the benefits oftheRAIMapplication are less evidentwith respect to the posi-tion domain due to the robustness of the Doppler observableIn the bottom right part of Figure 7 the horizontal velocityerrors obtained with the FDE techniques are compared as in

International Journal of Navigation and Observation 9

1

08

06

04

02

0

Danish(m

s)

Values upto 688

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

GPS Dan 56GG Dan 73

Forward-Backward1

08

06

04

02

0

(ms

)

Values upto 688

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 56GPS no RAIM 98GG no RAIM 100 GG FB 73

to 688

Subset1

08

06

04

02

0

(ms

)

Values up

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 70GG no RAIM 100 GG Sub 98

RAIM comparison1

08

06

04

02

0

(ms

)

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 70GPS FB 56GG Sub 98GG FB 73

GG Dan 73

GPS Dan 56

Figure 7 Horizontal velocity error

the position domain the Subset testing is characterized by thehighest reliable availability but also by the highest errors theother schemes provide similar performance

In Figures 8 and 9 the plots relative to the verticalcomponents of the position and velocity show the benefits ofRAIM use

The qualitative analysis provided by the previous plotsis confirmed by the results summarized in Tables 5 and 6 indetail the RAIM use improves significantly the performancein terms of RMS and maximum errors for the vertical andhorizontal components maintaining a high reliable availabil-ity in case of GG configurations The RMS horizontal errorsare halved and even better results are evident on the verticalcomponent The maximum horizontal and vertical errors forGG Subset configuration are degraded due to an erroneousmeasurements rejection in the presence of multiple blundersbetter results are obtained with the Forward-Backward andDanish methods

5 Conclusions

In signal-degraded environments such as urban canyonsGNSS navigation suffers the presence of gross errors which

strongly worsen the solution therefore in these scenariosthe use of RAIM algorithms is necessary In this workthree RAIM FDE schemes well known in literature [1718 20ndash23] are adopted Subset testing Forward-Backwardand Danish The first method is based uniquely on theGT while the others include the use of the LT too Thesemethods have been enriched adopting a preliminary checkon the satellite geometry to screen out configurations toopoor to be tested successfully and a separability test toavoid the exclusion of blunder-free measurements in caseof observations strongly correlated The main scope of thiswork is to verify the effectiveness of the RAIM schemes withthe proposed modifications in urban scenario Moreover thebenefit assessment of GLONASS inclusion is of interest too

The obtained results show the effectiveness of the adoptedalgorithms in terms of reliable availability and of RMS andmaximum errors The reliable availability is the percentageof time mission when the solution is declared reliable bythe adopted RAIM the highest value of this parameter isobtained with the Subset method which provides the largesterrors too The Forward-Backward and the Danish methodsare instead characterized by similar performances and by thesmallest errors demonstrating the validity of the separability

10 International Journal of Navigation and Observation

Danish

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

1500

100

500

0

(m)

GPS Dan 49GG Dan 76

1500

100

500

0

(m)

Forward-Backward

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 44GPS no RAIM 98GG no RAIM 100 GG FB 74

1500

100

500

0

(m)

Subset

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 76GG no RAIM 100 GG Sub 97

RAIM comparison

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 76GPS FB 44GG Sub 97GG FB 74

400

300

100

200

0

(m)

GG Dan 76

GPS Dan 49

Figure 8 Altitude

Table 4 Velocity availabilityreliable availability

No RAIMavailability

Subsetreliable availability

Danishreliable availability

Forward-backwardreliable availability

GPS 981 705 563 563GG 100 978 734 729

Table 5 Position results

RMS (m) MAX (m)H V H V

No RAIM GPS 549 856 12645 16859GG 348 654 2456 3722

Subset GPS 275 564 2990 3270GG 151 361 3216 3985

Forward-backward GPS 179 445 1597 2858GG 134 313 1597 2843

Danish GPS 232 561 1597 3431GG 160 381 1597 2815

Table 6 Velocity results

RMS (ms) MAX (ms)H V H V

No RAIM GPS 0968 1573 68750 108240GG 0042 0060 0442 0822

Subset GPS 0053 0084 0669 1251GG 0042 0067 0928 1337

Forward-Backward GPS 0047 0074 0649 1251GG 0036 0055 0367 0653

Danish GPS 0046 0073 0649 1251GG 0035 0054 0295 0642

International Journal of Navigation and Observation 11

1

08

06

04

02

0

Danish(m

s)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

GPS Dan 56GG Dan 73

Forward-Backward1

08

06

04

02

0

(ms

)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 56GPS no RAIM 98GG no RAIM 100 GG FB 73

