Doppler Blind Zone Analysis for Ground TargetTracking with Bistatic Airborne GMTI Radar

Michael MertensSensor Data and Information Fusion

Fraunhofer FKIEWachtberg, Germany

michael.mertens@fkie.fraunhofer.de

Thia KirubarajanElectrical and Computer Engineering

McMaster UniversityHamilton, Canada

kiruba@mcmaster.ca

Wolfgang KochSensor Data and Information Fusion

Fraunhofer FKIEWachtberg, Germany

wolfgang.koch@fkie.fraunhofer.de

Abstract—This paper investigates the Doppler blind zone ofbistatic transmitter and receiver configurations and its impacton the tracking of ground targets based on measurements fromairborne ground moving target indication (GMTI) radar. TheDoppler blind zone arises from the clutter cancellation byspace-time adaptive processing (STAP). In general, this posesa significant challenge in ground target tracking because low-Doppler targets can easily be hidden within this blind zone,leading to sequences of missed detections that strongly deterioratethe performance of a standard tracking filter. In this study thewidth of the bistatic Doppler blind zone is calculated and thisknowledge is incorporated into a UKF-MHT tracking algorithm.Based on simulation scenarios, it is demonstrated that in contrastto a monostatic configuration with sideways-looking radar, theminimum detectable velocity that characterizes the width of theDoppler blind zone does not need to be constant. Track resultsreveal the benefit of exploiting this additional knowledge.

Keywords: Target tracking, bistatic, Doppler blind zone,MHT, UKF, ground moving target indication (GMTI), radar.

I. INTRODUCTION

One of the main challenges in ground target tracking basedon measurements from airborne GMTI radar is the maskingof targets due to the Doppler blind zone of the radar. Theinformation on this blind zone can be incorporated into a track-ing algorithm by defining a target state dependent detectionprobability [1] that accounts for the degraded possibility toobtain a target measurement while it is located within the blindzone. This method has been applied to simulation scenarios[2] as well as real data [3], in all cases resulting in improvedtracking performance. This technique was also applied to thetracking of ground targets with a bistatic radar configuration[4]. But in all these cases, the width of the Doppler blind zonewas assumed to be a sensor parameter, thus constant. Thisstems from the fact that the width is known to be constantfor the case of monostatic sideways-looking radar that coversthe majority of ground target tracking experiments to date.But bistatic configurations with separated transmit and receiveantennas will play an increasing role in future reconnaissancesystems, e.g., to accomplish covert operations.The aim of this study is to calculate the true width of theDoppler blind zone for arbitrary bistatic configurations, toexamine its evolution in the course of time for a simulation

scenario and to incorporate the knowledge of the true blindzone width into a tracking algorithm.The paper is organized as follows: In the next section, thebasics of STAP and the calculation of the Doppler blind zonewidth are briefly discussed as well as the incorporation ofthe Doppler blind zone information into a Bayesian trackingfilter. In Section III, the analyzed simulation scenarios aswell as tracking results are presented and discussed. Finally,concluding remarks are given in Section IV.

II. THEORETICAL ASPECTS

A. Obtaining the Bistatic Doppler Blind Zone Width

The bistatic Doppler blind zone can generally be specifiedby its center clutter Doppler frequency f c

D or range-rate,respectively, and its width. For a given bistatic configurationwith position and velocity of transmitter (Tx) and receiver(Rx) given by the 3D vectors rTx, rTx, rRx and rRx, theclutter Doppler frequency at the location r on the ground isdetermined by

f cD =

1

λ

(r− rTx

||r− rTx||rTx +

r− rRx

||r− rRx||rRx

)(1)

where λ is the wavelength of the corresponding signal centerfrequency. The associated bistatic range-rate of the clutterpatch on the ground is then given by rc

B = −f cD · λ.

