autonomous ground vehicle path planning in urban...

1

Autonomous Ground Vehicle Path Planning in

Urban Environments using GNSS and Cellular

Signals Reliability Maps – Part II: Simulation and

Experimental ResultsSonya Ragothaman, Student Member, IEEE, Mahdi Maaref,

and Zaher M. Kassas, Senior Member, IEEE

Abstract—A framework for autonomous ground vehicle (AGV)path planning using global navigation satellite systems (GNSS)signals and cellular long term evolution (LTE) signals is evaluatedthrough several simulations and experiments. The objective ofpath planning is to prescribe the optimal path for the AGVto follow to reach a known target point. Optimality is definedas the shortest distance, while minimizing the AGV’s positionestimation error and guaranteeing that the AGV’s positionestimation uncertainty is below a desired threshold. In Part Iof this paper, signal reliability maps were introduced, whichprovides information about regions where large errors due tocellular signal multipath or obstructed GNSS line-of-sight (LOS)are expected. The signal reliability maps were shown to be usefulin calculating the position mean-squared error (MSE). Next,analytical expressions for the AGV state estimates and upperbound on the position bias due to multipath were derived. Finally,a path planning generator was developed, which minimized boththe path length and position MSE, while ensuring that theposition estimation uncertainty and position estimation bias dueto multipath to be below desired thresholds. In this paper, theaccuracy and efficacy of the proposed framework is analyzedthrough several simulations and experiments. Simulation resultsare presented demonstrating that utilizing ambient cellular LTEsignals together with GNSS signals (1) reduces the uncertaintyabout the AGV’s position, (2) increases the number of feasiblepaths to choose from, which could be useful if other consid-erations arise (e.g., traffic jams and road blockages due toconstruction), and (3) yields significantly shorter feasible paths,which would otherwise be infeasible with GNSS signals alone.Experimental results on a ground vehicle navigating in downtownRiverside, California, USA, are presented demonstrating a closematch between the simulated and experimental results.

Keywords—Path planning, trajectory optimization, GNSS, cel-lular signals, signals of opportunity, ground vehicles, geographicinformation systems (GIS).

NOMENCLATURE

rmax Upper bound on position bias.

χm Multipath interference.

ǫm Constant bias between cellular clock biases.

λmax(p, t) Maximum eigenvalue used in path planning.

This work was supported in part by the Office of Naval Research (ONR)under Grant N00014-16-1-2809 and in part by the National Science Founda-tion (NSF) under Grants 1929571 and 1929965.

S. Ragothaman was with the University of California, Riverside and isnow with The Aerospace Corporation. M. Maaref and Z. Kassas are withthe Department of Mechanical and Aerospace Engineering, The Universityof California, Irvine. (email: [email protected], [email protected],and [email protected]).

π Path from start to target location.

τi(x) Path delay between the x-th impulse to the

LOS path.

eθ Symbol timing error.

ξ Correlator spacing in the LTE receiver tracking

loop.

ζ Number of paths in the search space.

ai(x) Complex amplitude of signal path x and LTE

symbol i.bm,p Multipath bias assigned to signal reliability

map.

dLOS Length of the LOS path.

K Number of measurements used in cellular mea-

surement initialization.

L Number of subcarrier symbols in the pilot

sequence.

M Number of cellular base stations in the envi-

ronment.

MSE(p, t) Position MSE used in path planning.

N Number of GNSS satellites in the environment.

p Location index.

t Time.

Ts Sampling interval.

vǫ,m ∼ N (0, σ2ǫm

).

vAGV AGV’s constant speed.

vcell,m ∼ N (0, σ2cell,m).

vgnss,n ∼ N (0, σ2gnss,n).

X Number of impulses.

I. INTRODUCTION

To ensure safe and efficient operation of future autonomous

ground vehicles (AGVs), one must establish performance

guarantees prior to their deployment into the environment.

These performance guarantees consider the AGV’s sensing and

computation capabilities as well as environmental factors (e.g.,

road map, traffic, weather, time of day, etc.). Issues pertain-

ing to perception, navigation, and control of AGVs become

increasingly coupled [1]. In this respect, an AGV could plan

its path, which may temporarily detract it from its desired

final destination, in exchange for improving its situational

awareness and guaranteeing desired safety measures.

2

Path planning has been considered in the recent literature to

account for various sources of uncertainty (e.g., environmental,

sensing, driver intent, etc.).

Predicting global navigation satellite systems (GNSS) signal

power and availability was proposed in [2]–[11]. Such pre-

dictions could be useful for path planning purposes. In [12],

ground vehicles used path planning to predict GNSS quality

of service (QoS) along a route, focusing on QoS parame-

ters: availability, accuracy, reliability, and continuity. In [13],

[14], path planning was considered in a radio simultaneous

localization and mapping (SLAM) context to maximize the

information gathered from ambient signals to yield accurate

positioning and timing. Dilution of precision (DOP) of GNSS

satellites was used in [15] to perform path planning based

on uncertainty in GNSS-derived position estimates. In [16],

probability of arriving on-time in a bus network under travel

time uncertainty was solved using path planning. In [17], a

partially observable Markov decision process (POMDP) was

used for belief state planning to account for uncertainty from

noise in sensor data and the intentions of human drivers.

Maximizing the acquired information for simultaneous local-

ization and target tracking was performed in [18]. Underwater

acoustic transponders were localized in [19] using autonomous

surface vehicle path planning. Unmanned aerial vehicle (UAV)

path planning was considered in [20] to account for map,

location, and sensing uncertainty. In [21], UAV path planning

was considered to optimize received GPS signal quality. A

Markov decision process framework was used in [22] to

generate collision avoidance paths. Path planning to improve

state estimation with GNSS-based receivers has been proposed

using stochastic reachability [23], and GNSS localization error

maps [24]. In [25], a UAV’s path was optimized by consider-

ing the so-called obstructed line-of-sight (LOS) volumes and

multipath volumes.

This is the second of a two-part paper, which consider the

following problem, originally defined in [26]. An AGV is

equipped with receivers capable of producing pseudoranges to

overhead GNSS satellites (e.g., [27], [28]) and to cellular long-

term evolution (LTE) base stations in its environment (e.g.,

[29]–[32]). The AGV fuses these pseudoranges to produce an

estimate about its own position and clock bias and a reference

cellular base station clock bias. The AGV is also equipped with

a three-dimensional (3–D) building map of the environment

(e.g., [33]). Starting from a known point, the AGV desires

to reach a known target point by taking the shortest path,

while minimizing the AGV’s position estimation error and

guaranteeing that the AGV’s position estimation uncertainty is

below a desired threshold. Towards this objective, a so-called

signal reliability map is first generated that specifies which

signals are reliable to use at different locations and at different

times in the environment. Each point in the environment has

a corresponding signal reliability (a boolean measure) for the

different overhead GNSS satellites and nearby cellular base

stations. A reliable GNSS satellite means that there exists an

unobstructed LOS to that satellite. A reliable cellular base

stations means that the pseudorange bias due to multipath is

below a certain desired threshold. Next, equipped with this

signal reliability map, a path planning generator produces the

optimal path to the target point, if any. The path planning

generator also outputs other feasible paths the AGV could

take. These suboptimal, yet feasible paths could be useful,

should the AGV choose to not follow the optimal path, e.g.,

to avoid traffic jams and road blockages due to construction or

emergency. In addition, a table specifying the reliable GNSS

satellites and cellular base stations to use along the optimal

and feasible paths is generated. It is worth recalling that

Part I derived two path planning algorithms: one which is

suitable for short travel times and assumes that the GNSS

satellite geometry is fixed, while the other is suitable for long

travel times and considers GNSS satellite motion. The second

algorithm is more computationally involved.

