Adaptive Target Tracking in Slowly Changing Clutter

Transcription

1 Adaptive Target Tracing in Slowly Changing Clutter Thomas Hanselmann, Daro Mušici, Marimuthu Palaniswami Dept. of Electrical and Electronic Eng. The University of Melbourne Parville, VIC 30 Australia {t.hanselmann, d.musici, Abstract - False trac discrimination performance of a target tracing algorithm in a heavy clutter environment depends on the trac confirmation and the trac termination thresholds. The optimum value of these thresholds depends on the environment, in particular on the given probability of detection and on the existing clutter density. When tracing ground targets the probability of target detection is nominally constant, whereas the clutter measurement density varies significantly. Previously it was shown that, for a wide range of target signal to noise (+clutter) ratio in a uniform clutter density environment, and given the opportunity to set signal detection thresholds, the optimum value of clutter measurement density is almost constant (and the probability of detection will vary). We propose a scheme where the feedbac from the target tracing system corrects the detection thresholds for each sensor resolution cell to obtain the constant and optimal clutter measurement density in each cell, when the clutter statistics changes slowly. This results in better false trac discrimination capabilities of the tracer and also replaces the CFAR bloc in the signal processing unit. Keywords: Optimal signal detection probability, tracing, IPDA, trac existence, false trac discrimination, probability of detection feedbac, CFAR. 1 Introduction Fast clutter estimation based on an unbiased spatial estimator enables an adaptive feedbac to control the measurement generation process. Previously we have experimentally determined the optimal detection probability for a range of signal to noise ratios [1]. This showed a fairly low and constant optimal clutter density which we utilize in this paper to derive an adaptive Integrated Probabilistic Data Association (IPDA) algorithm that estimates clutter density and the probability of detection []. This leads to two significant performance improvements: faster true trac confirmation given a constant confirmed false trac rate and Acnowledgements: This research has been supported by the Melbourne Systems Lab and by the Australian Research Council Linage grant scheme. even more impressive at least a magnitude of order faster processing. Data association is the most crucial part in tracing, as it greatly determines the performance of a tracing system. Measurements of uncertain origin have to be associated with tracs of real targets, as well as false tracs which do not follow targets. The tas for the tracing system is now to use the available measurements and associate them with tracs of targets whose existence can only be nown in a probabilistic sense. Algorithms lie Generalized Pseudo-Bayesian Probabilistic Data Association (GPB1-PDA, [3]) or the Interacting Multiple Model Probabilistic Data Association (IMM-PDA, [4]) treat false trac discrimination in clutter and indirectly calculate the probability that that target is detectable (probability of true trac) by including a zero detection target model. The probability of the zero detection model is the complement of the probability that the target is detectable. Integrated Probabilistic Data Association (IPDA) recursively estimates the probability of target existence []. A further extension is the IPDA-MAP algorithm which uses a spatial clutter density map [6]. These algorithms and the observation that the optimal probability of detection varies while the optimal clutter density stays roughly constant (for details see [1]) are combined and extended to estimate the locally optimal probability of detection, see section.3. In each sensor resolution cell detection thresholds are modified to achieve the optimal clutter measurement density, which affects the probability of target detection. Measured clutter measurement density in each cell is part of the feedbac to the signal detection thresholds. The feedbac loop aims to deliver the optimal clutter density. In this submission an ideal feedbac loop is assumed. This results both in improved false trac discrimination capabilities of target tracer when compared to the fixed detection threshold case, and also replaces the CFAR bloc in the signal processing unit. Simulations show the false trac discrimination performance benefits of this approach when tracing a single target with constant radar cross section in an environment of heavy, non-uniform and slowly changing clutter. In IPDA the probability of existence is recursively estimated based on new measurements and their lielihoods of belonging to the trac under investigation. Based on the Bayes-Chapman-Kolmogorov equation,