The width on the other hand is not of physical nature butarises from a special signal processing technique that is usedto suppress the ground clutter in order to separate movingtarget returns from this clutter background: Eq. (1) indicatesthat whenever moving airborne platforms are involved, theclutter energy is no longer concentrated at zero Doppler.Instead, it becomes a 2D-structure distributed across the angle-Doppler plane, which cannot be suppressed by 1D-filtering ineither angle (spatial domain) or Doppler (time domain). Toaccount for this angle-Doppler coupling of the ground clutter,a multi-dimensional filtering is applied instead that is capableof yielding optimal clutter suppression in terms of signal-to-clutter ratio (SCR): the space-time adaptive processing (STAP)technique [5]–[7].The major task of STAP is the determination of the cluttercovariance matrix Q that contains the full knowledge of the

2331

Figure 1. Bistatic configuration with isorange ellipsoid determined bypositions of transmitter (Tx), receiver (Rx) and ground target. The isorangeellipse at z = 0 results from the intersection with the ground plane.

angle-Doppler coupling of the clutter for a certain (bistatic)range. In real scenarios, Q needs to be estimated fromtraining data due to the fact that ground clutter is in generalheterogeneous. In this work, however, the clutter is assumedhomogeneous to analyze solely the influence of the bistaticconfiguration on the Doppler blind zone width. Hence, Q canbe calculated and is thus fully known. For a given bistaticconfiguration as, e.g., shown in Fig. 1, the associated bistaticrange defines an ellipsoid with transmitter Tx and Rx asfoci. The intersection of this ellipsoid with the ground planeyields the corresponding isorange ellipse. Each clutter patchon this ellipse has a spatially dependent reradiating intensitywith which it enters the calculation of the clutter covariancematrix Q. Fig. 2 presents the exemplary distribution of thedominant clutter patches along the isorange ellipse contourfor the configuration shown in Fig. 1.The efficiency of the STAP clutter cancellation can be assessedby calculating the improvement factor (IF) which reveals anotch at the location of the clutter spectrum in the angle-Doppler plane. Under the assumed optimal conditions, thisfunction is given by [5]

IFopt = s∗(ϕL, ftD)Q−1s(ϕL, f

tD)· tr(Q)

s∗(ϕL, f tD)s(ϕL, f t

D)(2)

where s(ϕL, ftD) is the space-time signal reference (or steer-

ing) vector which models the target signal and introduces thedependency on look direction ϕL towards the target as wellas target Doppler frequency f t

D. It can be calculated as theKronecker product of a Doppler component b, which describesthe linear phase progression in Doppler across M pulses,and a spatial component a, which accounts for the phaseprogression across the N elements of the receive antenna,s(ϕL, f

tD) = b⊗ a with

b =[1 , e2πift

D , e2πi(2)ftD , ... , e2πi(M−1)ft

D

]>(3)

and

a =[1 , e2πiϕt

, e2πi(2)ϕt

, ... , e2πi(N−1)ϕt]>

(4)

f tD is the target Doppler frequency normalized to the pulse

repetition frequency (PRF) and ϕt is the normalized azimuth

Figure 2. Isorange ellipse with relevant clutter patches. The color indicatesthe relative CNR value of each clutter patch (red: maximum, blue: minimum,at least 5% of max. value)

angle being related to the direction of the impinging targetsignal return with respect to the antenna normal vector whichis given by

ϕt =d

λcosϕL cos θL (5)

The parameter d is the inter-element spacing of the arrayantenna and θL the elevation angle.The width of the bistatic Doppler blind zone in the bistaticrange-rate domain is described by the minimum detectablevelocity (MDV). It is determined by the half-width of thenotch in the IF distribution at −3 dB for a given azimuthlook direction. An exemplary 1D-IF distribution at a fixed lookangle is shown in Fig. 3. For the analysis presented in SectionIII, the following scheme is used to calculate the MDV at eachrevisit, given the positions of Tx, Rx and ground target:

1) determine parameters of isorange ellipsoid with Tx andRx as foci, target on ellipsoid surface

2) calculate isorange ellipse (intersection of ellipsoid withflat earth, containing target)

3) determine position and clutter-to-noise ratio (CNR) ofclutter patches on isorange ellipse illuminated by Tx,observable by Rx

4) calculate Q with contributions from all clutter patches,taking into account Tx sum beam illumination & Rx

Figure 3. Exemplary normalized improvement factor (IF) distribution for agiven look direction. The MDV is determined by the distribution’s half-widthat −3 dB. The red line indicates the bistatic range-rate of the ground clutterat the location related to the given look direction.