Part I of the journal focused on modeling, analytical deriva-

tions, and algorithm development [34]. This part presents com-

prehensive simulation and experimental results for different

realistic scenarios evaluating the accuracy and efficacy of the

proposed approach on a ground vehicle navigating in a deep

urban environment.

The simulation study considers three different AGV driving

scenarios, in which

• Scenarios 1 and 2 compare the feasible paths for two

AGVs, where one of the AGVs does not use cellular LTE

signals to produce an estimate of its state (i.e., the AGV

only uses GNSS signals). These scenarios demonstrate

that utilizing the freely available cellular signals in the

environment for AGV navigation: (i) reduce the position

estimation error and (ii) increase the number of feasible

paths to the target point.

• Scenario 3 compares the two path planning algorithms

which (i) assume fixed GNSS satellite geometry and (ii)

consider GNSS satellite motion, for a long travel time

(long trajectory). This scenario demonstrates the effect

of satellite motion on the performance of each of the

algorithms.

• Scenario 4 considers different combinations of receivers:

GPS only, GPS + cellular, GPS + Galileo, and GPS +

Galileo + cellular, to study the impact of adding different

types of signals.

The experimental study was conducted on a ground vehicle

driving in downtown Riverside, California, USA, using real

GPS and LTE signals. Three driving scenarios are considered,

in which

• Scenario 1 compares the experimental navigation per-

formance with the performance simulated by the path

planning generator. A close match is demonstrated be-

tween the optimal path generated experimentally and in

simulation.

• Scenario 2 evaluates the navigation performance when the

vehicle traverses the shortest path, which is an infeasible

path according to the path planning generator. This sce-

nario demonstrates that the path planning generator was

able to predict poor (unsafe) navigation performance.

• Scenario 3 considers long travel time (long trajectory)

and compares the two path planning approaches which (i)

assume fixed GNSS satellite geometry and (ii) consider

GNSS satellite motion. This scenario demonstrates an

3

improved navigation performance in the path planning

generator that accounts for GNSS satellite motion.

The significance of the proposed AGV path planning frame-

work is threefold and is clearly demonstrated in the simulation

and experimental results herein. First, it is shown that using

cellular signals in the environment “opens up” new areas

to navigate reliably and safely, which were infeasible with

GNSS only. This alleviates the need to equip the vehicle

with additional high-grade sensors that may violate cost, size,

weight, and power (C-SWaP) constraints. Second, it is shown

that the proposed approach can successfully predict whether

the AGV’s paths satisfy or violate a desired position estimation

uncertainty. This is crucial for safety considerations as the

shortest (or some other path) may not be safe to traverse.

Third, the optimal path accounts for both distance and position

mean-squared error (MSE) to ensure that lengthy, yet safe

paths (e.g., paths that require the AGV to leave and re-enter

the urban environment) are deweighted.

This paper is organized as follows. Section II overviews

the path planning generator developed in Part I. Section III

presents simulation results evaluating the performance of the

AGV path planning approach. Section IV presents experi-

mental results for different ground vehicle driving scenarios.

Section V gives concluding remarks.

II. OVERVIEW OF PATH PLANNING GENERATOR

The path planing generator developed in Part I is illustrated

in Fig. 1 (or Fig. 2 from the companion paper, Part I) [34]. The

generator accounts for position errors by calculating cellular

pseudorange measurement biases and whether the receiver has

a clear LOS to GNSS satellites. This is accomplished by

using a 3–D building map of the environment to generate

a so-called signal reliability map from which the expected

accuracy of GNSS- and cellular-based navigation solution

are produced. For GNSS signals, the signal reliability map

specifies to which GNSS satellites the AGV would has a

clear LOS for different locations at different times in the

environment. For cellular signals, the signal reliability map

specifies the expected pseudorange bias due to multipath.

The signal reliability map is used to calculate the position

MSE at different locations in the road network. Finally, the

path generator finds the optimal path by minimizing the

position MSE and distance, while guaranteeing that the bias

in the estimate due to multipath is below a desired threshold

as well as ensuring that the maximum position uncertainty is

below a desired threshold. The path generator also produces a

table of reliable GNSS satellites and cellular base stations for

the AGV to use as it executes the optimal path. Specifically,

GNSS measurements are used if the GNSS reliability map

at the closest location index classifies the satellite as having

LOS. Cellular measurements are used if the cellular reliability

map at the closest location index classifies the measurement

as having multipath-induced bias below a threshold.

III. SIMULATION STUDY

This section presents simulation results evaluating the per-

formance of the AGV path planning approach developed in

Optimal path

Table of reliableGNSS satellitesand cellulartowers

Fig. 1. Flowchart of the proposed path planning generator. The path planninggenerator is assumed to have knowledge of GNSS orbital data, cellular basestation positions, and 3–D environment map. The user inputs are: departuretime, start position, target position, position bias threshold, and positionuncertainty threshold. The thresholds are used as constraints to find the optimalpath. The outputs of the path planning generator are the optimal path and atable of reliable GNSS satellites and cellular base stations to use along theoptimal path.

Part I. The following subsections describe the simulation envi-

ronment setup, multipath simulation, and simulation scenarios,

followed the simulation results.

A. Simulation Environment Setup

The simulation environment considered an AGV navigating

downtown Riverside, California, USA. A 3–D building map of

this environment was obtained from ArcGIS online [35]. The

GNSS satellite constellation considered comprised GPS and

Galileo satellites, and the GNSS signal reliability map were

generated using the method described in Part I, Subsection IV-

A. Fig. 2 illustrates the GNSS satellites’ skyplot over Riverside

at time t = 11:00 am, coordinated universal time (UTC), on

August 23, 2018. The elevation and azimuth angles for both

GPS and Galileo satellites were obtained using the PyEphem

Python library [36]. Satellites with an elevation angle less

than 15◦ were not used, as signals from these satellites tend

to be severely degraded due to ionosphere, troposphere, and

multipath [37].

Fig. 3 illustrates the simulation environment, the start and

target points, and the location of the cellular base stations that

were surveyed by the authors. Cellular reliability maps were

generated: three base stations located inside the downtown

area and one base station located outside the downtown area.

The simulation settings over four scenarios are summarized in

Table I.

B. GNSS Simulation

The model presented in Part I, Subsection IV-A was used

to simulate the GNSS reliability maps using ArcGIS® [33].

The GNSS satellite ephemeris data was found on the North

American Aerospace Defense Command (NORAD) two-line

element data set [41]. A 3-D building map was obtained from

ArcGIS®, and the accuracy of the model is expected to be

4

GPS

Galileo

N

NW

W

S

E

SW SE

20

18

7

30

8

2

31

10

32

1126

122

14

Fig. 2. Skyplot of GNSS satellites over Riverside, California, USA, at 11:00am UTC, August 23, 2018. The skyplot shows the elevation and azimuthangles of GNSS satellites. The green and pink circles correspond to GPS andGalileo satellites respectively. The numbers correspond to the pseudorandomnoise (PRN) code for each satellite [38], [39]. Data source: [40].