Subset1

08

06

04

02

0

(ms

)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 70GG no RAIM 100 GG Sub 98

RAIM comparison1

08

06

04

02

0

(ms

)

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 70GPS FB 56GG Sub 98GG FB 73

GG Dan 73

GPS Dan 56

Figure 9 Vertical velocity error

check module (which cannot be applied to Subset method)The proposed algorithms have been tested on both positionand velocity domains showing comparable robustness

GPSGLONASS combination shows evident perform-ance improvements for all the considered parameters rela-tive to GPS only configurations

References

[1] B Hoffmann-Wellenhof H Lichtenegger and J CollinsGlobalPositioning System Theory and Practice Springer New YorkNY USA 1992

[2] ED Kaplan and J Hegarty ldquoFundamentals of satellite naviga-tionrdquo in Understanding GPS Principles and Applications E DKaplan Ed ArtechHouseMobile Communications Series 2ndedition 2006

[3] A Angrisano M Petovello and G Pugliano ldquoGNSSINSintegration in vehicular urban navigationrdquo in Proceedings ofthe 23rd International Technical Meeting of the Satellite Divisionof the Institute of Navigation (GNSS rsquo10) pp 1505ndash1512 TheInstitute of Navigation Portland Ore USA September 2010

[4] A Angrisano M Petovello and G Pugliano ldquoBenefits ofcombined GPSGLONASS with low-cost MEMS IMUs forvehicular urban navigationrdquo Sensors vol 12 no 4 pp 5134ndash5158 2012

[5] B Parkinson and J J Spilker Global Positioning System TheoryAnd Applications vol 1-2 American Institute of Aeronauticsand Astronautics Washington DC USA 1996

[6] C Cai Precise point positioning using dual-frequency GPS andGLONASSmeasurements [MS thesis] UCGEReport no 20291Department of Geomatics Engineering University of CalgaryCalgary Canada 2009

[7] A Angrisano GNSSINS integration methods [PhD thesis]ldquoParthenoperdquo University of Naples 2010

[8] C Cai and Y Gao ldquoA combined GPSGLONASS navigationalgorithm for use with limited satellite visibilityrdquo Journal ofNavigation vol 62 no 4 pp 671ndash685 2009

[9] A Angrisano S Gaglione G Pugliano R Robustelli RSantamaria and M Vultaggio ldquoA stochastic sigma model forGLONASS satellite pseudorangerdquo Applied Geomatics vol 3 no1 pp 49ndash57 2011

[10] ICD-GLONASS Global Navigation Satellite System GLONASSInterface Control Document version 51 Moscow Russia 2008

[11] SC-159 of the RTCAMinimum Operational Performance Stan-dards for Global Positioning SystemWide Area AugmentationSystem Airborne Equipment Document DO-229D RTCAWashington DC USA 2006

[12] E M Mikhail Observations and Least Squares Harper amp Row1976

12 International Journal of Navigation and Observation

[13] D E Wells and E J Krakiwsky The Methods of Least SquaresLecture Notes no 18 Department of Surveying EngineeringUniversity of Brunswick 1971

[14] S Hewitson and J Wang ldquoGNSS receiver autonomous integritymonitoring (RAIM) performance analysisrdquo GPS Solutions vol10 no 3 pp 155ndash170 2006

[15] G Y Chin J H Kraemer and R G Brown ldquoGPS RAIMscreening out bad geometries underworst-case bias conditionsrdquoNavigation Journal of the Institute of Navigation vol 39 no 4pp 407ndash427 1992

[16] R G Brown and G Y Chin ldquoGPS RAIM calculation ofthreshold and protection radius using chi-square methods-a geometric approachrdquo Global Positioning System Institute ofNavigation vol 5 pp 155ndash179 1997

[17] M Petovello Real-time integration of a tactical-grade IMUand GPS for high-accuracy positioning and navigation [PhDthesis] UCGE Report no 20173 Department of GeomaticsEngineering University of Calgary Calgary Canada 2003