2332

array element pattern5) calculate improvement factor at Rx look direction to-

wards ground target6) determine MDV given by half-width of IF at −3 dB

B. Exploiting the Doppler Blind Zone Information for Track-ing with Bistatic GMTI Measurements

When a target is masked by the Doppler blind zone (orDoppler notch), target measurements are strongly suppresseddue to clutter cancellation by STAP and the receive antenna isunable to detect it although such a target may move at a con-siderable speed. Thus, the detection probability Pd is directlyinfluenced by the existence of this blind zone. Following theapproach presented in [1], the detection probability is modeledin such a way that the influence of the bistatic Doppler notchis taken into account and can be written as a function of thetarget state at time step k, xk = [r>k , r

>k ]>, as

Pd(xk, rTx, rRx) =

P0d

(1− e

− log 2

(nb(xk,rTx,rRx)

MDV(xk,rTx,rRx)

)2)(6)

where P0d is the detection probability for a target range-rate

well outside the blind zone interval and the Doppler notchfunction nb(xk, rTx, rRx) measures the distance to the bistaticDoppler blind zone center. It can easily be shown that, inCartesian coordinates, it is identical to the bistatic range-rategiven by

nb(xk, rTx, rRx) =rk − rTx

||rk − rTx||rk +

rk − rRx

||rk − rRx||rk (7)

The MDV is no longer a fixed sensor parameter as in [1], [4]but is calculated instead at each revisit based on the schemepresented in Section II-A. The particular form of the detectionprobability in (6) is chosen such that if the notch functionequals the current width of the Doppler blind zone then Pddrops to 1/2. Hence, target detections become more and moreunlikely as the target moves inside the Doppler notch regionand for the case that the target’s bistatic range-rate matchesthe range-rate of the surrounding clutter, then the detectionprobability drops to zero.The tracking filter used in this study is based on the Bayesianformalism [9], [10]: The probability density p(xk|Zk) thatdescribes the target state xk at time step k, conditionedon the measurement sequence Zk = {Z1,Z2, ...,Zk} withZk = {zmk }

nkm=1 and measurement zmk , is sequentially updated

yielding the posterior density

p(xk|Zk) =p(Zk|xk) p(xk|Zk−1)∫dxk p(Zk|xk) p(xk|Zk−1)

(8)

In the prediction step, for the prior p(xk|Zk−1) a Gaussianshaped posterior density p(xk−1|k−1|Zk−1) is assumed thatis propagated to the actual time step k by utilizing a linearmotion model with additive white Gaussian process noise.In the filter update step, the estimate based on the motionmodel is improved by incorporating the sensor data. For the

calculation of the posterior density, the single-target likelihoodfunction p(Zk|xk) is needed. It reflects all possibilities tointerpret the sensor output and contains a simple sensor model,relevant for the tracking algorithm, given by the detectionprobability Pd and the false alarm density ρf . Its standardformulation is [9]

p(Zk|xk) = (1−Pd) +Pdρf

nk∑m=1

N (zmk ;Hkxk,Rk) (9)

