PERFORMANCE EVALUATION OF AUTOMOTIVE RADARS USING CARRIER-PHASE DIFFERENTIAL GPS 1

Performance Evaluation of Automotive RadarsUsing Carrier-Phase Differential GPS

Shuqing Zeng, Member, IEEE,

Abstract—We describe a centimeter-level ground-truth systembased on GPS relative positioning. One of the goals of thesystem is for performance evaluation of automotive radars bycreating objective test procedures for the radars. In support ofthis goal, an effective scheme is used to handle signal attenuationor blockage that leads to the changes of satellite visible mapand cycle slip. Multi-platform GPS measurements and low-costvehicle dynamic sensor data are integrated for vehicle trajectoryreconstruction. Experimental results are presented to illustratethe system’s actual centimeter-level accuracy and the superiorperformance over Kalman smoothing. The effectiveness of theproposed ground-truth system is demonstrated by evaluatingmono-pulse short range radars whose accuracy is about sub-meter level.

Index Terms—Global Positioning System, DifferentialCarrier-phase GPS, Vehicle Trajectory Reconstruction,Bayesian Network, Automotive Radar Performance Evaluation

I. INTRODUCTION

In recent years, extensive research in intelligent transporta-tion systems (ITS) has concentrated on active safety anddriver assistance (ASDA) applications with the purpose ofincreasing the safety of the driver and the passengers [2].To obtain the necessary information of surrounding vehiclesfor the ASDA systems, multiple sensors including radarsare mounted on vehicles. These sensors directly affect theperformance of the systems [23]. As a consequence, it isimportant to perform objective evaluation for those sensorsunder real driving scenarios.

We propose a ground-truth system for sensor performanceevaluation using GPS-based vehicle trajectory reconstruction.It is known that differential GPS (DGPS) provides signif-icant improvement in accuracy over a plain GPS [14]. Inorder to achieve centimeter-level positioning within a shortbaseline, carrier phase observations are preferred to codeobservations because their measurement noise is lower (mmlevel) and multipath effects are limited to 0.25λ, or 4.5 cmat L1 (1,575.42 MHz) [13]. A carrier phase measurementis however ambiguous by an integer number of cycles, theoften used approaches apply the Kalman filtering techniques

S. Zeng is with the Electrical and Controls Integration Laboratory, GeneralMotors Research and Development Center, Warren, MI, 48090 USA e-mail:zengshuq@gmail.com.

Manuscript was drafted in June 15, 2009 and revised in September 28,2009.

to jointly estimate the receiver positions (and velocities) andthe ambiguities [10]–[13], [17], [19]. These approaches havean issue in handling the changes of satellite visible map andexperience noticeable latency [9] during cycle slips, due totheir temporal stationary assumption of the ambiguities.

In order to address the issue, we use a Bayesian network(BN) [20] to handle the changes of satellite visible map andsignal attenuation or blockage that leads to the unknownambiguity to be different after the cycle slip compared withits value before the slip. BN chooses decoupled single-difference ambiguities as a part of its state vector, and nocomplicated processing on the state covariance matrices isneeded when the satellite visible map is changed. The Leastsquares AMBiguity Decorrelation Adjustment (LAMBDA)method [22] is employed to fix the ambiguities to integers.Experiments are conducted to demonstrate the effectivenessof the proposed algorithm to handle changes of satellitevisible map, cycle slips, and insufficient number of visiblesatellites by fusing data from GPS and vehicle dynamicsensors.

To demonstrate the promise and effectiveness of theground-truth system, we implement the proposed system inan instrumented vehicle (see Fig. 1) and apply the proposedobjective test procedures to the performance evaluation ofmono-pulse short range radars.