2 posterior probabilities are calculated from the prior probabilities and the new measurements. IPDA nicely treats also the possibility of not having a target as well. This is done in conjunction with a Marov model for target existence propagation. There are two models: Marov chain One and Marov chain Two. The first one is a special case of the second where target existence is equal to the target being detectable, whereas in the second model they are distinct. The clutter map extension is based on [7] and as shown there the spatial estimator is able to give reasonable clutter density estimates with only scans. This is due to the unbiased estimate of the inverse clutter density which the IPDA algorithm relies on to calculate the data association probabilities. In the design of tracing systems for radar or sonar, the probability of detection is a central parameter. The probability of detection should be high enough to capture true targets but low enough to prevent overwhelming numbers of false detection. While there has been some investigation in the optimal probability of detection, there has been little research in adaptive feedbac of the probability of detection for improved measurement generation, which is the process of turning the analog (amplitude) signal into discrete measurements of position and is further described in section.1. Li and Bar-Shalom have developed a hybrid conditional average algorithm [8] to determine a temporal and spatially constant probability of detection. Similarly, Hong and Evans have developed a theoretical approximation framewor to estimate the probability of detection [9], assumed to be constant over space and time. Willett et al. [] has introduced some feedbac from the PDA filter to the detector to allow for a temporary and spatially varying threshold, integrating Bayesian detection based on prior probabilities of expected location and covariance of target measurements. While the first two publications are dealing with no a priori nowledge (all measurements are treated equally), the latter one is changing the tracing setup by incorporating nowledge based on measurements. This may be beneficial in some applications but in general varying clutter distributions might introduce some bias. Furthermore, two applications on adaptive detection threshold optimization for tracing in clutter are reported by Fortmann [11] and Gelfand in [1], where the second paper is an improvement of the earlier wor by Fortmann, with regard to the optimization and modeling. In [1] a modified Riccati equation is used to minimize the mean-square state estimation error over detection thresholds. Two optimization algorithms, prior and posterior to the reception of the set of measurements Y at time are proposed. However, there is no direct feedbac based on the clutter density involved, rather number of measurements m (γ) are modeled as sum of the number of false and target measurements by m F (P fa(γ)) + m D (P d(γ)), where γ is the detection threshold. In this paper, Monte Carlo simulations based on the IPDA-MAP algorithm [], are used to determine the true and false trac discrimination performance. To compare the true tracs statistics the confirmation threshold is chosen such that the rate of confirmed false tracs scans is about one in 50, which seems reasonable for practical applications. Four experiments have been designed to compare results and a fifth experiment is outlined and only some preliminary results are reported thereof. The first two experiments use uniform high and low clutter densities with different probability of detections. The third and forth experiment use non-uniform clutter density with low and heavy clutter areas with ideally adapted P d in experiment three and spatially constant non-ideal P d for experiment four. This is to investigate a proof of concept and maximal possible gains. This idea is currently developed in a fifth experiment for an extended publication later with spatial clutter-map estimator in IPDA-MAP algorithm and probability of detection map (Pd-MAP). The first four experiments use ideal feedbac, meaning the clutter density and therefore the optimal probability of detections are nown, whereas the fifth experiment uses the clutter density estimated by the spatial inverse density estimator. In all experiments the signal to nose ratio is assumed to be nown spatially. In practice this would have to be estimated as well and one method how to do this can be found in [13]. Data flow in an IPDA-MAP tracing system.1 Data preprocessing and detection thresholding Fig..1 shows the signal flow in the experiment. The IPDA-MAP algorithm performs the tracing part, delivers probabilities of target existence which are then used in true trac detection module to obtain confirmed tracs and estimates the spatial clutter density ˆρ(x, y), Figure 1: Processing flow from raw data to true trac detection with the IPDA-MAP algorithm. The probability of detection P d is a consequence of signal processing which generates measurements when the signal energy is higher than the threshold in a hard limiter. Thus, the probability of target detection is correlated with the probability of false alarm or clutter measurement generation. Fig..1 shows the classification made in the threshold detection unit into noise (= negatives ) and measurements (= positives ) with respect to the amplitude threshold X t corresponding to a probability of detection P d. Based on the threshold and the two