This function reflects the nk + 1 hypotheses that either all nkmeasurements are false alarms or that measurement m is thecorrect target measurement, all others are false alarms.Due to the bistatic configuration, the measurement equation isnonlinear, zk = (rk, ϕk, θk, rk)> = h(xk) with bistatic rangerk, azimuth angle ϕk, elevation angle θk and bistatic range-raterk. This nonlinearity is accounted for by using the UnscentedKalman Filter (UKF) [11] for the calculation of the hypothesesfor each bistatic measurement. For track extraction, a ten-tative track is initialized with the measurement in Cartesiancoordinates. Therefore, the Unscented Transformation is usedto transform the bistatic measurements zbk into the Cartesiancoordinate space, yielding zcart

k . And as the target moves inthe x-y plane only, this additional knowledge is incorporatedby performing a pseudo-filtering step on zcart

k , following thelogic in [12].The final step is now to include the detection probability thatcontains the knowledge of the bistatic Doppler blind zone intothe tracking filter. But before it can be substituted into thelikelihood function (9), the bistatic nonlinear notch functionnb(xk, rTx, rRx) is linearized [1] around the predicted targetstate xk|k−1:

nb(xk, rTx, rRx) ≈ zbf − Hbfxk (10)

This yields a fictitious bistatic measurement zbf and fictitiousbistatic measurement matrix Hb

f which are calculated by

zbf = nb(xk|k−1, rTx, rRx) + Hbfxk|k−1 (11)

Hbf = − ∂

∂xknb(xk, rTx, rRx)

∣∣xk=xk|k−1

(12)

In that way, the exponential in (6) can be rewritten as aGaussian, yielding

Pd(xk, rTx, rRx) = P0d

(1− cN (zbf ; Hb

fxk,Q))

(13)

with c = MDV√log(2)/π

and Q = MDV2

2 log(2) . The substitution of the

detection probability into the likelihood function finally leadsto an increased number of hypotheses, 2(nk + 1), to interpreta given sensor output which includes the hypothesis that thetarget is not detected due to the Doppler notch masking.The derived tracking scheme is implemented into a track-oriented MHT algorithm, [10]. In order to mitigate the ex-ponential growth of hypotheses, the standard mixture reduc-tion methods [13] gating, pruning and merging are applied.For track extraction and track maintenance, a sequentiallikelihood-ratio test based algorithm [13], [14] is implemented.

2333

III. SIMULATION SCENARIOS AND NUMERICAL RESULTS

In the first part of this section, the MDV as a function of timeis analyzed for two different simulation scenarios. The secondpart compares the tracking performance of three target trajec-tories, based on a different handling of the MDV informationin the tracking algorithm. For obtaining the simulation resultspresented in this section, the parameters listed in Table I wereused. A uniform linear array (ULA) with equidistant spacingbetween elements was chosen as antenna for Tx and Rx.

A. Examination of the MDV for Sideways-Looking Radar

Based on the method described in the previous section forobtaining the width of the Doppler blind zone at each revisit,the MDV was calculated for the simulation scenarios shown inFigs. 4 and 5. The upper plot presents the linear trajectories oftransmitter (Tx), receiver (Rx) and ground target and the lowerplot reveals the corresponding MDV as a function of time,respectively. The sensor platforms move on parallel paths andfor both Tx and Rx a sideways-looking antenna configurationwas chosen to guarantee that the target is illuminated by Txand within the field of view of Rx throughout the scenario.It should be noted, that the only difference between thesetwo scenarios is the trajectory of Tx. In the first case, thetarget is situated in roughly the same direction for Tx and Rx,whereas in the second case the illuminated area on the groundcontaining the target is in between Tx and Rx. Interestingly,this change obviously leads to a significantly different shape

Figure 4. The upper plot shows the simulation scenario 1 with the trajectoriesof Tx (red), Rx (blue) and ground target (black). The lower plot presents thecalculated value of the bistatic MDV as a function of time.