[18] W Baarda A Testing Procedure for Use in Geodetic NetworksNetherlands Geodetic Commission Publication on GeodesyNew Series 2 5 Delft The Netherlands 1968

[19] A K Brown ldquoReceiver autonomous integrity monitoring usinga 24-satellite GPS constellationrdquo Navigation Journal of TheInstitute of Navigation vol 5 pp 21ndash33 1998 Red Book ofRAIM

[20] H Kuusniemi User-level reliability and quality monitoringin satellite-based personal navigation [PhD thesis] TampereUniversity of Technology Tampere Finland 2005

[21] H Kuusniemi A Wieser G Lachapelle and J TakalaldquoUser-level reliability monitoring in urban personal satellite-navigationrdquo IEEE Transactions on Aerospace and ElectronicSystems vol 43 no 4 pp 1305ndash1318 2007

[22] A Angrisano S Gaglione and C Gioia ldquoRAIM algorithmsfor aided GNSS in urban scenariordquo in Proceedings of theUbiquitous Positioning Indoor Navigation and Location BasedService Helsinki Finland October 2012

[23] A LeickGPS Satellite Surveying JohnWiley amp Sons HobokenNJ USA 3rd edition 2004

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 Navigation and Observation 9

1

08

06

04

02

0

Danish(m

s)

Values upto 688

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

GPS Dan 56GG Dan 73

Forward-Backward1

08

06

04

02

0

(ms

)

Values upto 688

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 56GPS no RAIM 98GG no RAIM 100 GG FB 73

to 688

Subset1

08

06

04

02

0

(ms

)

Values up

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 70GG no RAIM 100 GG Sub 98

RAIM comparison1

08

06

04

02

0

(ms

)

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 70GPS FB 56GG Sub 98GG FB 73

GG Dan 73

GPS Dan 56

Figure 7 Horizontal velocity error

the position domain the Subset testing is characterized by thehighest reliable availability but also by the highest errors theother schemes provide similar performance

In Figures 8 and 9 the plots relative to the verticalcomponents of the position and velocity show the benefits ofRAIM use

The qualitative analysis provided by the previous plotsis confirmed by the results summarized in Tables 5 and 6 indetail the RAIM use improves significantly the performancein terms of RMS and maximum errors for the vertical andhorizontal components maintaining a high reliable availabil-ity in case of GG configurations The RMS horizontal errorsare halved and even better results are evident on the verticalcomponent The maximum horizontal and vertical errors forGG Subset configuration are degraded due to an erroneousmeasurements rejection in the presence of multiple blundersbetter results are obtained with the Forward-Backward andDanish methods

5 Conclusions

In signal-degraded environments such as urban canyonsGNSS navigation suffers the presence of gross errors which

strongly worsen the solution therefore in these scenariosthe use of RAIM algorithms is necessary In this workthree RAIM FDE schemes well known in literature [1718 20ndash23] are adopted Subset testing Forward-Backwardand Danish The first method is based uniquely on theGT while the others include the use of the LT too Thesemethods have been enriched adopting a preliminary checkon the satellite geometry to screen out configurations toopoor to be tested successfully and a separability test toavoid the exclusion of blunder-free measurements in caseof observations strongly correlated The main scope of thiswork is to verify the effectiveness of the RAIM schemes withthe proposed modifications in urban scenario Moreover thebenefit assessment of GLONASS inclusion is of interest too

The obtained results show the effectiveness of the adoptedalgorithms in terms of reliable availability and of RMS andmaximum errors The reliable availability is the percentageof time mission when the solution is declared reliable bythe adopted RAIM the highest value of this parameter isobtained with the Subset method which provides the largesterrors too The Forward-Backward and the Danish methodsare instead characterized by similar performances and by thesmallest errors demonstrating the validity of the separability

10 International Journal of Navigation and Observation

Danish

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

1500

100

500

0

(m)

GPS Dan 49GG Dan 76

1500

100

500

0

(m)

Forward-Backward

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 44GPS no RAIM 98GG no RAIM 100 GG FB 74

1500

100

500

0

(m)

Subset

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 76GG no RAIM 100 GG Sub 97

RAIM comparison

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 76GPS FB 44GG Sub 97GG FB 74

400

300

100

200

0

(m)