Start point

Target point

LTE Tower

Fig. 3. Simulation environment showing the start and target points andlocation of four cellular base stations. This figure was obtained with ArcGIS®

[33].

around 4.13 meters based on a study of OpenStreetMap [?],

[42]. A Python toolbox in ArcGIS® was created to generate

point features with reliability map information for a specified

time interval. GNSS LOS was calculated by generating a line

feature of fixed length along the LOS between the GNSS satel-

lite and the point feature location. GNSS LOS was calculated

at 5 second intervals, and times with changed visibility were

recorded as tuples according to Part I, Subsection IV-A. For the

experimental section, the GNSS reliability map was calculated

on the day of the experiment.

C. Multipath Simulation

The model presented in Part I, Subsection IV-B was used

to simulate pseudorange biases caused by multipath. The

TABLE ISIMULATION SETTINGS

Parameter Definition Value

N Number of GNSS satellites 14

MNumber of cellular base

stations4

t Time in UTC (Scenario 1 & 2)August 23, 2018,

11:00 am

{σ2gnss,n}Nn=1

GNSS measurement noisevariance

5 m2

{σ2cell,m}Mm=1

Cellular measurement noisevariance

5 m2

X Number of impulsesAn output of

Wireless Insite

ai(x)Complex amplitude of signal

path x and LTE symbol iAn output of

Wireless Insite

τi(x)Path delay between the x-th

impulse to the LOS pathAn output of

Wireless Insite

Ts Sampling interval 3.25× 10−8 s

LNumber of subcarrier symbols

in the pilot sequence200

ξCorrelator spacing in the LTE

receiver tracking loop0.5

eθ Symbol timing error 0

complex channel impulse responses on a grid of receiver

locations were generated using Wireless Insite X3D model

[43] to calculate multipath bias bm,p according

bm,p , χm + cτi(0)− dLOS, (1)

for each cellular base station and each receiver location index

p. In (1):

• c is the speed of light

• dLOS is the length of the LOS path and is equal to the

distance between the receiver and the transmitter in each

simulated receiver location.

• τi(0) is the time of flight of the first received peak and

is an output of Wireless Insite.

• χm is the multipath interference bias and is calculated

using equations (7) and (8) described in Part I, Subsection

IV-B. The required parameters to construct χm are given

in Table I, among which X , ai(x), and τi(x) are outputs

of Wireless Insite, for each receiver location.

The simulated induced multipath biases {bm,p}4m=1 obtained

from (1) for all four transmitters and 1000 receiver locations

(i.e., {pi}1000i=1 on the grid map) are shown in Fig. 4. The

multipath-induced bias was simulated at several location in-

dices in the environment without order. The spacing between

location indices was 8 meters.

The position MSE and largest eigenvalue of the position

estimation error covariance were calculated from the GNSS

and cellular signal reliability map as described in Part I,

Section V. The chosen spacing between location indices is

8 meters.

D. Simulation Scenario Description

The output of the path planning generator is studied over

three scenarios. In the first two scenarios, two AGVs were

5

0 200 400 600 800 1000

Receiver location indices

-2

0

2

4

6

Multip

ath

bia

s [m

]

Tower 2

0 200 400 600 800 1000


-4

-2

0

2

4

6

Multip

ath

bia

s [m

]

Tower 3

0 200 400 600 800 1000


-5

0

5

Multip

ath

bia

s [m

]

Tower 4

0 200 400 600 800 1000


-5

0

5

Multip

ath

bia

s [m

]

Tower 1

Fig. 4. The simulated induced multipath bias for all cellular base stationsobtained from (1). The multipath-induced bias was simulated at severallocation indices in the environment without order. The spacing betweenlocation indices was 8 meters.

considered to be present in the urban environment. Both

AGVs had the same start position, target position, and time of

departure. Moreover, the optimization problem for each AGV

used the same threshold values λmax and rmax. The optimal

and feasible paths for both vehicles were calculated using

Approach A described in Part I, Section VI, which does not

account for GNSS satellite motion. AGV A was equipped with

only GPS and Galileo receivers, while AGV B was equipped

with GPS, Galileo, and cellular LTE receivers. The difference

between the two scenarios was the choice of thresholds.

In the third scenario, an AGV was present in an urban

environment and was equipped with GPS, Galileo, and cellular

LTE receivers, similar to AGV B in the previous two scenarios.

The AGV was prescribed a long trajectory, and the start and

target locations are chosen differently compared to the first

scenario. A trajectory is considered long if it is expected

to take longer than 15 minutes to traverse, or if there is a

sharp change in the GNSS LOS along the path. The optimal

and feasible paths were calculated using the two approaches

for generating paths discussed in Part I, Section VI, where

Approach A does not account for GNSS satellite motion, while

Approach B accounts for GNSS satellite motion. The optimal

and feasible paths for both approaches were compared.

A fourth simulation scenario considers four receiver com-

binations (i) GPS only, (ii) GPS + cellular, (iii) GPS +

Galileo, and (iv) GPS + Galileo + cellular. The position RMSE

and maximum eigenvalue metrics are calculated over a few

locations to analyse the impact of adding receivers to the

simulated positioning accuracy.

The simulation results for each scenario are presented next.

E. Simulation Results

1) Scenario 1: Table II shows the thresholds used for both

AGV A and AGV B. As discussed in Part I, Sections V–VI,

the user-specified thresholds are rmax and λmax, from which

ηmax is computed according to equation (16) in Part I, and

ηm corresponds to the m-th element of R−T

a 1(N+M)×1ηmax.

The thresholds were chosen such that rmax +√λmax is

approximately half the width of the street. The thresholds were

chosen to bound the error statistics such that the vehicle does

not calculate position to be in the middle of a building or at

a different location index further up the street. It is important

to know the correct closest location index because the set

of reliable transmitters is different for each location index.

Using the reliable transmitters at an adjacent location index

can cause the AGV-mounted receiver to use measurement that

is not reliable.

TABLE IISCENARIO 1 THRESHOLDS


rmax Position bias threshold 4 m

λmaxEigenvalue constraint

threshold4 m2

ηmax Pseudorange error threshold 1 m

ηmWeighted pseudorange error

threshold

√5 m

For the given simulation settings, AGV A had no feasible

path which satisfies the constraints. One path was returned by

the proposed algorithm by relaxing the eigenvalue constraint

to λmax = 4.44 m2. Fig. 5 (a) illustrates this path. Table III

presents this path’s distance, total RMSE, maximum eigen-

value, and the cost function value. For a given path π, the

total RMSE was calculated according to

Total RMSE =

√√√√∑p∈π

MSE(p)

h(π),

where h(·) denotes the number of locations in the path π. In

contrast, AGV B had four feasible paths without the need to

relax the eigenvalue constraint (i.e., with λmax = 4), with Path

B1 being the optimal path. Fig. 5 (b) illustrates these paths and

Table III compares them.

TABLE IIISCENARIO 1 RESULTS

Path DistanceTotal

RMSE

Maximum

eigenvalue

CostFunction

Value

AGV A Path A1⋆ 1006 m 4.37 m 4.44 m2 16397

AGV B Path B1 995 m 3.91 m 3.53 m2 13108

Path B2 1016 m 3.91 m 3.74 m2 13158

Path B3 1006 m 3.95 m 3.91 m2 13358

Path B4 1004 m 3.96 m 3.74 m2 13408

⋆ No feasible path was found for AGV A. This path was found after

relaxing the the eigenvalue constraint.

The following can be concluded from the above results.

First, including cellular LTE signals made the optimization

problem feasible, without having to relax the constraint. Sec-

ond, including cellular LTE signals resulted in several feasible

paths to choose from (besides the optimal path), which could

be useful if other considerations arise, e.g., traffic jams and

road blockages due to construction. Third, while the optimal

6

path ended up yielding the shortest distance together with the

total RMSE, a tradeoff between the shortest path and the total

RMSE can be seen in the other feasible paths (e.g., Path B2

has lower total RMSE than Path B3 but has longer distance).