of the calculated MDV. In the following, the main differenceswill be analyzed and explained.For scenario 1, the MDV remains constant throughout thescenario, but it is about three times larger than the minimumvalue in scenario 2. The reason for this can be found bylooking at the distribution of the clutter patches on the isorangeellipse compared to the Doppler isolines on the ground. Thisis shown for each scenario based on the bistatic configurationat revisit 10 in Fig. 6. For a better visualization, only thoseclutter patches are displayed which contribute most to theclutter spectrum (at least 5% of the maximum CNR value).The color index refers to the relative CNR value of eachclutter patch. In the upper plot, associated with scenario 1,the relevant clutter patches cover a broad interval of clutterDoppler frequencies, whereas in the lower plot, associated withscenario 2, the relevant clutter patches only spread over a smallDoppler frequency interval.Thus, the width of the Doppler blind zone is strongly relatedto the number of different Doppler frequencies covered by thedominant clutter patches, because this defines the size of theresulting clutter spectrum in the Doppler frequency domainwhich will be suppressed by STAP.Besides the different magnitudes of the (minimum) MDVvalue for the two scenarios, the MDV as a function of timefor the second scenario reveals a remarkable shape: Afterremaining constant at 3 m/s for about 25 revisits, the MDVrapidly increases to about 12 m/s. The width of the Doppler

Figure 5. The upper plot shows the simulation scenario 2 with the trajectoriesof Tx (red), Rx (blue) and ground target (black). The lower plot presents thecalculated value of the bistatic MDV as a function of time.

2334

Table ISIMULATION PARAMETERS

No. of revisits 80Ground target speed vt = 25m/sTx, Rx platform speed vp = 100m/sPlatform altitude zp = 3000mNo. of array elements N = 18No. of pulses / CPI M = 18Wavelength (center frequency) λc = 0.03mAntenna element spacing d = λ/2Pulse repetition frequency PRF = 4000HzSignal bandwidth B = 10MHzEmitted power Ps = 200 kWRange standard deviation σr = 25mRange-rate standard deviation σr = 1m/sAzimuth standard deviation σϕ = 1◦

Elevation standard deviation σθ = 1◦

Process noise σp = 0.5m/s2

Gating λg = 18Pruning λp = 0.001Merging λm = 10Detection probability P0

D = 0.9

blind zone then reduces back to its original value. After a fewrevisits, the same rapid increase and decrease of the MDV canbe observed. Finally, the MDV remains at 3 m/s until the endof the scenario.This evolution of the width of the Doppler blind zone canbe explained by analyzing the plots presented in Fig. 7. Foreach of the revisits 10, 26, 30, 40, 50 and 75, the left plotexhibits the bistatic configuration, the isodoppler contours, theisorange ellipse and relevant clutter patches with at least 5%of the maximum CNR value and the right plot illustrates thedistribution of the clutter patches along the isorange ellipsecompared to the run of the Doppler isolines, respectively.In the first part of the scenario, the two platforms approach thetarget in x-direction, leading to a decrease of the bistatic range.On the other hand, the baseline, i.e., the distance betweenTx and Rx remains constant over time. This results in anellipsoid that becomes smaller in overall size but also moreand more cigar-shaped along the baseline. The intersectionof this isorange ellipsoid with the ground plane at z = 0then leads to an isorange ellipse which becomes smaller andfinally consists only of a single intersection point when thetarget is located right in the center between the two platforms.In the second half of the scenario, when the target crossesthe baseline between Tx and Rx, the bistatic range increasesagain. This results in a larger isorange ellipsoid and thus alsoin an isorange ellipse on the ground increasing in size. Thisconsiderable change in size of the isorange ellipse in thecourse of the scenario can well be observed by examiningthe corresponding plots in Fig. 7.At revisit 10, the isorange ellipse is comparably large withthe relevant clutter patches covering only a small part of theellipse contour in the vicinity of the target. As already shownin the lower plot of Fig. 6, the clutter patches only spread overa small Doppler frequency interval. At revisit 26, the clutterpatches which contribute most to the clutter spectrum are nowdistributed over a larger part of the smaller isorange ellipse