GG Dan 76

GPS Dan 49

Figure 8 Altitude

Table 4 Velocity availabilityreliable availability

No RAIMavailability

Subsetreliable availability

Danishreliable availability

Forward-backwardreliable availability

GPS 981 705 563 563GG 100 978 734 729

Table 5 Position results

RMS (m) MAX (m)H V H V

No RAIM GPS 549 856 12645 16859GG 348 654 2456 3722

Subset GPS 275 564 2990 3270GG 151 361 3216 3985

Forward-backward GPS 179 445 1597 2858GG 134 313 1597 2843

Danish GPS 232 561 1597 3431GG 160 381 1597 2815

Table 6 Velocity results

RMS (ms) MAX (ms)H V H V

No RAIM GPS 0968 1573 68750 108240GG 0042 0060 0442 0822

Subset GPS 0053 0084 0669 1251GG 0042 0067 0928 1337

Forward-Backward GPS 0047 0074 0649 1251GG 0036 0055 0367 0653

Danish GPS 0046 0073 0649 1251GG 0035 0054 0295 0642

International Journal of Navigation and Observation 11

1

08

06

04

02

0

Danish(m

s)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

GPS Dan 56GG Dan 73

Forward-Backward1

08

06

04

02

0

(ms

)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 56GPS no RAIM 98GG no RAIM 100 GG FB 73

Subset1

08

06

04

02

0

(ms

)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 70GG no RAIM 100 GG Sub 98

RAIM comparison1

08

06

04

02

0

(ms

)

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 70GPS FB 56GG Sub 98GG FB 73

GG Dan 73

GPS Dan 56

Figure 9 Vertical velocity error

check module (which cannot be applied to Subset method)The proposed algorithms have been tested on both positionand velocity domains showing comparable robustness

GPSGLONASS combination shows evident perform-ance improvements for all the considered parameters rela-tive to GPS only configurations

References

[1] B Hoffmann-Wellenhof H Lichtenegger and J CollinsGlobalPositioning System Theory and Practice Springer New YorkNY USA 1992

[2] ED Kaplan and J Hegarty ldquoFundamentals of satellite naviga-tionrdquo in Understanding GPS Principles and Applications E DKaplan Ed ArtechHouseMobile Communications Series 2ndedition 2006

[3] A Angrisano M Petovello and G Pugliano ldquoGNSSINSintegration in vehicular urban navigationrdquo in Proceedings ofthe 23rd International Technical Meeting of the Satellite Divisionof the Institute of Navigation (GNSS rsquo10) pp 1505ndash1512 TheInstitute of Navigation Portland Ore USA September 2010

[4] A Angrisano M Petovello and G Pugliano ldquoBenefits ofcombined GPSGLONASS with low-cost MEMS IMUs forvehicular urban navigationrdquo Sensors vol 12 no 4 pp 5134ndash5158 2012

[5] B Parkinson and J J Spilker Global Positioning System TheoryAnd Applications vol 1-2 American Institute of Aeronauticsand Astronautics Washington DC USA 1996

[6] C Cai Precise point positioning using dual-frequency GPS andGLONASSmeasurements [MS thesis] UCGEReport no 20291Department of Geomatics Engineering University of CalgaryCalgary Canada 2009

[7] A Angrisano GNSSINS integration methods [PhD thesis]ldquoParthenoperdquo University of Naples 2010

[8] C Cai and Y Gao ldquoA combined GPSGLONASS navigationalgorithm for use with limited satellite visibilityrdquo Journal ofNavigation vol 62 no 4 pp 671ndash685 2009

[9] A Angrisano S Gaglione G Pugliano R Robustelli RSantamaria and M Vultaggio ldquoA stochastic sigma model forGLONASS satellite pseudorangerdquo Applied Geomatics vol 3 no1 pp 49ndash57 2011

[10] ICD-GLONASS Global Navigation Satellite System GLONASSInterface Control Document version 51 Moscow Russia 2008

[11] SC-159 of the RTCAMinimum Operational Performance Stan-dards for Global Positioning SystemWide Area AugmentationSystem Airborne Equipment Document DO-229D RTCAWashington DC USA 2006

[12] E M Mikhail Observations and Least Squares Harper amp Row1976

12 International Journal of Navigation and Observation

[13] D E Wells and E J Krakiwsky The Methods of Least SquaresLecture Notes no 18 Department of Surveying EngineeringUniversity of Brunswick 1971