The work that is most closely related to BN is by Changand et al. [3] who develop a recursive algorithm to computethe least-squares estimates of positions and ambiguities; how-ever, a simple vehicle motion model is used. This makes theirproposed algorithm susceptible to errors under the conditionof insufficient number of visible satellites. Additionally, using

RF2 Radar

LF2

Radar

LEFT

GPS Receiver

RIGHT

GPS Receiver

RF Radar

LF

Radar

RS Radar

Fig. 1. An instrumented vehicle for range sensor ground truthing

coupled double-difference ambiguities as a part of the statevector requires a complex and ad hoc scheme to decouplestate covariance matrices when satellites drop out or emerge.In this paper, we propose a more generic Bayesian frameworkwhere measurements from other sensor modalities can beeasily integrated. In particular, we enhance ambiguity de-termination by augmenting vehicle motion model with low-cost vehicle dynamic sensors. We choose decoupled single-difference ambiguities as a part of its state vector, andno similar complicated processing on the state covariancematrices is used when the satellite visible map is changed.

Kalman filtering is usually used to fuse data from GPSand inertial navigation system (INS) [6], [17]. [4] describesa dead-reckoning and GPS integration system using a variantof unscented Kalman filter (UKF). An interesting work in [5]utilizes artificial neural networks (ANN) to fuse uncompen-sated measurements from INS and DGPS. However, thesestudies focus on real-time navigation applications contrast toour vehicle trajectory reconstruction, and the satellite visiblemap is assumed to be same during the operation, which maynot hold in practice.

An interesting work related to the ground-truth systemfor automotive radars is by Ference et al. [7], [8]. Theydevelop an independent measurement system including high-resolution laser rangefinders and cameras. Target tracking isemployed to estimate the target velocity, which is susceptibleto time jitters and possible erroneous data association. In thisarticle, we use GPS Doppler measurements from multiplereceivers that can be directly translated to relative velocitymeasurement (at an accuracy of center-meter per second).

Ploeg et al. [18] propose a promising development al-lowing for nondestructive testing of pre-crash systems ina hardware-in-the-loop (HIL) setup. This work does notprovide methods to evaluate sensor performance in realistictraffic scenarios; instead, it offers possibility to preciselycontrol the trajectories of other traffic participants, increasingthe level of reproducibility, effectiveness and safety of thetesting process. Miller et al. [15] suggest radio-frequencyidentification (RFID) assisted localization that can be usedas ground-truth instrumentation in an indoor environment.

The rest of this article is organized as follows. A shortdescription of the proposed ground truth system is presentedin Section II. Section III outlines the Bayesian network toobtain the optimal estimates of the GPS phase ambiguitiesand vehicle trajectories. In Section IV, experimental resultsare presented to illustrate the system’s superior performanceover Kalman smoothing. The results of short range radarperformance evaluation are presented in Section V. Finallywe give concluding remarks in Section VI.

II. GROUND TRUTH SYSTEM DESIGN

Fig. 2 illustrates the layout of the proposed ground truthsystem where two vehicles are considered. For each vehicle

we mount two NovaTel c⃝ GPS receivers on the roof. Theposition and pose of the vehicle are estimated in the localgeodetic coordinate system (north-east-up) with the basereceiver as the origin.

X

Y

(x ,y )R R

(x ,y )L L

XY

(x ,y )RR

(x ,y )LL

Base

Host

Target

North

East

Fig. 2. 2-D layout of the ground truth system

The instrumentation diagram is shown in Fig. 3. The Tx/Rxmodule in Base Station is a transceiver that broadcasts thebase receiver’s measurement. Private control area network(CAN) buses are added in the vehicles to interconnect themodules. Vehicle State Estimation integrates the measure-ments from GPS Receivers and Dead Reckoning Sensorsand generates CAN messages with the position and poseestimates of the vehicle. The Tx/Rx modules in the vehiclesreceive signals from the base station and estimates of theother vehicle, and then broadcast the estimate of the vehiclewith GPS time stamp. Radars in Host Vehicle are the rangesensors whose performance is evaluated. The Data Loggerrecords all the CAN messages including radar measurementsand estimates of the vehicle state by GPS.

GPS

Receiver Tx/Rx

Vehicle State

Estimation

Radars GPS

Receivers

Data Logger Dead Reckon-

ing Sensors

Tx/RxVehicle State

Estimation

GPS

Receivers

Dead Reckon-

ing Sensors

Tx/Rx

Host Vehicle Target Vehicle

Base Station

CAN CAN

Fig. 3. The instrumentation diagram of the ground truth system

Fig. 4 outlines the block flowchart of the data processing.