contour, covering a much larger interval of clutter Dopplerfrequencies compared to revisit 10, which leads to the largeMDV value. This is also true for the situation at revisit 30 withan even smaller isorange ellipse contour. But as the isorangeellipse becomes smaller, the total number and thus also thenumber of dominant clutter patches is reduced because theextension of the ellipse in cross-range direction as seen fromRx decreases. At revisit 40, only two clutter patches remaincorresponding to a single look direction of Rx. Interestingly,these two clutter patches obviously lead to almost the samewidth of the Doppler blind zone as the several clutter patchesat revisit 10. This can be explained by the higher CNR valuesdue to the smaller bistatic range. In the following revisits,the two platforms overtake the target in x-direction, leadingto an increase in bistatic range and thus a growing isorangeellipse contour. The dominant clutter patches again cover alarger Doppler frequency interval leading to an increase ofthe MDV, as plotted for revisit 50. After several revisits, thedistribution of the relevant clutter patches along the isorangeellipse contour is again limited to the vicinity of the target andonly spread over a small Doppler frequency interval resultingin the original MDV value.

B. Tracking Scenario

In the second part of this section, the MDV information isused in a 3D-UKF single-target MHT algorithm which hasbeen presented in Sec. II-B and applied to the following

Figure 6. Doppler contours with 200Hz spacing and distribution of relevantclutter patches along isorange ellipse for scenario 1 (upper plot) and scenario2 (lower plot) at revisit 10. The color indicates the relative CNR value ofeach clutter patch (red: maximum, blue: minimum, at least 5% of max. value)

2335

Figure 7. For the bistatic configuration of scenario 2, shown are the isodoppler contour with 200Hz spacing, the isorange ellipse and relevant clutter patcheswith at least 5% of max. CNR value (left plot), and the right plot illustrating the distribution of the clutter patches along the isorange ellipse compared to therun of the Doppler isolines for revisits 10, 26, 30, 40, 50 and 75, respectively. The red isoline corresponds to zero clutter Doppler frequency and the colorbardenotes Doppler in Hz.

setup: Based on the general bistatic configuration of scenario2, the ground target now moves along one of three possibletarget trajectories, as shown in Fig. 8. The first case is thestraight line motion as considered in the previous part, whereasthe other two possible target paths are based on windingtrajectories. The red lines at each trajectory of Fig. 8 indicatetarget positions at which the bistatic range-rate is below thetrue MDV. Thus, in these regions the target is masked bythe bistatic Doppler blind zone. Within this blind zone, only

sporadic measurements occur because the detection probabilityis strongly reduced but not equal to zero for most of the time.Fig. 9 presents the true evolution of the corresponding MDVfor each of the three possible target trajectories. The overallshape remains the same, but for trajectories B and C the MDVdoes not drop to its original value at about half of the scenariotime, as is the case for trajectory A.Four different tracking algorithms that differ in the processingof the bistatic Doppler blind zone information were employed:

2336

Figure 8. Trajectories of the ground target for cases A, B and C. The redbold lines indicate regions with strongly reduced detection probability due toDoppler blind zone masking.

For the first algorithm, the MDV was assumed to be constantand equal to the overall minimum value, which can be regardedas the optimistic case. The second algorithm also assumed thatthe MDV is constant, but in this case the overall maximumvalue was used, which corresponds to the pessimistic case. Thevariation of the MDV was considered in the third trackingalgorithm, being the realistic case. For reference, a trackingalgorithm was used which does not process any information onthe bistatic Doppler blind zone. This was achieved by settingthe MDV to zero, thus assuming an infinitely narrow blindzone. In order to assess the performance of each algorithm,the track continuity was determined which is defined as theability of the algorithm to maintain a once extracted track untilthe final revisit. The results in terms of the aforementionedmeasure of performance for all combinations of trackingalgorithm and target trajectory are presented in Table II andare based on 100 Monte Carlo runs.As expected, the algorithm which does not exploit any in-formation on the bistatic Doppler blind zone is not capableof maintaining a track at all for any of the three differenttarget trajectories. In this case, the masking of the target bythe bistatic Doppler blind zone leads to a sequence of misseddetections for several subsequent revisits. The only possibilityfor the tracking algorithm to interpret this sensor output is toestablish the missed detection hypothesis. As a consequence,the track score drops below a predefined threshold within afew revisits, resulting in the termination of the track. In all

Figure 9. Distribution of the calculated minimum detectable velocity forcases A, B and C.