[14] S Hewitson and J Wang ldquoGNSS receiver autonomous integritymonitoring (RAIM) performance analysisrdquo GPS Solutions vol10 no 3 pp 155ndash170 2006

[15] G Y Chin J H Kraemer and R G Brown ldquoGPS RAIMscreening out bad geometries underworst-case bias conditionsrdquoNavigation Journal of the Institute of Navigation vol 39 no 4pp 407ndash427 1992

[16] R G Brown and G Y Chin ldquoGPS RAIM calculation ofthreshold and protection radius using chi-square methods-a geometric approachrdquo Global Positioning System Institute ofNavigation vol 5 pp 155ndash179 1997

[17] M Petovello Real-time integration of a tactical-grade IMUand GPS for high-accuracy positioning and navigation [PhDthesis] UCGE Report no 20173 Department of GeomaticsEngineering University of Calgary Calgary Canada 2003

[18] W Baarda A Testing Procedure for Use in Geodetic NetworksNetherlands Geodetic Commission Publication on GeodesyNew Series 2 5 Delft The Netherlands 1968

[19] A K Brown ldquoReceiver autonomous integrity monitoring usinga 24-satellite GPS constellationrdquo Navigation Journal of TheInstitute of Navigation vol 5 pp 21ndash33 1998 Red Book ofRAIM

[20] H Kuusniemi User-level reliability and quality monitoringin satellite-based personal navigation [PhD thesis] TampereUniversity of Technology Tampere Finland 2005

[21] H Kuusniemi A Wieser G Lachapelle and J TakalaldquoUser-level reliability monitoring in urban personal satellite-navigationrdquo IEEE Transactions on Aerospace and ElectronicSystems vol 43 no 4 pp 1305ndash1318 2007

[22] A Angrisano S Gaglione and C Gioia ldquoRAIM algorithmsfor aided GNSS in urban scenariordquo in Proceedings of theUbiquitous Positioning Indoor Navigation and Location BasedService Helsinki Finland October 2012

[23] A LeickGPS Satellite Surveying JohnWiley amp Sons HobokenNJ USA 3rd edition 2004

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 International Journal of Navigation and Observation

Danish

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

1500

100

500

0

(m)

GPS Dan 49GG Dan 76

1500

100

500

0

(m)

Forward-Backward

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 44GPS no RAIM 98GG no RAIM 100 GG FB 74

1500

100

500

0

(m)

Subset

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 76GG no RAIM 100 GG Sub 97

RAIM comparison

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 76GPS FB 44GG Sub 97GG FB 74

400

300

100

200

0

(m)

GG Dan 76

GPS Dan 49

Figure 8 Altitude

Table 4 Velocity availabilityreliable availability

No RAIMavailability

Subsetreliable availability

Danishreliable availability

Forward-backwardreliable availability

GPS 981 705 563 563GG 100 978 734 729

Table 5 Position results

RMS (m) MAX (m)H V H V

No RAIM GPS 549 856 12645 16859GG 348 654 2456 3722

Subset GPS 275 564 2990 3270GG 151 361 3216 3985

Forward-backward GPS 179 445 1597 2858GG 134 313 1597 2843

Danish GPS 232 561 1597 3431GG 160 381 1597 2815

Table 6 Velocity results

RMS (ms) MAX (ms)H V H V

No RAIM GPS 0968 1573 68750 108240GG 0042 0060 0442 0822

Subset GPS 0053 0084 0669 1251GG 0042 0067 0928 1337

Forward-Backward GPS 0047 0074 0649 1251GG 0036 0055 0367 0653

Danish GPS 0046 0073 0649 1251GG 0035 0054 0295 0642

International Journal of Navigation and Observation 11

1

08

06

04

02

0

Danish(m

s)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

GPS Dan 56GG Dan 73

Forward-Backward1

08

06

04

02

0

(ms

)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 56GPS no RAIM 98GG no RAIM 100 GG FB 73

Subset1

08

06

04

02

0

(ms

)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 70GG no RAIM 100 GG Sub 98

RAIM comparison1

08

06

04

02

0

(ms

)

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 70GPS FB 56GG Sub 98GG FB 73