The multi-step process begins with the acquisition of themeasurements from GPS receivers and dead-reckoning sen-sors. The first step jointly estimates the GPS ambiguities and2-D vehicle state in the base coordinate frame as shown inFig. 2. The details of this block will be presented in SectionsIII. The second step aligns the data from both vehicles byGPS time stamp, and then computes the target’s relativeposition and velocity in the host vehicle coordinate frame.Given the radar’s position and pose in the host vehicle frame,the third step computes the target vehicle’s relative positionand velocity in the radar coordinate frame. The fourth stepassociates the radar data with the estimated ground truth.The GPS and CAN time stamps are employed to alignthe data from the two sources. The fifth step generates theperformance evaluation plots.

2-D Vehicle

Attitude

Host Measurements

2-D Vehicle

Attitude

Tgt Relative

Position & Velocity

Sensor

Location

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Sensor Coord. Frame

Host Radar

Measurements

Alignment & Association

with Ground Truth

Tgt Measurements

Performance Evaluation

Report

1.

2.

3.

4.

5.

Fig. 4. The data processing diagram of the ground truth system

III. BAYESIAN NETWORK

As shown in Fig. 5, at time instant t we denote the vehiclestate by xt, the observation by the vector ot, and the j-thsatellite ambiguity by aj . Let the entire vehicle trajectory beexpressed as X = [xt]

T for t = 1, ..., τ , all the ambiguitiesof the visible satellites as a = [aj ]

T for j = 1, ...,M , andall the observations as O = [ot]

T for t = 1, ..., τ . Thus thejoint probability of the entire trajectory X can be written as

P (X,a,O) = P (x1)

τ∏t=2

P (xt|xt−1,ut)

τ∏t=1

P (ot|xt, ajt) (1)

where P (x1) is the prior distribution for the initial vehiclestate; P (xt|xt−1,ut) is the vehicle motion model, param-eterized by the control input ut; and P (ot | xt, ajt) isobservation model, assuming the known correspondence jt(corresponding satellite ambiguity for observation ot).

We assume Gaussian white noise is used in motion andobservation models. A Gaussian distribution N(x, Q) isdenoted by information array [R, z] where z = Rx andQ = R−1R−T . The motion of the vehicle is modeled bythe discrete-time linear model:

Gtxt+1 = Ftxt + ut + wt+1 (2)

x1

x2

x3

xτ

a1

a2

a3

a4

o1 o

2o3

oτ

u2

u3 u

T

aM

Fig. 5. Bayesian network representation of the carrier-phase DGPSproblem, where x is the state of the vehicle, a the ambiguity ofsatellites, u the control input, and o the observation vector includingthe measurements from GPS and vehicle dynamic sensor.

where Ft and Gt are the state transition matrices, ut thevector of control inputs, and wt+1 the process noises withidentity covariance matrix, i.e., wt+1 ∼ N (0, I).

For short-baseline relative positioning, the observationmodel for double differences is expressed as

ot = Hxtxt +Hata+ νt (3)

where ot is the observation vector denoting all the mea-surements at time instant t; Hxt and Hat the correspondingobservation matrices, respectively; and νt the measurementnoises with identity covariance matrix, i.e., νt ∼ N (0, I).

A. Least Squares

We use maximum likelihood estimation (MLE) for theentire trajectory X and the vector of all satellite ambigui-ties a, given the observations O and the control input U(U = [ut], t = 1, ..., τ ). Let us stack all unknowns X anda in the vector γ = [X,a]. The MLE estimate γ is thenobtained by minimizing the negative logarithm of the jointdistribution (1) as

γ = argminγ

− logP (X,a,O) (4)

Let us assume the initial vehicle state x1 is distributed asx1 ∼ [Rx1 , zx1 ] and the prior distribution of the ambiguityvector as a ∼ [Ra, za]. Plugged into the motion model(2) and the observation model (3), we can write (4) as thefollowing least-squares problem