Table IISIMULATION RESULTS (100 MONTE CARLO RUNS)

Scenario 2, Trajectory A Track Continuity

Optimistic case (minimum MDV used) 15%Pessimistic case (maximum MDV used) 100%Realistic case (correct MDV used) 97%No Doppler blind zone processing (MDV = 0) 0%

Scenario 2, Trajectory B Track Continuity

Optimistic case (minimum MDV used) 21%Pessimistic case (maximum MDV used) 99%Realistic case (correct MDV used) 98%No Doppler blind zone processing (MDV = 0) 0%

Scenario 2, Trajectory C Track Continuity

Optimistic case (minimum MDV used) 12%Pessimistic case (maximum MDV used) 13%Realistic case (correct MDV used) 19%No Doppler blind zone processing (MDV = 0) 0%

other cases, the algorithms were capable of extracting andmaintaining tracks by making use of the knowledge on thebistatic Doppler blind zone.In the following, the track results for the algorithms whichexploit the knowledge of the blind zone will be analyzed:For the first and second scenario setup (trajectory A andB), the algorithm which assumes the width of the bistaticDoppler blind zone to be equal to the minimum MDV yieldsonly a small number of successfully maintained tracks. Theexplanation for this can be found by examining the corre-sponding plots in Fig. 10 which illustrates the evolution ofthe bistatic target range-rate together with the limits of thebistatic Doppler blind zone based on the true, the maximumand the minimum MDV. The target moves into the actual blindzone several revisits before the blind zone limit related tothe minimum MDV is reached. Thus, a sequence of misseddetections occurs with the tracking algorithm being unableto interpret this situation correctly. Hence, in most cases thetrack score quickly decreases leading to the termination ofthe track. On the other hand, the algorithm which uses themaximum MDV yields an optimal performance. This can beexplained as follows: Due to the larger width of the blindzone, this algorithm puts weight into the hypothesis that thetarget is masked by the bistatic Doppler blind zone well beforethe target actually enters the blind zone region. But as targetmeasurements are still available and the unnormalized weightof such a filtered measurement hypothesis is higher by severalorders of magnitude than that of the blind zone hypothesis,the influence of the falsely set width of the bistatic Dopplerblind zone is obviously marginal in the considered cases.Finally, the algorithm which processes the correct MDV atevery revisit shows the expected behavior as it yields a nearlyoptimal performance for the target trajectories A and B. Theresults for the third scenario setup (trajectory C) reveal thatby solely exploiting the knowledge of the bistatic Dopplerblind zone, a good tracking performance cannot be achievedin every situation. Here, the target moves within the blind

2337

Figure 10. Evolution of the bistatic target range-rate (black bold line) andwidth of the bistatic Doppler blind zone (black solid line) for trajectories A,B and C. The red and blue dashed lines indicate the blind zone limits basedsolely on the maximum or minimum MDV, respectively.

zone in a way which obviously cannot be followed by anyof the tracking algorithms due to the lack of measurements.As the target moves out of the blind zone, in most cases thenewly available measurements are no longer located within theexpectation gate of the track and are thus discarded.In summary, the following statements can be made: Theincorporation of the varying MDV is straight-forward andyields expected results in the examined simulation scenarios.The algorithms using a constant MDV are of course onlytheoretical approaches because without actually calculating theMDV those values remain unknown. But these considerationsreveal how important it is not to underestimate the width ofthe blind zone. On the other hand, one might be tempted tosimply set the MDV to a very large value, as the results forcases A and B indicate an almost perfect performance. Butthis approach would lead to a poor performance especiallyin situations with low detection probability, because then theblind zone hypothesis would outperform the correct misseddetection hypothesis due to the larger weight, surely deterio-rating the tracking performance in certain cases.A possibility to improve the tracking performance is to com-bine the knowledge of the bistatic Doppler blind zone withroad-map information, because then the tracking algorithmhas improved information about the possible target positionswithin the blind zone. At a crossing, for example, the algorithmestablishes a new road hypothesis for each possible junctionand in that way maintaining all possible target trajectories. As

soon as a new target measurement is available, the algorithmcan then easily associate the measurement with one of theavailable road hypotheses. This was already explored for themonostatic case in [15].