GG Dan 73

GPS Dan 56

Figure 9 Vertical velocity error

check module (which cannot be applied to Subset method)The proposed algorithms have been tested on both positionand velocity domains showing comparable robustness

GPSGLONASS combination shows evident perform-ance improvements for all the considered parameters rela-tive to GPS only configurations

References

[1] B Hoffmann-Wellenhof H Lichtenegger and J CollinsGlobalPositioning System Theory and Practice Springer New YorkNY USA 1992

[2] ED Kaplan and J Hegarty ldquoFundamentals of satellite naviga-tionrdquo in Understanding GPS Principles and Applications E DKaplan Ed ArtechHouseMobile Communications Series 2ndedition 2006

[3] A Angrisano M Petovello and G Pugliano ldquoGNSSINSintegration in vehicular urban navigationrdquo in Proceedings ofthe 23rd International Technical Meeting of the Satellite Divisionof the Institute of Navigation (GNSS rsquo10) pp 1505ndash1512 TheInstitute of Navigation Portland Ore USA September 2010

[4] A Angrisano M Petovello and G Pugliano ldquoBenefits ofcombined GPSGLONASS with low-cost MEMS IMUs forvehicular urban navigationrdquo Sensors vol 12 no 4 pp 5134ndash5158 2012

[5] B Parkinson and J J Spilker Global Positioning System TheoryAnd Applications vol 1-2 American Institute of Aeronauticsand Astronautics Washington DC USA 1996

[6] C Cai Precise point positioning using dual-frequency GPS andGLONASSmeasurements [MS thesis] UCGEReport no 20291Department of Geomatics Engineering University of CalgaryCalgary Canada 2009

[7] A Angrisano GNSSINS integration methods [PhD thesis]ldquoParthenoperdquo University of Naples 2010

[8] C Cai and Y Gao ldquoA combined GPSGLONASS navigationalgorithm for use with limited satellite visibilityrdquo Journal ofNavigation vol 62 no 4 pp 671ndash685 2009

[9] A Angrisano S Gaglione G Pugliano R Robustelli RSantamaria and M Vultaggio ldquoA stochastic sigma model forGLONASS satellite pseudorangerdquo Applied Geomatics vol 3 no1 pp 49ndash57 2011

[10] ICD-GLONASS Global Navigation Satellite System GLONASSInterface Control Document version 51 Moscow Russia 2008

[11] SC-159 of the RTCAMinimum Operational Performance Stan-dards for Global Positioning SystemWide Area AugmentationSystem Airborne Equipment Document DO-229D RTCAWashington DC USA 2006

[12] E M Mikhail Observations and Least Squares Harper amp Row1976

12 International Journal of Navigation and Observation

[13] D E Wells and E J Krakiwsky The Methods of Least SquaresLecture Notes no 18 Department of Surveying EngineeringUniversity of Brunswick 1971

[14] S Hewitson and J Wang ldquoGNSS receiver autonomous integritymonitoring (RAIM) performance analysisrdquo GPS Solutions vol10 no 3 pp 155ndash170 2006

[15] G Y Chin J H Kraemer and R G Brown ldquoGPS RAIMscreening out bad geometries underworst-case bias conditionsrdquoNavigation Journal of the Institute of Navigation vol 39 no 4pp 407ndash427 1992

[16] R G Brown and G Y Chin ldquoGPS RAIM calculation ofthreshold and protection radius using chi-square methods-a geometric approachrdquo Global Positioning System Institute ofNavigation vol 5 pp 155ndash179 1997

[17] M Petovello Real-time integration of a tactical-grade IMUand GPS for high-accuracy positioning and navigation [PhDthesis] UCGE Report no 20173 Department of GeomaticsEngineering University of Calgary Calgary Canada 2003

[18] W Baarda A Testing Procedure for Use in Geodetic NetworksNetherlands Geodetic Commission Publication on GeodesyNew Series 2 5 Delft The Netherlands 1968

[19] A K Brown ldquoReceiver autonomous integrity monitoring usinga 24-satellite GPS constellationrdquo Navigation Journal of TheInstitute of Navigation vol 5 pp 21ndash33 1998 Red Book ofRAIM

[20] H Kuusniemi User-level reliability and quality monitoringin satellite-based personal navigation [PhD thesis] TampereUniversity of Technology Tampere Finland 2005