γ = argminγ

∥Raa− za∥2 + ∥Rx1x1 − zx1∥2︸ ︷︷ ︸a priori

+τ−1∑t=1

∥Ftxt −Gtxt+1 + ut∥2︸ ︷︷ ︸process model

+τ∑

t=1

∥Hxtxt +Hatat − ot∥2︸ ︷︷ ︸observation

(5)

Following [25], (5) is equivalent to solving the followingover-constraint linear system

γ = argminγ

∥Aγ − b∥2 (6)

where

A =

0 Ra

Rx 0Hx1 Ha1

F1 −G1 0Hx2 Ha2

F2 · 0· ·· −GT ·

HxT HaT

b =

zazzo1

u1

o2

u2

...uT−1

oT

For numerical stability, QR factorization can be employed

to find the least-squares estimate of γ. However, directlyapplying the QR operation to A for a long observationsequence can be computationally ineffective because thecomplexity of the operation is O(n3) with n the trajectorylength.

Similarly as in [1], [24], A is sparse and nicely structured.Let A =

[A b

]. Apply Givens rotation to A from the

top to the bottom to entries at each time instant aimed atelimination of non-zero elements. Following [3], [16], [25]a fast recursive implementation whose temporal complexityscales up linearly with the number of time cycles can bedeveloped.

B. Handling the Change of Ambiguity Vector

The fixed-dimension assumption for a in (5) is not validdue to following scenarios shown in Fig. 6:

• A new satellite shows up at time t + 1 in (a). al isadded to the ambiguity vector, i.e., anew = [a, al]. Thenew observation ot+1 depends on al, besides ai, aj , andak.

• A satellite i drops out in (b). The link from the ob-servation ot+1 to ambiguity ai is removed because thecorresponding satellite is no longer visible. We keep thevector a untouched.

• A cycle slip event is detected from time t to t+1 in (c).The link from ai to ot+1 is removed, and new ambiguityvalue a′i is added to be estimated. Although ai and a′i arerelated to the same satellite i, they have different valuesand need to be estimated separately. The new variablea′i needs to be appended to the ambiguity vector, i.e.,anew = [a, a′i].

Therefore an effective scheme can be used to handledimension changes of the ambiguity vector as follows:

1) Preset the dimension of the ambiguity vector a tothe maximum number of possible ambiguities in thetrajectory;

xt

xt+1

ai aj ak

ot ot+1

ut ut+1

al

New

(a)

xt

xt+1

ai aj ak

ot ot+1

ut ut+1

Down

(b)

xt

xt+1

ai aj ak

ot ot+1

ut ut+1

Down

ai

New

'

(c)

Fig. 6. Illustrative scenarios of the ambiguity vector dimensionchanges from time instant t to t + 1. (a) A new ambiguity al isadded due to a new satellite coming up. (b) The satellite i dropsout. (c) A cycle slip is detected for i-th satellite.

2) Each phase measurement is linked to an assignedcomponent of a;

3) At beginning, no assignment is made for a;4) Use procedure outlined in Fig. 6 to assign a new

component of a;5) Minimum norm solution of 6 is sought if the matrix

A is rank deficient due to unassigned components.Otherwise, least-squares solution is sought.

C. Integration of Vehicle Dynamic Sensors

First let the components of the vehicle state xt at timet be expressed as xt = [et, nt, ut, et, nt, ut]

T where et, nt,and ut are the displacements along East, North, and Up axisof the local geodetic coordinate system, respectively; and et,nt, and ut are the corresponding derivatives with respect totime.

We write the vehicle motion equation as

xt+1 = f(xt,ut) + wt+1 (7)

where ut is the vector of control inputs, including the yaw-rate measurement ωH and the longitudinal acceleration aH ,and wt+1 are a Gaussian white noise vector. (7) can be

expanded as

et+1 = et + et∆T + we

nt+1 = nt + nt∆T + wn

ut+1 = ut + ut∆T + wu

et+1 = (v + aH∆T ) cos(θ + ωH∆T ) + we (8)nt+1 = (v + aH∆T ) sin(θ + ωH∆T ) + wn (9)ut+1 = ut + wu

where v and θ denote the magnitude and orientation of thevehicle velocities in the horizontal plane, respectively, andwe, wn, wu, we, wn, and wu are the components of thenoise vector wt+1.