Target point

Start point Path A1: optimal

(a) (b)

Path B1: optimalPath B2: feasiblePath B3: feasiblePath B4: feasible

Fig. 5. Simulation results for Scenario 1. (a) The optimal path for AGVA, generated after relaxing the eigenvalue constraint from λmax = 4 toλmax = 4.44. (b) The optimal path and three feasible paths for AGV Bwithout relaxing the eigenvalue constraint (i.e., with λmax = 4). The optimalpath Path B1 was shorter and produced less total RMSE than all other paths:Path A1, Path B2, Path B3, and Path B4. This figure was obtained withArcGIS® [33].

2) Scenario 2: This scenario is similar to Scenario 1, except

that the eigenvalue constraint is relaxed even further to obtain

several feasible paths for AGV A. Table IV shows the new

thresholds used for both AGV A and AGV B.

TABLE IVSCENARIO 2 THRESHOLDS




threshold5 m2

ηmax Pseudorange error threshold2

√

5m

ηmWeighted pseudorange error

threshold2 m

By changing the constraints from Scenario 1, the number of

feasible paths for AGV A increased from zero to two, while

the number of feasible paths for AGV B increased from four

to twelve possible paths. Fig. 6 (a) illustrates these paths and

Table V compares them. Fig. 6 (b)–(d) illustrates all these

paths and Table V compares them.

The following can be concluded from the above results.

First, while both AGV A and AGV B found optimal and

feasible paths, the optimal path for AGV B was significantly

shorter than that for AGV A. Hence, utilizing cellular signals

“opened up” areas in the environment that were otherwise

infeasible with GNSS only. Second, slightly relaxing the con-

straint resulted in many new feasible paths versus Scenario 1,

with the optimal path Path B1 in Scenario 2 being reasonably

shorter than the optimal path in Scenario 1 (namely, 33%shorter) with a slightly larger RMSE (namely, 11% higher).

3) Scenario 3: In this scenario, the optimal and feasible

paths are compared for Approach A and Approach B of the

path planning generator. The AGV is equipped with GPS,

Galileo, and cellular LTE receivers. Approach A does not

account for GNSS satellite motion, while Approach B accounts

TABLE VSCENARIO 2 RESULTS

Path DistanceTotal

RMSE

Maximum

eigenvalue

CostFunction

Value

AGV A Path A1 1006 m 4.37 m 4.44 m2 16397

Path A2 1013 m 4.44 m 4.44 m2 17012

AGV B Path B1 748 m 4.34 m 4.28 m2 11724

Path B2 995 m 3.91 m 3.53 m2 13108

Path B3 1016 m 3.91 m 3.74 m2 13158

Path B4 1006 m 3.95 m 3.74 m2 13358

Path B5 1004 m 3.95 m 3.74 m2 13408

Path B6 1013 m 3.97 m 4.28 m2 13412

Path B7 1006 m 3.97 m 4.28 m2 13462

Path B8 1014 m 4.17 m 4.28 m2 14605

Path B9 1493 m 4.08 m 4.20 m2 21519

Path B10 1491 m 4.18 m 4.28 m2 22515

Path B11 1750 m 4.11 m 4.28 m2 24401

Path B12 1756 m 4.11 m 4.28 m2 25397

Target point

Start point

Path A1: optimalPath A2: feasible


Path B5: feasiblePath B6: feasiblePath B7: feasiblePath B8: feasible


(b)(a)

(d)(c)

Fig. 6. Simulation results for Scenario 2. (a) The feasible paths for AGV A,where Path A1 is the optimal path. (b) Four feasible paths for AGV B whichproduced the lowest cost function, i.e., Paths B1 – B4. (c) Paths B5 – B8 forAGV B in order of lowest to highest cost function value. (d) Paths B9 – B12for AGV B in order of lowest to highest cost function value. This figure wasobtained with ArcGIS® [33].

for GNSS satellite motion. Table II and Table VI show the

simulation settings for this scenario. The value vAGV was

chosen at a time when there were sharp changes in the costs

and constraints over the duration of the AGV’s trajectory due

to GNSS satellite motion. The value ζ was chosen such that

the search space for Approach B included all paths that were

feasible using Approach A.

7

TABLE VISCENARIO 3 SETTINGS


t Time in UTCDecember 26, 2018,

3:04 pm

vAGV Vehicle speed 3.2 m/s

ζSearch space size for path

planning generator4534

For the given simulation settings, there are eight feasible

paths according to Approach A, and 279 feasible paths ac-

cording to Approach B. Fig. 7 shows the first eight feasible

paths using either approach and Table VII compares them.

TABLE VIISCENARIO 3 RESULTS

Path DistanceTotal

RMSE

Maximum

eigenvalue

Cost

Function

Value

ApproachA

Path A1 1600 m 2.97 m 3.22 m2 14934

Path A2 1603 m 2.97 m 3.22 m2 15029

Path A3 1862 m 2.94 m 2.90 m2 17042

Path A4 1865 m 2.94 m 2.90 m2 17137

Path A5 1854 m 2.97 m 3.22 m2 17190

Path A6 1857 m 2.97 m 3.22 m2 17285

Path A7 2116 m 2.94 m 2.90 m2 19298

Path A8 2119 m 2.94 m 2.90 m2 19393

ApproachB

Path B1 1605 m 2.84 m 3.55 m2 12336

Path B2 1608 m 2.84 m 3.55 m2 12526

Path B3 1609 m 2.82 m 3.55 m2 13165

Path B4 1612 m 2.83 m 3.55 m2 13345

Path B5 1864 m 2.76 m 3.69 m2 13829

Path B6 1855 m 2.80 m 3.69 m2 13831

Path B7 1854 m 2.83 m 3.69 m2 13861

Path B8 1863 m 2.79 m 3.69 m2 13866

The following can be concluded from the results. First,

new feasible paths became available in Approach B. There

were 48 feasible paths with lower cost than Path A1. This

occurred because after the start time, there was a significant

decrease in the maximum eigenvalue in several areas in the

road network, which resulted in a large increase in the number

of feasible paths. Clearly, there was large discrepancy between

the simulation results of both approaches, which demonstrates

that accounting for satellite motion is necessary for long

trajectories. Second, there were feasible paths according to

Approach A that were in fact infeasible, e.g., Paths A1 (the

optimal path), A2, A5 and A6. An AGV that takes any of these

paths will suffer from poor navigation performance. Even if

the optimal path for Approach A was the same as that of

Approach B, the table of reliable GNSS satellites and cellular

base stations produced by Approach A does not account for

satellite motion and may become unusable as GNSS satellites’

LOS geometry change over long durations. This may cause

the AGV to ignore measurements that are in fact reliable, or

(a) (b)

(c) (d)

Target point

Start point

Path A1: optimalPath A2: feasiblePath A3: feasiblePath A4: feasible

Path A5: feasiblePath A6: feasiblePath A7: feasiblePath A8: feasible



Fig. 7. Simulation results for Scenario 3. (a) Four feasible paths fromApproach A which produced the lowest cost function, i.e., Paths A1 – A4. (b)Paths A5 – A8 from Approach A in order of lowest to highest cost functionvalue. (c) Paths B1 – B4 from Approach B in order of lowest to highest costfunction value. (d) Paths B5 – B8 from Approach B in order of lowest tohighest cost function value. This figure was obtained with ArcGIS® [33].

accept measurements that are unreliable, thus further affecting

the navigation performance. This result further demonstrates

the importance of accounting for satellite motion for long

trajectories.