[21] H Kuusniemi A Wieser G Lachapelle and J TakalaldquoUser-level reliability monitoring in urban personal satellite-navigationrdquo IEEE Transactions on Aerospace and ElectronicSystems vol 43 no 4 pp 1305ndash1318 2007

[22] A Angrisano S Gaglione and C Gioia ldquoRAIM algorithmsfor aided GNSS in urban scenariordquo in Proceedings of theUbiquitous Positioning Indoor Navigation and Location BasedService Helsinki Finland October 2012

[23] A LeickGPS Satellite Surveying JohnWiley amp Sons HobokenNJ USA 3rd edition 2004

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 Navigation and Observation 11

1

08

06

04

02

0

Danish(m

s)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98GG no RAIM 100

GPS Dan 56GG Dan 73

Forward-Backward1

08

06

04

02

0

(ms

)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS FB 56GPS no RAIM 98GG no RAIM 100 GG FB 73

Subset1

08

06

04

02

0

(ms

)

Values upto 108

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS no RAIM 98 GPS Sub 70GG no RAIM 100 GG Sub 98

RAIM comparison1

08

06

04

02

0

(ms

)

468588 475788 479388472188 482988 486588 49018812 10 13 10 14 10 15 10 16 10 17 10 18 10

GPS Sub 70GPS FB 56GG Sub 98GG FB 73

GG Dan 73

GPS Dan 56

Figure 9 Vertical velocity error

check module (which cannot be applied to Subset method)The proposed algorithms have been tested on both positionand velocity domains showing comparable robustness

GPSGLONASS combination shows evident perform-ance improvements for all the considered parameters rela-tive to GPS only configurations

References

[1] B Hoffmann-Wellenhof H Lichtenegger and J CollinsGlobalPositioning System Theory and Practice Springer New YorkNY USA 1992

[2] ED Kaplan and J Hegarty ldquoFundamentals of satellite naviga-tionrdquo in Understanding GPS Principles and Applications E DKaplan Ed ArtechHouseMobile Communications Series 2ndedition 2006

[3] A Angrisano M Petovello and G Pugliano ldquoGNSSINSintegration in vehicular urban navigationrdquo in Proceedings ofthe 23rd International Technical Meeting of the Satellite Divisionof the Institute of Navigation (GNSS rsquo10) pp 1505ndash1512 TheInstitute of Navigation Portland Ore USA September 2010

[4] A Angrisano M Petovello and G Pugliano ldquoBenefits ofcombined GPSGLONASS with low-cost MEMS IMUs forvehicular urban navigationrdquo Sensors vol 12 no 4 pp 5134ndash5158 2012

[5] B Parkinson and J J Spilker Global Positioning System TheoryAnd Applications vol 1-2 American Institute of Aeronauticsand Astronautics Washington DC USA 1996

[6] C Cai Precise point positioning using dual-frequency GPS andGLONASSmeasurements [MS thesis] UCGEReport no 20291Department of Geomatics Engineering University of CalgaryCalgary Canada 2009

[7] A Angrisano GNSSINS integration methods [PhD thesis]ldquoParthenoperdquo University of Naples 2010

[8] C Cai and Y Gao ldquoA combined GPSGLONASS navigationalgorithm for use with limited satellite visibilityrdquo Journal ofNavigation vol 62 no 4 pp 671ndash685 2009

[9] A Angrisano S Gaglione G Pugliano R Robustelli RSantamaria and M Vultaggio ldquoA stochastic sigma model forGLONASS satellite pseudorangerdquo Applied Geomatics vol 3 no1 pp 49ndash57 2011

[10] ICD-GLONASS Global Navigation Satellite System GLONASSInterface Control Document version 51 Moscow Russia 2008

[11] SC-159 of the RTCAMinimum Operational Performance Stan-dards for Global Positioning SystemWide Area AugmentationSystem Airborne Equipment Document DO-229D RTCAWashington DC USA 2006

[12] E M Mikhail Observations and Least Squares Harper amp Row1976

12 International Journal of Navigation and Observation

[13] D E Wells and E J Krakiwsky The Methods of Least SquaresLecture Notes no 18 Department of Surveying EngineeringUniversity of Brunswick 1971

[14] S Hewitson and J Wang ldquoGNSS receiver autonomous integritymonitoring (RAIM) performance analysisrdquo GPS Solutions vol10 no 3 pp 155ndash170 2006