Given that ωH∆T is a small quantity, (8)-(9) can beapproximated by

et+1 = et − ntωH∆T +et − ntωH∆T√

e2t + n2t

aH∆T

nt+1 = nt + etωH∆T +nt + etωH∆T√

e2t + n2t

aH∆T

respectively, with the noise terms ϵ omitted.Linearizing in (7) using Taylor expansion by the neighbor-

hood of y∗, we obtain

xt+1 = F ′txt + f(x∗,vt)− F ′x∗ (10)

where F ′t is the Jacobian matrix with respect to xt near to

the point x∗.Given ϵ distributed as [Uϵ, zϵ], we multiply both sides of

(10) by Uϵ, and this leads to (2) with Gt = Uϵ, Ft = UϵF′t ,

and ut = Uϵf(x∗,u)− Fx∗.

Second, the longitudinal velocity from wheel encodersvH can be treated as another measurement equation vH =√e2 + n2, which is appended to GPS observations as ex-

pressed in (3). This observation equation can be easilylinearized and normalized in the neighborhood of y∗ as

vH = Hdx+ (v∗H −Hdx∗) + νd (11)

where Hd =[0 0 0 e√

e2+n2

n√e2+n2

0]

and νd ∼N (0, 1).

IV. VEHICLE EXPERIMENTS AND RESULTS

The vehicle (Fig. 1) with two GPS receivers mounted onthe roof was manually driven, and a data set about 160seconds in length was collected on a public suburban roadwith blockages caused by nearby buildings and tree canopies.Since the distance between the two receivers is a knownconstant, the deviation from the constant is an indicator ofthe positioning performance.

0 20 40 60 80 100 120 140 160 1801

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as [m

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(b)

Fig. 7. (a) The upper plot illustrates the estimated distance betweenthe two GPS antennas vs. the ground truth. The black solid linedenotes the ground truth. The lower plot shows the number ofvisible satellite at each time instant. The black diamonds indicatethe instants when a phase cycle slip is detected. (b) The comparisonbetween the two-antenna distances using integer and float ambiguityvectors, which is illustrated by the blue dotted and red solid lines,respectively.

A. Handling Ambiguity Vector Dimension Changes

The upper plot of Fig. 7(a) shows the comparison betweenBN and Kalman smoothing. As we mentioned earlier, thedistance between the two GPS antennas is a known constant(1.59 meter) denoted by the black solid straight line. Themagenta dashed line is the result of the estimated two-antennadistance by the Kalman smoothing method [21] with theambiguity vector including the only four common visiblesatellites in the whole data set due to its incapacity ofhandling change of satellite visible map. The red solid line isthe two-antenna distance by the BN smoothing method. Be-

sides the four common satellites, BN uses all measurementsfrom the other additional visible satellites. The dimensionof the ambiguity vector is preset to 60, and the number ofambiguities is initially set to 0 for both the left and rightreceivers. After the processing, the number of ambiguitiesgrow up to 52 and 44 nonzero entries for the left and rightreceivers, respectively. The blue curve in the lower plot ofFig. 7 shows the number of visible satellites varies alongtime, and the black diamonds denote the detected cycle-slipevents by BN.

Fig. 7(b) shows the estimated two-antenna distances usinginteger and float ambiguity solutions. The solid red andblue dotted lines are the results using float and integerambiguity, respectively. The mean absolute errors vs. groundtruth for integer and float solutions are 7.3 centimeters and4.4 centimeters, respectively. The comparison shows that theperformance using the integer solution is clearly better thanthat using float solution.

The upper plot of Fig. 7(a) clearly shows BN’s superiorperformance of the resulting relative positioning over the sim-pler Kalman smoothing implementation due to the fact thatmore information is integrated for BN. Fig. 7(b) shows thatBN has an accuracy of centimeters, and this is sufficientlyprecise for the ground truth system of automotive radars insub-meter accuracy.