4) Scenario 4: This scenario compares four receiver com-

binations (i) GPS only, (ii) GPS + cellular, (iii) GPS +

Galileo, and (iv) GPS + Galileo + cellular. The position RMSE

and maximum eigenvalue metrics are calculated over a few

locations to demonstrate the impact of adding receivers to the

expected positioning accuracy. The path planning metrics are

calculated using the simulation settings in Table IV. Fig. 8

shows the position RMSE and maximum eigenvalue metrics.

Based on Fig. 8, it is obvious that using receivers (i) GPS

only and (iv) GPS + cellular + Galileo is expected to yield the

worst and best navigation performance, respectively. This can

be seen based on both the position RMSE and eigenvalue con-

straint metrics. The RMSE with receiver (iii) GPS + Galileo

was lower than (ii) GPS + cellular in some locations. This

result is expected because more Galileo satellites than cellular

base stations were present (namely, 7 versus 4). However,

there are some locations where receiver (ii) GPS + cellular

outperforms than (iii) GPS + Galileo. This is especially true

for the maximum eigenvalue metric, which corresponds to the

maximum position uncertainty and the upper bound on the

position bias. It can be seen that there is one location where

the maximum eigenvalue constraint is satisfied for (iii) GPS

+ cellular, but not for (iii) GPS + Galileo. This shows that

although (iii) GPS + Galileo performs better than (ii) GPS +

cellular for most locations, there are some locations that using

cellular signals can “open up” areas in the environment that

8

(a)

(c)

(e)

(g)

RMSE < 5

5<RMSE<10

10<RMSE<15

RMSE > 15

N=A

(b)

(d)

(f)

(h)

3 < λmax < 3:53:5 < λmax < 44 < λmax < 4:5

N=A

λmax < 3

4:5 < λmax < 5

(i) GPS only

(ii) GPS +cellular

(iii) GPS +Galileo

(iv) GPS +

Galileocellular +

Position RMSE λmax constraint

Fig. 8. Simulation results for Scenario 4. The shown receiver combinationsare (a)–(b) GPS only, (c)–(d) GPS + cellular, (e)–(f) GPS + Galileo, and (g)–(h) GPS + Galileo + cellular. The left column (a), (c), (e), (g) correspondsto simulated position RMSE. The right column (b), (d), (f), (h) correspondsto the simulated largest eigenvalue metric. N/A corresponds to the situationin which the vehicle-mounted receiver did not have a sufficient number ofmeasurements to estimate the vehicle’s position. This figure was obtainedwith ArcGIS® [33].

were otherwise infeasible with GNSS only.

IV. EXPERIMENTAL STUDY

This section presents experimental results for ground vehi-

cle path planning in an urban environment with real GNSS

and cellular LTE singals. The next subsection describes the

experimental setup and the scenarios considered, while the

following subsection discusses the obtained results.

A. Experimental Setup and Scenario Description

A vehicle was equipped with a consumer-grade cellular

omnidirectional Laird antenna to receive cellular LTE signals

[44]. The signals were down-mixed and sampled using a

National Instruments (NI) dual-channel universal software

radio peripheral (USRP)–2954R®, driven by a GPS-disciplined

oscillator (GPSDO) [45]. The vehicle was also equipped

with a Septentrio AsteRx-i V® integrated GNSS and inertial

measurement unit (IMU) module, which is equipped with a

dual antenna, multi-frequency GNSS receiver and a Vector-

nav VN-100 micro-electromechanical system (MEMS) IMU.

Septentrio’s post-processing software development kit (PP-

SDK) was used to process carrier phase observables collected

by the AsteRx-i V® and by a nearby differential GPS base

station to obtain a carrier phase-based navigation solution. This

integrated GNSS-IMU real-time kinematic (RTK) system was

used to produce the vehicle’s ground truth path. The GNSS

receiver also produced GNSS pseudorange measurements,

which were used as discussed in Part I, Sections III–IV.

Signals from cellular LTE base stations were processed with

the Multi-channel Adaptive TRansceiver Information eXtrac-

tor (MATRIX) software-defined receiver (SDR) to produce

pseudoranges [32], [46]. The experimental setup is shown in

Fig. 9.

Storage

USRP{2954R R©

IntegratedGNSS-IMU

Cellular antennas

(b) (c)

(a)

Fig. 9. Experimental setup. (a) A depiction of the vehicle used to conduct theexperiment, which was equipped with the AsteRx-i V® GNSS-IMU module,antennas, USRP–2954R® , and laptop for storage and processing. (b) Thehardware setup mounted on top of the vehicle. (c) The hardware setup placedinside the vehicle.

The experiment was conducted in downtown Riverside, Cal-

ifornia, USA. The characteristics of the four LTE base stations

are summarized in Table VIII and their locations are depicted

in Fig. 10. The red X’s signify locations where the vehicle was

stationary for a few seconds. The measurement noise variances

and cellular clock bias parameters were calculated at this time.

Two locations were used to receive measurements from all the

cellular base stations in the environment.

TABLE VIIICHARACTERISTICS OF THE LTE BASE STATIONS

TowerService

provider

Carrier frequency

(MHz)Cell ID

Bandwidth

(MHz)

1 AT&T 1955 219 20

2 AT&T 1955 348-350 20

3 Verizon 2145 392 20

4 Verizon 2145 79 20

Due to the hardware setup used in the experiment, the

GPS receiver and LTE receiver clocks were not synchronized,

which implies that each receiver had a different clock bias,

denoted δtrgnss and δtrcell , respectively. To account for this,

the GPS receiver’s clock bias in Part I, equation (1), namely

δtrgnss , was included into the state xr, while the difference

between the LTE receiver’s clock bias and the first LTE base

stations clock bias, namely (δtrcell − δtcell,1) was included in

the state xr. Therefore, the state vector that was estimated

was xr =[rT

r , cδtrgnss , c(δtrcell − δtcell,1)]T

. The matrix B

in Part I, equation (5) was adjusted in accordance with this

9

LTE tower 1

LTE tower 2

LTE tower 4

LTE tower 3

Fig. 10. Location of four LTE base stations in downtown Riverside,California, whose signals were used. The red X’s signify locations wherethe measurement noise variances and cellular clock bias parameters werecalculated. Two locations were used to receive measurements from all thecellular base stations in the environment. This figure was obtained withArcGIS® [33].

new state to become

B ,

[1N×1 0N×1

0M×1 1M×1

]. (2)

The matrix B shown here is to be used when the GNSS

and LTE receiver clocks are not synchronized. The clock bias

matrix from Part I should be used when the GNSS and LTE

receiver clocks are not synchronized.

This section considers three experimental scenarios. The

first scenario compares the experimental navigation perfor-

mance (i.e., path length, total RMSE, maximum eigenvalue,

cost function) versus the navigation performance predicted

by the offline path planning generator. Eight GPS satellites

were present at the time of the experiment and four LTE base

stations were used. Fig. 11 depicts the start and target points

for the ground vehicle. The path planning approach described

in Section III was executed offline with the settings in Table

IX. The spacing between location indices where the position

MSE was simulated was 8 meters. The LTE measurement

noise variances were calculated using the sample variance

from received pseudoranges, while the vehicle was stationary

over K = 100 samples. The perturbation parameters ǫm and

σ2ǫ,m were also calculated, while the vehicle was stationary

over K = 10 samples. The path planning generator returned

an optimal path and a feasible path depicted in Fig. 11.

