Sensor-based Determination of Angular Misalignment and Lane Confi'gurationof a Radar Sensor for ACC-Applications

Werner Kederer, Juirgen Detlefsen

Technische Universitat Muinchen, Germany

Abstract - In this article a method to determine theangular misalignment of a radar sensor in automo-tive cruise control (ACC) is presented. It is impor-tant to know this misalignment error to avoid errorsstemming from an incorrect assignment of precedingvehicles and lanes. The algorithm determines themisalignment error with high accuracy based on thedata of the radar sensor itself. The proper selectionof the radar sensor data is based on additionalinformation derived from a yaw rate sensor. Themethod, which further may be used for theidentification of the lane configuration, has beentested successfully in simulations and also using realdata measurements.

I. INTRODUCTION

In the recent years, automotive applications ofmicrowave sensors have become of wide interest withthe goal of enhancing safety and comfort for drivers. Animportant application is that of autonomous cruisecontrol (ACC), which means that a safe distance to apreceding vehicle is kept constant by means of aforward looking radar sensor measurement. As this taskis only related to vehicles in the car's own lane, angulardiscrimination with respect to the along track directionis very important. As these sensors are now built veryrobust and reliable for mass production, it has to beensured that the azimuthal alignment of the sensor iskept within the allowed mechanical tolerances. Anymisalignment can cause errors with respect to theevaluation of the current traffic environment. Thereforeit is necessary that the misalignment is recognised.Small errors can be corrected by the sensor's software.In other cases the system has to report the error to theuser and to terminate the sensor's function. In thisarticle an effective method to derive the angularmisalignment from measured object tracks is presented.It is based on the assumption that all moving traffickeeps in average moving along the centre of theindividual lanes. The observed radar tracks are relatedto the expected data tracks of a ACC radar sensor using

additional information of a yaw rate sensor. In case of asignificantly different deviation between the expectedstatistical behaviour of the traffic objects and themeasurement results the misalignment information isderived to be further taken into consideration for thedata evaluation process. The method has been testedsuccessfully in simulations and using real datameasurements.

II. DETERMINATION OF ANGULARMISALIGNMENT

The angular and distance information of the observedvehicular echoes are evaluated in a Cartesian coordinatesystem assuming no sensor alignment error as shown infigure la. The origin of the coordinate system representsthe driver's own position. The simulated radar data isgenerated by assuming an exponentially decreasingdistribution with a standard deviation of 0.3m for thelateral position of the vehicles centred around thelongitudinal axis of each lane. According to figure la athree lane scenario has been assumed. If the sensor datais simulated for an azimuthal sensor misalignment, thedistribution of the radar positions of the observedvehicles is tilted with respect to the longitudinal axis ofthe 3 lanes. The observed two dimensional distributionis projected along the assumed longitudinal direction.This produces a histogram of observed lateral positionsof all vehicular plots (figure lb). The structure of thehistogram strongly depends on the alignment betweenthe vehicular axis and the lanes. Isolated peaks ofgreatest magnitude can be expected, when the sensor iscorrectly aligned, which means that the vehicularlongitudinal axis and the lanes are in parallel. A welldiscriminating criteria for the best alignment is obtainedby evaluating the sum of the nonlinearly weightednumber of plots belonging to each histogram bin. Thisprocedure is carried out for all possible rotation anglesresulting in a overall maximum at a certain angle, whichis assumed to be the best estimate of the misalignmenterror. In order to obtain an unambiguous maximum, thegraph of this function has to be smoothed.

Simulation of maladjustment at 2°

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Figure 2: Determination ofmisalignment error

The evaluation procedure first has been tested usingsimulated data, obtained by a specific simulation toolwhich has been designed to generate realistic sensor

data streams adopted to the sensor in use andincorporating possible sensor misalignments. The datacould have been collected by an ACC-sensor in a

highway scene during a longer period of time provided,no lane changing occurred. Bent road data is filtered outby the yaw rate sensor in practical applications. Thedata in figure a assume a misalignment of 20 and an

exponentially decreasing distribution of the lateralpositions of the vehicles centered in the middle of thelanes with a standard deviation of 0.3m. To clearlydemonstrate the principle of evaluation the standarddeviation has been chosen rather small. The projectionalong the vehicular axis results in the histogram of Fig.lb, which shows a relatively broad lateral distributionaccording to the extreme misalignment. The alignmentcriterion is the sum of the nonlinearly weighted numbersof radar targets contained in the individual histogrambins. This criterion is evaluated for all rotation anglesover the possible range of ±40 in steps of 0.10. Theresulting graph, which is displayed in figure 2, isnormalised by its maximum. The maximum indicates an

alignment error of 20, which is in complete agreementwith the simulation parameters. This information now

can be used to calculate the histogram for the projectionbeing carried out along the correct axis of longitudinalmotion. This results in three narrow peaks, shown inFig. Id.