B. Fusion of Data from Vehicle Dynamic Sensors

Using the data set, we simulate a 15-second-length timewindow in which the number of visible satellites is controlledin each processing run. In each run two individual executionswith different approaches are completed: 1) fusion approach- use vehicle dynamic data and 2) non-fusion approach - notuse vehicle dynamic data. A total of nine runs are executed,with the number of visible satellites varying from zero toeight. In this experiment, synchronized yaw rate and vehiclelongitudinal speed are used.

Fig. 8(a) shows the left receiver’s trajectories of the firstrun. The inset small graph shows that the vehicle is drivenfrom the point A to B with no visible satellite. The black lineis the ground truth that is derived using the original data setwith all the available data from GPS and dynamic sensors.The blue dash-dotted is the estimated trajectory using thedegraded GPS data set without fusion. On the other hand,the green dashed line is estimated trajectory under the samecondition but vehicle dynamic data is fused. Clearly, fusionwith vehicle dynamic data enhances positioning during GPSsignal dropout.

Fig. 8(b) shows the mean errors in the GPS-dropoutwindow for all the nine runs. The horizontal axis is thenumber of visible satellites. The blue diamonds are the meanposition error without fusion of different runs. Similarly, redrectangles are the mean position error with fusion. The greencircle are the mean velocity error without fusion of different

-140 -120 -100 -80 -60 -40 -20 0 20 40-120

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Mea

n er

ror

[m o

r m

/s]

Pos w/o FUSPos w FUSVel w/o FUSVel w FUS

(b)

Fig. 8. (a) The estimated trajectories of the left antenna usingand without using vehicle dynamic data vs. the ground truth. Thesatellites are artificially blocked from the point A to B in the insetplot. (b) The mean errors of the position and velocity estimates asa function of the number of visible satellites.

runs. Similarly, red triangles are the mean velocity errorwith fusion. In all the runs, fusion with vehicle dynamicdata outperforms the corresponding non-fusion approach.However, as the trend shown in Fig. 8(b), the performanceimprovement dwindles along with the increasing number ofsatellites. Particularly, the improvement is invisible whensufficient number of satellites (i.e., four satellites) is availabledue to the domination of precise GPS measurements.

In summary, although fusion with vehicle dynamic dataimproving relative positioning and ambiguity resolution inhigh dynamic maneuver scenarios, one can clearly observethat the centimeter-level accuracy degrades to sub-meter levelquickly when less than four satellites are visible.

V. PERFORMANCE EVALUATION OF AUTOMOTIVERADARS

Fig. 2 illustrates the layout of the proposed ground truthsystem where two vehicles are considered. For each vehiclewe mount two GPS receivers on the roof. The position andpose of the vehicles are estimated in the local geodeticcoordinate system (north-east-up) with the base receiver asthe origin. The radars are mounted behind the front and rearbumpers in the host vehicle as shown in Fig. 1. The field-of-view of the radars is about 60 degrees, and the maximumsensing range is 30 meters.

A. Test Scenarios with a Point Target

As shown in Fig. 9(a) two short range radars (LF andRF) are placed on the test vehicle with two GPS receivers(GPS-L and GPS-R). A steel pipe with diameter of 7.6centimeters and length of 91 centimeters was placed at asurveyed position in the base coordinate frame. The receivertrajectories in Fig. 9(b) show the vehicle was driven backand forth with the target at the vehicle bore-sight. (c) showsthe measurement scatter plot vs. the ground truth wherethe measurements of the two sensors are registered to thebase coordinate frame. The black and blue circles denotethe radars LF and RF, respectively. On the other hand, thered diamond denotes the truth position of the steel pipe. Wenote that the measurements form a narrow ellipse, whichreveals the fact that the lateral accuracy of the radar is inferiorto the longitudinal accuracy, due to the internal physicalcharacteristics of mono-pulse radars. Fig. 9(d) depicts thetwo radars’ range rate measurements vs. the ground truth.The top and bottom subplots are for the radars LF and RF,respectively. The red dots and blue curves are the radars’measurement and the ground truth, respectively. The cyandots on the ground truth curves denote missing detections,which are defined as the radar’s failure of reporting objectswhile the target is in the field-of-view of the radar. One canclearly observe the errors of range rate measurements. Thisis an issue for the short range radars in which range rate isestimated by range tracking instead of direct measurement(e.g., Doppler frequency shift detection).