The second scenario evaluates the navigation performance

if the vehicle chooses to take the shortest path (path 3 in Fig.

11) instead of the optimal or feasible path. The settings for

Scenario 2 are identical to those in experimental Scenario 1.

The third scenario compares the two approaches for gener-

ating paths discussed in Section Part I, Section VI, where Ap-

proach A does not account for satellite motion and Approach B

does account for satellite motion. A vehicle was driven along

Target point

Cellular

Start point

tower

Cellulartower

Path 1: optimal

Path 2: feasible

Path 3: shortest(infeasible)

Fig. 11. The optimal path and feasible path returned by the path planninggenerator. Path 3 is the shortest path between the start and target points but isinfeasible as it violates the constraints. This figure was obtained with ArcGIS®

[33].

TABLE IXEXPERIMENT SETTINGS FOR SCENARIOS 1 AND 2


N Number of satellites 8

MNumber of cellular base

stations4

t Start time (UTC)August 24, 2018,

6:34 am



threshold30 m2

ηmaxPseudorange error

threshold2

√

10

KNumber of cellular

measurements used forinitialization

10

{σ2gnss,n}Nn=1


{7.1, 5.1, 3.9,6.9, 7.1, 6.7,5.8, 9.5} m2

{σ2cell,m

}Mm=1Cellular measurement

noise variance{8.7, 4.4, 7.8,

4.6}m2

a long trajectory, which was infeasible according to Approach

A but feasible according to Approach B. The experimental

results along this path were compared to the simulated results

from Approaches A and B. Table X provides the settings for

Scenario 3 that differ from Scenario 1.

The experimental results for the three scenarios are pre-

sented next.

B. Experimental Results

1) Scenario 1: The purpose of this scenario is to compare

the simulated path planning navigation results with the ex-

perimental navigation results. The vehicle was driven along

the optimal path, then the feasible path, and it was assumed

that the satellite geometry over the two paths did not change

10

TABLE XEXPERIMENT SETTINGS FOR SCENARIO 3


vAGV Vehicle speed 3.2 m/s

t Start time (UTC)December 26, 2018,

3:00 pm

{σ2gnss,n}Nn=1


{7.7, 4.5, 5.6,7.2, 4.9, 9.0,8.6, 8.7} m2

drastically. The time difference between the two paths was 5minutes and 40 seconds, which is below the threshold time

for long trajectories (15 minutes). It was also confirmed that

there are no sharp changes in the GNSS reliability maps along

the path. Table XI compares the navigation performance (i.e.,

path length, total RMSE, maximum eigenvalue, cost function)

along the optimal and feasible paths returned by the simulated

results versus those returned experimentally.

TABLE XISCENARIO 1: SIMULATED AND EXPERIMENTAL NAVIGATION RESULTS

ALONG OPTIMAL AND FEASIBLE PATHS

Path length Total RMSE

Path Simulation Experiment Simulation Experiment

Path 1: optimal 872 m 878 m 6.55 m 6.63 m

Path 2: feasible 884 m 886 m 7.19 m 7.47 m

Maximum eigenvalue Cost function value

Path Simulation Experiment Simulation Experiment

Path 1: optimal 27.91 m2 27.27 m2 55939 42216

Path 2: feasible 27.91 m2 26.85 m2 68688 60029

Note the close match between the simulated and experi-

mental navigation performance. In particular despite the differ-

ences in the simulated and experimental cost function values,

Path 1 performed better than Path 2, as predicted by the path

planning generator.

The simulated RMSE at each location and the actual RMSE

are compared in Fig. 12. Also shown in Fig. 12 are the

vehicle’s ground truth path versus the path estimated with

GNSS and cellular LTE signals. From Fig. 12, it can be seen

that the simulated RMSE closely follows the experimentally

estimated path. The simulated RMSE at each location and the

actual position error are compared in Fig. 12. It can be seen

that the experimental errors are close to the simulated RMSE

for some times.

There are some discrepancies between the simulated and

experimental results. In one particular area of Fig. 12 (depicted

with a dashed circle), the experimental RMSE was 19.51 m,

while the simulated RMSE at that area was smaller than 5m. This result can also be seen in Fig. 13 (b) (depicted with

dashed circles) from 108 s to 110 s. It can additionally be

seen that the simulated RMSE increases to 17.01 m there

after. There are also unexpectedly high experimental position

errors that do not match the simulated RMSE from 41 s to

45 s. This may be due to the fact that the simulator does not

account for attenuation due to trees (there was dense foliage

near both areas). This result reveals that accurate knowledge

of the environment could be crucial for accurately simulating

the position MSE. The foliage was not included in the 3–

D map because it was not surveyed or available online prior

to the experiment. However, existing software packages (e.g.,

Wireless Insite) could simulate foliage effects. There are also

areas in Fig. 13 (b) where the simulated RMSE is larger

than the experimental RMSE, such as from 60 s to 80 s.

This is a period of time where the vehicle was stationary,

and the actual measurement noise variances may be smaller

than the those calculated in the initialization step. This can be

addressed in future work by parameterizing the measurement

noise variances according to the carrier-to-noise ratio (C/N0)

instead of assuming it is constant.

2) Scenario 2: This scenario evaluates the navigation per-

formance for a vehicle using Dijkstra’s path planning algo-

rithm to execute the path with the shortest length. In other

words, the path planning algorithm does not account for

navigation performance. Path 3 in Fig. 11 is chosen which

has a corresponding distance of 629 m between the start and

target points. As shown in Fig. 12 (c) and (f), path 3 was

deemed infeasible by the path planning generator as several

areas had a simulated RMSE over 20 m, and one area had an

insufficient number of measurements to produce an estimate

for xr.

The experimental RMSE along the entire path was 12.12 m

in areas where the navigation solution was computed, which

is twice as large as the position RMSE of the other two paths.

The dashed circle depicted in Fig. 12 (f) shows the area where

the vehicle was unable to estimate its position from GNSS

and cellular signals, which is consistent with Fig. 12 (c). The

result in this scenario highlights the importance of planning

the path of an AGV to avoid situations where the AGV could

not estimate its state.

3) Scenario 3: This scenario computes the simulated nav-

igation performances using Approach A and Approach B of

the path planning generator, and compares the results with

experimental data. The experimental data was collected along

a path that was infeasible according to Approach A but feasible

according Approach B. This path is shown in Fig. 14.

Table XII compares the navigation performance along this

path as returned by the simulated results versus those found

experimentally.

TABLE XIISCENARIO 3: SIMULATED AND EXPERIMENTAL NAVIGATION RESULTS

ALONG THE CHOSEN PATH

DistanceTotal

RMSE

Maximum

eigenvalue

Cost

FunctionValue

Experiment data 1187 m 5.78 m 27.93 m2 34890

Simulation data(Approach A)

1152 m 5.98 m 31.49 m2 35773

Simulation data(Approach B)

1152 m 5.94 m 29.19 m2 35369

It can be seen that the experimental results (total RMSE,

maximum eigenvalue, and cost function) agree more with

Approach B than Approach A. These results demonstrate an

11

(a)

(d)

(b)

(e)

Start point

RMSE < 5

5<RMSE<10

10<RMSE<15

RMSE > 15

N=A

Estimated pathGround truth path

(c)

(f)

Target point Start point

Start point

Target pointTarget point

Path 1: Optimal Path 2: Feasible Infeasible path

Fig. 12. Simulated and experimental results along the optimal path (a), (d) and feasible path (b), (e). Here, (a), (b) show the simulated RMSE values atlocations along the path, while (d), (e) compare the vehicle’s experimentally estimated path from GNSS and cellular signals versus the ground truth path fromthe GNSS-IMU with RTK module. Simulated and experimental results along the shortest (but infeasible) path (c), (f). Here (c) shows the simulated RMSEvalues, while (f) compares the vehicle’s experimentally estimated path from GNSS and cellular measurements. The dashed circle in (c) specifies the area inwhich the simulator did not have a sufficient number of measurements to estimate the vehicle’s position (corresponding to an RMSE of N/A), which matchesthe same area in (f) at which there weren’t sufficient pseudorange measurements from GNSS and cellular signals to estimate the vehicles’s position. Thisfigure was obtained with ArcGIS® [33].

improvement in the path planning generator when satellite

motion is accounted for.