[15] G Y Chin J H Kraemer and R G Brown ldquoGPS RAIMscreening out bad geometries underworst-case bias conditionsrdquoNavigation Journal of the Institute of Navigation vol 39 no 4pp 407ndash427 1992

[16] R G Brown and G Y Chin ldquoGPS RAIM calculation ofthreshold and protection radius using chi-square methods-a geometric approachrdquo Global Positioning System Institute ofNavigation vol 5 pp 155ndash179 1997

[17] M Petovello Real-time integration of a tactical-grade IMUand GPS for high-accuracy positioning and navigation [PhDthesis] UCGE Report no 20173 Department of GeomaticsEngineering University of Calgary Calgary Canada 2003

[18] W Baarda A Testing Procedure for Use in Geodetic NetworksNetherlands Geodetic Commission Publication on GeodesyNew Series 2 5 Delft The Netherlands 1968

[19] A K Brown ldquoReceiver autonomous integrity monitoring usinga 24-satellite GPS constellationrdquo Navigation Journal of TheInstitute of Navigation vol 5 pp 21ndash33 1998 Red Book ofRAIM

[20] H Kuusniemi User-level reliability and quality monitoringin satellite-based personal navigation [PhD thesis] TampereUniversity of Technology Tampere Finland 2005

[21] H Kuusniemi A Wieser G Lachapelle and J TakalaldquoUser-level reliability monitoring in urban personal satellite-navigationrdquo IEEE Transactions on Aerospace and ElectronicSystems vol 43 no 4 pp 1305ndash1318 2007

[22] A Angrisano S Gaglione and C Gioia ldquoRAIM algorithmsfor aided GNSS in urban scenariordquo in Proceedings of theUbiquitous Positioning Indoor Navigation and Location BasedService Helsinki Finland October 2012

[23] A LeickGPS Satellite Surveying JohnWiley amp Sons HobokenNJ USA 3rd edition 2004

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 International Journal of Navigation and Observation

[13] D E Wells and E J Krakiwsky The Methods of Least SquaresLecture Notes no 18 Department of Surveying EngineeringUniversity of Brunswick 1971

[14] S Hewitson and J Wang ldquoGNSS receiver autonomous integritymonitoring (RAIM) performance analysisrdquo GPS Solutions vol10 no 3 pp 155ndash170 2006

[15] G Y Chin J H Kraemer and R G Brown ldquoGPS RAIMscreening out bad geometries underworst-case bias conditionsrdquoNavigation Journal of the Institute of Navigation vol 39 no 4pp 407ndash427 1992

[16] R G Brown and G Y Chin ldquoGPS RAIM calculation ofthreshold and protection radius using chi-square methods-a geometric approachrdquo Global Positioning System Institute ofNavigation vol 5 pp 155ndash179 1997

[17] M Petovello Real-time integration of a tactical-grade IMUand GPS for high-accuracy positioning and navigation [PhDthesis] UCGE Report no 20173 Department of GeomaticsEngineering University of Calgary Calgary Canada 2003

[18] W Baarda A Testing Procedure for Use in Geodetic NetworksNetherlands Geodetic Commission Publication on GeodesyNew Series 2 5 Delft The Netherlands 1968

[19] A K Brown ldquoReceiver autonomous integrity monitoring usinga 24-satellite GPS constellationrdquo Navigation Journal of TheInstitute of Navigation vol 5 pp 21ndash33 1998 Red Book ofRAIM

[20] H Kuusniemi User-level reliability and quality monitoringin satellite-based personal navigation [PhD thesis] TampereUniversity of Technology Tampere Finland 2005

[21] H Kuusniemi A Wieser G Lachapelle and J TakalaldquoUser-level reliability monitoring in urban personal satellite-navigationrdquo IEEE Transactions on Aerospace and ElectronicSystems vol 43 no 4 pp 1305ndash1318 2007

[22] A Angrisano S Gaglione and C Gioia ldquoRAIM algorithmsfor aided GNSS in urban scenariordquo in Proceedings of theUbiquitous Positioning Indoor Navigation and Location BasedService Helsinki Finland October 2012

[23] A LeickGPS Satellite Surveying JohnWiley amp Sons HobokenNJ USA 3rd edition 2004

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