B. Lane Change Warning Scenario

This lane change warning (LCW) scenario (see Fig. 10(a))begins with the host traveling on a flat paved road at speedof 32 kilometers per hour. Behind the host in the same laneis a single target vehicle traveling at a higher speed than thatof the host. The target changes to the right lane of the hostand then passes the host. The three radars (i.e., RR, RR2,and RS) whose field-of-views are shown in Fig. 10(a) are tobe evaluated.

Since the target vehicle is in motion, we cannot mean-ingfully visualize radar measurements in the base coordinate

frame. However, the measurements can be illustrated to thecoordinate of the moving target vehicle since both the hostand target vehicles’ position and pose are precisely estimatedby the GPS based ground-truth system. Fig. 10(b) shows theresulting scatter plot for the radar measurements for multipleLCW test runs in the target vehicle’s frame. The cyan lefttriangles, magenta diamonds, and black asterisks are themeasurements of the target vehicle from the radars RR, RR2,and RS, respectively. The blue rectangle is the true externalboundary of the target vehicle on while the scatter pointsshould lie if the radars were accurate. However, the positionmeasurements have a large offset from their true values (theblue rectangle) due to the coarse angular resolution of mono-pulse radars. Fig. 10(c) depicts the three radars’ range ratemeasurements vs. the ground truth. The subplots from top tobottom are for the radars RR, RR2, and RS, respectively. Thered dots and blue curves are the radars’ measurement and theground truth, respectively. Comparing with the results usingthe point target in Fig. 9(d), the range rate measurements ofthe target vehicle degraded significantly. This is partially dueto data association error in the tracking loop of the radars.

C. Rear Cross Traffic Alert Scenario

Rear Cross Traffic Alert (RCTA) systems warn drivers tooncoming traffic before they back their cars into the travellane. As shown in Fig. 11(a), this scenario begins when thehost is about to pull out from a parking spot. Behind thehost is a target vehicle traveling at 16 kilometers per hourapproaching from the right side of the host. The four radars(i.e., LS, LR2, RR2, and RS) are to be evaluated.

Similarly, Fig. 11(b) shows the scatter plot of the radarmeasurements for multiple RCTA test runs in the targetvehicle coordinate frame. The red asterisks, blue diamonds,magenta diamonds, and black asterisks are measurementsfrom the radars LS, LR2, RR2, and RS, respectively. Theblue rectangle is the true external boundary of the targetvehicle on which the measurements should lie on if the radarswere accurate. Fig. 11(c) depicts the four radars’ range ratemeasurements vs. the ground truth. The subplots from top tobottom are for the radars LS, LR2, RR2, and RS, respectively.Similar significant measurement errors are observed as in theLCW scenario.

D. Parking Lot Scenario

As shown in Fig. 12(a), the host is being parked in reversebetween two stationary vehicles in a parking lot. The sixradars (i.e., LS, LR2, LR, RR, RR2, and RS) are to beevaluated. This test is designed to investigate the causes ofpossible false-brakes by a low-speed rear collision avoidancesystem.

As in the scenarios with a point target, Fig. 12(b) showsthe measurement scatter plot of the parking lot scenario with

GPS-R

GPS-L

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(d)

Fig. 9. (a) Two short range radars (LF and RF) are placed on the test vehicle with two GPS receivers (GPS-L and GPS-R). A steel pipe isplaced at a known position in the base coordinate frame. (b) The trajectory of the host vehicle, and the steel pipe is shown as the magentacircle. (c) Radar measurement scatter plot. (d) Radar range rate measurements vs. the ground truth.

multiple runs in the base coordinate frame. The red asterisks,blue diamonds, black diamonds, cyan left triangles, magentadiamonds, and black asterisks are the measurements of thetwo target vehicles from the radars LS, LR2, LR, RR, RR2,and RS, respectively. The blue rectangle is the true externalboundary of the target vehicle on which the measurementsshould lie if the radars were accurate. One can observe someblack diamonds (LR) and magenta diamonds (RR2) locatedin the middle of two stationary vehicles. These LR and RR2measurements are so offset from the truth (the blue rectangle)that “ghost” targets are reported by the two radars. This isan issue with mono-pulse radars when two equidistant targetsshow up as a target in the middle. These “ghost” targets leadto false activation of automatic brake system if they are usedby the collision avoidance system.