The experimental results also show that the chosen path is

feasible because it satisfies the constraint, which is consistent

with Approach B but not consistent with Approach A. This

shows that accounting for GNSS satellite motion can lead to

prescribed paths that are shorter or have less error.

V. CONCLUSION

This paper considered the problem where an AGV equipped

with GNSS and cellular receivers desires to reach a target loca-

tion by taking the shortest path with minimum position MSE,

while guaranteeing that the bias in the position estimate and

the position uncertainty are below desired thresholds. Part I of

this paper discussed algorithms to generate signal reliability

maps and path planning. This part presented simulation and

experimental results demonstrating the efficacy and accuracy

of the path planning approach for several driving scenarios.

The simulation results revealed that the path planning approach

(1) reduced the uncertainty about the AGV’s position, (2)

increased the number of feasible paths to choose from, which

could be useful if other considerations arise (e.g., traffic jams

and road blockages due to construction), and (3) yielded

significantly shorter feasible paths, which would otherwise

be infeasible with GNSS signals alone. The experimental

results carried out on a ground vehicle navigating in downtown

Riverside, California, USA, demonstrated a close match with

the simulated results.

ACKNOWLEDGMENT

The authors would like to thank Joe Khalife, Kimia

Shamaei, and Cody Simons for their help with the data

collection.

REFERENCES

[1] T. Luettel, M. Himmelsbach, and H. Wuensche, “Autonomous groundvehicles– concepts and a path to the future,” Proceedings of the IEEE,vol. 100, no. Special Centennial Issue, pp. 1831–1839, May 2012.

[2] S. Saab and Z. Kassas, “Map-based land vehicle navigation system withDGPS,” in Proceedings of IEEE Intelligent Vehicle Symposium, vol. 1,June 2002, pp. 209–214.

[3] S. Saab and Z. Kassas, “Power matching approach for GPS coverageextension,” IEEE Transactions on Intelligent Transportation Systems,vol. 7, no. 2, pp. 156–166, June 2006.

[4] Y. Lee, Y. Suh, and R. Shibasaki, “Ajax GIS application for GNSSavailability simulation,” Journal of Civil Engineering, vol. 11, no. 6,pp. 303–310, November 2007.

12

(b)

(a)

Fig. 13. Simulated position RMSE and experimental position error along theoptimal path (a) and feasible path (b). The simulated position RMSE valuesare shown by red dots, while the experimental position error is shown withblue dots.

Estimated pathGround truth path

Start point

Target point

Fig. 14. The chosen path which is infeasible according to Approach A, andfeasible according to Approach B. Experimental results are shown of the ve-hicle’s experimentally estimated path from GNSS and cellular measurements.This figure was obtained with ArcGIS® [33]

[5] J. Bradbury, M. Ziebart, P. Cross, P. Boulton, and A. Read, “Codemultipath modelling in the urban environment using large virtual realitycity models: Determining the local environment,” Journal of Navigation,vol. 60, no. 1, pp. 95–105, 2007.

[6] L. Wang, P. Groves, and M. Ziebart, “Multi-constellation GNSS per-formance evaluation for urban canyons using large virtual reality citymodels,” Journal of Navigation, vol. 65, pp. 459–476, 2012.

[7] J. Isaacs, A. Irish, F. Quitin, U. Madhow, and J. Hespanha, “Bayesianlocalization and mapping using GNSS SNR measurements,” in Proceed-

ings of IEEE/ION Position, Location, and Navigation Symposium, May2014, pp. 445–451.

[8] A. Irish, J. Isaacs, D. Iland, J. Hespanha, E. Belding, and U. Madhow,“Demo: ShadowMaps, the urban phone tracking system,” in Proceedings

of ACM MOBICOM, Septmeber 2014, pp. 283–286.

[9] T. Suzuki and N. Kubo, “N-LOS GNSS signal detection using fish-eyecamera for vehicle navigation in urban environments,” in Proceedings

of the International Technical Meeting of The Satellite Division of the

Institute of Navigation, September 2014, pp. 1897–1906.

[10] L. Wang, P. Groves, and M. Ziebart, “Smartphone shadow matching forbetter cross street GNSS positioning in urban environments,” Journal of

Navigation, vol. 69, no. 3, pp. 411–433, 2015.

[11] L.-T. Hsu, Y., Gu, and S. Kamijo, “3d building model-based pedestrianpositioning method using GPS/GLONASS/QZSS and its reliability cal-culation,” GPS Solutions, vol. 3, pp. 413–428, 20 2016.

[12] H. Karimi and D. Asavasuthirakul, “A novel optimal routing for naviga-tion systems-services based on global navigation satellite system qualityof service,” Journal of Intelligent Transportation Systems, vol. 18, no. 3,pp. 286–298, May 2014.

[13] Z. Kassas, A. Arapostathis, and T. Humphreys, “Greedy motion planningfor simultaneous signal landscape mapping and receiver localization,”IEEE Journal of Selected Topics in Signal Processing, vol. 9, no. 2, pp.247–258, March 2015.

[14] Z. Kassas and T. Humphreys, “Receding horizon trajectory optimiza-tion in opportunistic navigation environments,” IEEE Transactions on

Aerospace and Electronic Systems, vol. 51, no. 2, pp. 866–877, April2015.

[15] A. Nowak, “Dynamic GNSS mission planning using DTM for precisenavigation of autonomous vehicles,” Journal of Navigation, pp. 483–504, May 2017.

[16] Y. Zheng, Y. Zhang, and L. Li, “Reliable path planning for bus networksconsidering travel time uncertainty,” IEEE Intelligent Transportation

Systems Magazine, vol. 8, no. 1, pp. 35–50, 2016.

[17] C. Hubmann, J. Schulz, M. Becker, D. Althoff, and C. Stiller, “Au-tomated driving in uncertain environments: Planning with interactionand uncertain maneuver prediction,” IEEE Transactions on Intelligent

Vehicles, vol. 3, no. 1, pp. 5–17, March 2018.

[18] F. Meyer, H. Wymeersch, M. Frohle, and F. Hlawatsch, “Distributedestimation with information-seeking control in agent networks,” IEEE

Journal on Selected Areas in Communications, vol. 33, no. 11, pp. 2439–2456, November 2015.

[19] J. Garcia, J. Farrell, Z. Kassas, and M. Ouimet, “Autonomous surfacevehicle measurement location planning for optimal underwater acoustictransponder localization,” IEEE Transactions on Aerospace and Elec-

tronic Systems, 2018, accepted.

[20] A. Shem, T. Mazzuchi, and S. Sarkan, “Addressing uncertainty inUAV navigation decision-making,” IEEE Transactions on Aerospace and

Electronic Systems, vol. 44, no. 1, pp. 295–313, January 2008.