Fig. 3a displays the target positions stemming from realradar data in a typical traffic scene analog to figure la.The radar plots are accumulated over a time period ofabout 8 minutes. The data is selected by the current yawrate, which means that only this data is kept forprocessing which have been observed while the vehiclewas not changing its direction of motion. Further,experience shows that only data from objects havingdistances not exceeding a maximum value containsignificant information. As can be anticipated already

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from the unfiltered data plots (Fig. 3a), there areaccumulations of targets according to the grid of threelanes. The evaluation as given in Fig. 3b results in ameasured misalignment of 0.4° which corresponds verywell to the sensor's misaligment, which was deliberatelyproduced by rotating manually the sensor 0.50 to theright.

first experiment, this has been tested for a few real datascenarios.

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Figure 3a: Data plot of a real traffic scene for about 8minutes

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Figure 3b: Determination ofmisalignment error

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Figure 4: Distribution model of lateral positions withequal amplitudes

Fig. 4 shows the distribution model of lateral positionsfor a three lane highway. In this case Gaussiandistributions of equal amplitudes with a standarddeviation of about a quarter lane width of 0.85m havebeen assumed for the lateral positions of vehicles. Theyare spaced by the regular lane width of 3,75m, whichhas been typical for that particular German highwayenvironment. The model parameters are the three peakamplitudes and a lateral shift of the distribution. Thedistribution model has to be matched to the observedhistogram. For this purpose the radar positions given inFig. 3a were used, where the observed angular positionsfor a drive period of about 8 minutes have beenaccumulated. The plots are projected along thelongitudinal axis with the misalignment of the sensoralready taken into account. A matching procedure forthe unknown amplitudes of the model distribution and alateral shift is carried out applying a least square fitcriterion. This results in the best fit model distributiongiven in Fig. 5.

III. LANE STRUCTURE IDENTIFICATION

It can be anticipated from Fig. Id, that the alignedhistogram of lateral positions with maximum contrastand distinct peaks, can be used to deduce laneconfiguration. In this case, the three narrow peaksindicate a three-lane road and their symmetry withrespect to the vehicular position means that the vehicleis using the middle lane. It can be expected, that lanestructure determination can be done automatically basedon that information. One approach would be to use aconfiguration model of the expected highwayenvironment and to compare the expected angulardistributions of vehicles to the observed data. This alsocould be done using variable geometrical parametersand adjusting those by identifying an optimum fit. In a

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Figure 5: Histogram of lateral positions, best fit modeldistribution (solid line)

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The obtained fit parameter could also be compared toother distribution models with a different number oflanes, thus enabling a possible discrimination betweendifferent lane configurations. The obtained lateral shiftalso is an indication of the vehicles position with respectto the lane configuration. This has been tested in apreliminary experiment for the same data.

values (-3,75m; Om; 3,75m) for lateral shift have beenapplied. Each start value implies a hypothesis for thelane the radar vehicle is using.

The best fit, marked with an asterisk, is obtainedassuming that the radar vehicle is in the center line,confirming the actual situation.

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Figure 6: Test hypotheses for lane configuration

The results are shown in Fig. 6. The various shiftedmodel distributions which have been plotted as a dashedline, have to be matched to the observed histogram. Toaccelerate the optimization process three discrete start

IV. CONCLUSION

In this article an effective novel method, whichdetermines the misalignment of radar sensors frommeasured radar data, is presented. The method is basedon the statistical behaviour of cars which drive onhighways in average along the longitudinal axis of theindividual lanes. It was shown that histograms generatedof the object's lateral position under the assumption ofan angular deviation between sensor axis and directionof motion allow to determine a possible angularmisaligment of the sensor. Further, it is shown that anevaluation of the optimum histogram has the potential toobtain information about the lane configuration and thevehicle's own position with respect to this confi-guration. Such sensory information may be used in thefuture as one source of information to realise auto-nomous lateral guidance of vehicles.

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