VI. CONCLUSIONS AND FUTURE WORKIn this paper, we have described the design, analysis, and

testing of a ground-truth system based on carrier-phase DGPS

as an independent measurement system. An effective schemebased on Bayesian network is used to handle the changesof satellite visible map and cycle slip. Experiments areconducted to demonstrate the scheme’s superior performanceover the Kalman smoothing implementation, and the accuracyof trajectory reconstruction reaches 5 centimeters if at leastfour satellites are visible. To show the effectiveness of theproposed ground-truth system, mono-pulse short range radaris chosen as an example sensor for evaluation. The radar’sperformance is reported under extensive testing cases suchas the scenarios using a point target, lane change warning,rear cross traffic alert, and rear parking. The results of thoseobjective tests is consistent with the characteristics of themono-pulse radars.

Although promising results have been achieved using theproposed GPS-based ground truth system, we observe thatthe centimeter-level accuracy of the system degrades quicklyas insufficient number of satellites is visible in environmentssuch as “urban canyon”. So the use of the proposed system

HostTarget

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Fig. 10. (a) A typical lane change scenario with two vehicles. Eachvehicle is equipped with two GPS receivers. Three short range radars(RS, RR2 and RR) are placed on the host vehicle. (b) Measurementscatter plot for multiple LCW runs in the coordinate of the targetvehicle. (c) Radar range rate measurements vs. ground truth for aLCW test run.

is generally restricted to open-sky areas. In response to this

availability issue, future work may enhance the system witha high accuracy six degree-of-free inertia measurement unit(IMU), or simultaneous location and mapping (SLAM) usingrangefinder data.

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Target

Host

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ers)

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R)

Vehicle target, SRR Range rate−Ground Truth

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)

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R)

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(RR

)

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(c)

Fig. 11. (a) A typical rear cross traffic alert (RCTA) scenario withfour vehicles. Both the host and target vehicles are equipped withtwo GPS receivers. Four short range radars (RS, RR2 and RR)are placed on the host vehicle. (b) Measurement scatter plot formultiple RCTA test runs in the target vehicle coordinate frame. Theradar measurements are transformed into the coordinate of the targetvehicle. (c) Radar range rate measurements vs. ground truth for aRCTA test run.

26 24 22 20 18 16 14 12 10 8

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(b)

Fig. 12. (a) A typical rear parking scenario with three vehicles. Thehost vehicle equipped with two GPS receivers was being parked inreverse and pulled out six times. Magenta and green curves showthe trajectories of the two GPS receivers. Six short range radars (i.e.,LS, LR2, LR, RR, RR2, and RS) are placed on the host vehicle.(b) Measurement scatter plot of the rear parking scenario with allthe six test runs in the base coordinate frame.

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Shuqing Zeng (M’03) received his PhD degreein Computer Science from the Michigan StateUniversity, East Lansing, Michigan, in 2004.

Since 2004, he has been with the Research andDevelopment Center, General Motors Corporate,Warren, MI, where he currently holds the positionof Senior Research Scientist. From 2005 to 2007,he served as the newsletter Editor of AutonomousMental Development TC, IEEE Computational In-

telligence Society. He is currently an AssociateEditor of the International Journal of Humanoid

Robotics. His research interests include computer vision, sensor fusion,autonomous driving, and active-safety applications on vehicle.

Dr. Zeng has served as a reviewer to the IEEE TRANSACTIONS ONPATTERN ANALYSIS AND MACHINE INTELLIGENCE and as a judgeto the Intelligent Ground Vehicle Competition. He is a member of the TartanRacing team who won the first place of the Defense Advanced ResearchProjects Agency Urban Challenge on November 3, 2007.