[21] J. Isaacs, C. Magee, A. Subbaraman, F. Quitin, K. Fregene, A. Teel,U. Madhow, and J. Hespanha, “GPS-optimal micro air vehicle naviga-tion in degraded environments,” in Proceedings of American Control

Conference, June 2014, pp. 1864–1871.

[22] X. Zhou, X. Yu, and X. Peng, “UAV collision avoidance based onvarying cells strategy,” IEEE Transactions on Aerospace and Electronic

Systems, vol. 55, no. 4, pp. 1743–1755, August 2019.

[23] A. Shetty and G. Gao, “Predicting state uncertainty for GNSS-basedUAV path planning using stochastic reachability,” in Proceedings of ION

GNSS Conference, 2019, pp. 131–139.

[24] G. Zhang and L. Hsu, “A new path planning algorithm using a GNSSlocalization error map for UAVs in an urban area,” Journal of Intelligent

and Robotic Systems, vol. 94, pp. 219–235, 2019.

[25] S. Ragothaman, M. Maaref, and Z. Kassas, “Multipath-optimal UAVtrajectory planning for urban uav navigation with cellular signals,”in Proceedings of IEEE Vehicular Technology Conference, September2019, pp. 1–6.

[26] S. Ragothaman, “Path planning for autonomous ground vehicles usingGNSS and cellular LTE signal reliability maps and GIS 3-D maps,”Master’s thesis, University of California, Riverside, USA, 2018.

[27] T. Pany, Navigation Signal Processing for GNSS Software Receivers.Artech House, 2010.

[28] M. Braasch and A. Dempster, “Tutorial: GPS receiver architectures,front-end and baseband signal processing,” IEEE Aerospace and Elec-

tronic Systems Magazine, vol. 34, no. 2, pp. 20–37, February 2019.

[29] J. del Peral-Rosado, J. Lopez-Salcedo, G. Seco-Granados, F. Zanier,P. Crosta, R. Ioannides, and M. Crisci, “Software-defined radio LTEpositioning receiver towards future hybrid localization systems,” in Pro-

ceedings of International Communication Satellite Systems Conference,October 2013, pp. 14–17.

[30] K. Shamaei, J. Khalife, and Z. Kassas, “Exploiting LTE signals fornavigation: Theory to implementation,” IEEE Transactions on Wireless

Communications, vol. 17, no. 4, pp. 2173–2189, April 2018.

13

[31] M. Driusso, C. Marshall, M. Sabathy, F. Knutti, H. Mathis, andF. Babich, “Vehicular position tracking using LTE signals,” IEEE Trans-

actions on Vehicular Technology, vol. 66, no. 4, pp. 3376–3391, April2017.

[32] K. Shamaei and Z. Kassas, “LTE receiver design and multipath analysisfor navigation in urban environments,” NAVIGATION, Journal of the

Institute of Navigation, vol. 65, no. 4, pp. 655–675, December 2018.[33] Esri. [Online]. Available: https://www.arcgis.com[34] S. Ragothaman, M. Maaref, and Z. Kassas, “Autonomous ground vehicle

path planning in urban environments using GNSS and cellular signalsreliability maps – part I: Models and algorithms,” IEEE Transactions on

Aerospace and Electronic Systems, 2018, submitted.[35] “Downtown buildings,” https://services.arcgis.com/Fu2oOWg1Aw7azh41

/arcgis/rest/services/DowntownBuildings/FeatureServer/.[36] Pyephem. [Online]. Available: https://rhodesmill.org/pyephem/[37] E. Kaplan and C. Hegarty, Understanding GPS/ GNSS: Principles and

applications, 3rd ed. Artech House, 2017.[38] Navstar GPS, “Space segment/navigation user interfaces interface spec-

ification IS-GPS-200,” http://www.gps.gov/technical/icwg/, December2015.

[39] European GSC, “Galileo open service signal in space interface controldocument (OS SIS ICD),” https://www.gsc-europa.eu/electronic-library/programme-reference-documents, December 2016.

[40] GNSS Radar. [Online]. Available:http://www.taroz.net/GNSS-Radar.html

[41] North American Aerospace Defense Command (NORAD), “Two-lineelement sets,” http://celestrak.com/NORAD/elements/.

[42] H. Fan, A. Zipf, Q. Fu, and P. Neis, “Quality assessment for buildingfootprints data on openstreetmap,” International Journal of Geographi-

cal Information Science, vol. 28, no. 4, pp. 700–719, 2014.[43] Remcom. [Online]. Available: https://www.remcom.com[44] Laird phantom 3G/4G multiband antenna NMO

mount white TRA6927M3NB. [Online]. Available:https://www.lairdtech.com/products/phantom-series-antennas

[45] National instrument universal software radio peripheral-2954R. [Online].Available: http://www.ni.com/en-us/support/model.usrp-2954.html

[46] Z. Kassas, J. Khalife, K. Shamaei, and J. Morales, “I hear, thereforeI know where I am: Compensating for GNSS limitations with cellularsignals,” IEEE Signal Processing Magazine, pp. 111–124, September2017.

Sonya Ragothaman is an embedded control sys-tems engineer at The Aerospace Corporation. Shereceived her B.S. and M.S. degrees in Electrical En-gineering from the University of California, River-side (UCR) in 2016 and 2018, respectively. She wasa researcher at the Autonomous Systems Perception,Intelligence, and Navigation (ASPIN) laboratoryfrom 2016–2018. Her interests are in opportunisticnavigation, geographic information systems (GIS),and intelligent transportation systems.

Mahdi Maaref is a postdoctoral research fellow atUCI and a member of the ASPIN Laboratory. Hereceived the B.E degree in Electrical Engineeringfrom the University of Tehran in 2008 and M.Sc.degree in Electrical Engineering-Power System atthe same University in 2011 and Ph.D. degree inElectrical Engineering at Shahid Beheshti Univer-sity, Tehran, Iran in 2016. He was a visiting researchcollaborator at the University of Alberta, Edmonton,Canada in 2016. His research interests include au-tonomous ground vehicles, opportunistic perception,

and autonomous integrity monitoring.

Zaher (Zak) M. Kassas (S98-M08-SM11) is anassistant professor at the University of California,Irvine and director of the ASPIN Laboratory. Hereceived a B.E. in Electrical Engineering from theLebanese American University, an M.S. in Electricaland Computer Engineering from The Ohio StateUniversity, and an M.S.E. in Aerospace Engineeringand a Ph.D. in Electrical and Computer Engineeringfrom The University of Texas at Austin. He receivedthe 2018 National Science Foundation (NSF) Fac-ulty Early Career Development Program (CAREER)

award and the 2018 Office of Naval Research (ONR) Young InvestigatorProgram (YIP) award. He also received the 2018 IEEE Walter Fried Award,2018 Institute of Navigation (ION) Samuel Burka Award, and the 2019 IONCol. Thurlow Award. His research interests include cyber-physical systems,estimation theory, navigation systems, autonomous vehicles, and intelligenttransportation systems.

https://www.arcgis.com

https://rhodesmill.org/pyephem/

http://www.gps.gov/technical/icwg/

http://www.taroz.net/GNSS-Radar.html

http://celestrak.com/NORAD/elements/

https://www.remcom.com

https://www.lairdtech.com/products/phantom-series-antennas

http://www.ni.com/en-us/support/model.usrp-2954.html

autonomous ground vehicle path planning in urban...

Documents