IV. CONCLUSION

This paper investigated the bistatic Doppler blind zone and itsimpact on the tracking of ground targets by airborne GMTIradar. It was presented how the width of the blind zonecan be calculated for a given bistatic configuration and howthis additional information can be processed by a trackingalgorithm. Based on simulation scenarios it was demonstratedthat, in contrast to the monostatic case with sideways-lookingradar, the minimum detectable velocity is not constant forcertain bistatic configurations. The obtained track results interms of track continuity finally reveal the benefit of exploitingthis additional knowledge.Future work will focus on the impact of exploiting road-map information on the tracking performance in a bistaticsetting. In addition, the influence of a two-dimensional antennaelement pattern will be explored.

ACKNOWLEDGMENT

The authors would like to thank U. Nickel for fruitful discus-sions on STAP and M. Daun for her help with the 3D-UKFimplementation.

REFERENCES

[1] W. Koch and R. Klemm, Ground Target Tracking with STAP Radar,IEE Proc. Radar, Sonar and Navigation, vol. 148, issue 3, pp. 173-185,2001.

[2] M. Mertens and M. Ulmke, Ground Moving Target Tracking with Con-text Information and a Refined Sensor Model, Proc. of 11th InternationalConference on Information Fusion 2008, Cologne, 2008.

[3] R. Kohlleppel and M. Mertens, Indication and Tracking of GroundMoving Targets with the PAMIR System: Experimental Results, Proc.of International Radar Symposium IRS 2009, Hamburg, 2009.

[4] M. Daun, W. Koch, and R. Klemm, Tracking of Ground Targets withBistatic Airborne Radar, Proc. of IEEE Radar Conference RadarCon2008, Rome, 2008.

[5] R. Klemm, Principles of Space-Time Adaptive Processing, 3rd Edition,IET Radar, Sonar and Navigation Series 21, 2006.

[6] J. R. Guerci, Space-Time Adaptive Processing for Radar, Artech House,Boston, London, 2003.

[7] J. Ward, Space-Time Adaptive Processing for Airborne Radar, TechnicalReport 1015, MIT, Lincoln Laboratory, 1994.

[8] N. J. Willis, Bistatic Radar, Scitech Pub Inc, January, 2007.[9] Y. Bar-Shalom and X.-R. Li, Estimation and Tracking: Principles,

Techniques, and Software, Artech House, Boston, 1993.[10] S. Blackman and R. Popoli, Design and Analysis of Modern Tracking

Systems, Norwood, MA, Artech House, 1999.[11] S. J. Julier, J. K. Uhlmann, Unscented Filtering and Nonlinear Estima-

tion, Proceedings of the IEEE, Vol. 92, No. 3., pp. 401-422, 2004.[12] C. R. Berger, M. Daun, and W. Koch, Low complexity track initialization

from a small set of non-invertible measurements, EURASIP Journal onAdvances in Signal Processing, p.1-15, 2008.

[13] W. Koch, Advanced Target Tracking Techniques, Advanced Radar Signaland Data Processing, Educational Notes RTO-EN-SET-086, Paper 2,France, 2006.

[14] G. van Keuk, Sequential Track Extraction, IEEE Transactions onAerospace and Electronic Systems, vol. 34, issue 4, pp. 1135-1148,1998.

[15] M. Mertens and U. Nickel, GMTI Tracking in the Presence of Dopplerand Range Ambiguities, Proc. of 14th International Conference onInformation Fusion 2011, Chicago, 2011.

2338