3 pdfs, four probabilities can be calculated. The two according to the positive classification, which generates measurements for the tracing stage, are of particular interest. These are the probability of true accepted trac measurements, i.e. the probability of detection, P r(t P ) = P d (TP=true positives), and the probability noise signals regarded as trac measurements, i.e. the probability of false alarm, P r(f P ) = P fa (FP=false positives). A receiver operating curve (ROC) with the confirmation threshold as threshold parameter can be used to determine the performance. Fig.. shows the ROC with two amplitude threshold values X t1 and X t with corresponding detection probabilities P d1 and P d. The area under the bent curve is the figure of merit and the larger it is the better the performance. Ideally the probability of confirmed false tracs, P r(cf T ), should be zero and the probability of confirmed true tracs, P r(ct T ), should be one. The figure of merit is then 1, whereas the diagonal line corresponds to a figure of merit of 0.5, indicating a trac confirmed as a false trac would be as liely as a trac confirmed as true trac, and hence a random classification, as obtained by throwing a fair coin, would tae place. Figure : Analog amplitude pdfs for target signal and noise signal, pdf(x noise) and pdf(x signal&noise), respectively.. Tracing The measurements will then be validated if they are inside some gating window determined by the IPDA algorithm on a trac by trac basis. These validated measurements are then associated with corresponding tracs. Based on a Marov chain model and Bayesian inference the probability of target existence is calculated for these tracs which are then classified as confirmed or terminated tracs, depending on whether the probability of target existence exceeds a confirmation threshold T c or falls below a termination threshold T t, respectively. In an ideal situation the remaining tracs stay unconfirmed and over time their probability of existence will wander towards one or zero depending on whether it is a true or false trac. In practice some of the confirmed tracs are false tracs that got misclassified due to the overlapping probability distributions, see Fig... Figure 3: True trac (TT) and false trac (FT) histogram statistics as a function of the probability of trac existence P {χ} at some time t. Figure 4: Receiver Operating Curve (ROC)..3 Mathematical Notation for IPDA- MAP A similar notation is used as in [1] but extended for IPDA-MAP and because P d in the general case is not constant anymore but rather a function of target position where the gating window V is located: P d = V P d (z)p d (z)dz, with measurement probability density function p d (.), modeled as Gaussian lielyhood function centered at the predicted observation ẑ 1. The integral is approximated as in (5) for fast approximate evaluation. To distinguish the approximated spatial varying probability of detection from the traditional constant P d a bar-symbol is used: Pd. P d (z i ) denotes the estimated probability of detection by the Pd-MAP. If there are no measurements P d is approximated by P d (ẑ 1 ). The following notation is used: SNR db SN R P d P fa ρ fa V rc signal to noise ratio in db signal to noise ratio probability of detection probability of false measurement clutter density resolution cell volume

4 This gives the relations: SNR = 1 SNR db (1) P fa = P 1+SNR d () ρ fa = P fa /V rc (3) V rc = x y (4) x = 3σ x (5) y = 3σ y (6) σ x = σ y = 5m (7) where the relation () is given in [14, 15]. x and y are approximate side lengths of the resolution cell 1 area, assuming equal distributions x and 1 y within the cell area, yielding a variance of x 1 and y 1, respectively. Equating these expressions with the zeromean Gaussian observation noise variances σx and σy, yields expressions (5) and (6). Fig.. shows how tracs are confirmed based on the Monte Carlo simulation. The number of confirmed false tracs is evaluated and the confirmation threshold T c is varied until the sum of confirmed false trac scans divided by the number of scans and runs is roughly one out of 50. The target motion model is: x +1 = F x + ν (8) x = [x, ẋ, y, ẏ] T (9) [ ] [ ] FT 0 1 T F =, F 0 F T = () T 0 1 where T is the sampling time, (x, y) and (ẋ, ẏ) are the position and velocity coordinates, respectively. ν is zero-mean white Gaussian noise with nown variance E[ν νl T ] = Qδ(, l) (11) [ ] [ ] T QT 0 4 T 3 Q = q, Q 0 Q T = 4 (1) T with q = The observation model is given by: T 3 T z = Hx + w (13) [ ] H = (14) w is zero-mean white Gaussian noise with nown variance: E[w wl T ] = Rδ(, l) (15) [ ] σ R = x 0 0 σy (16) The Marov chain model one for the probability of target existence conditioned on the set of observations Z 1 of all observations z i, i = 1,.., m made at previous times = 0,.., l 1 is as follow: [ ] P {χ Z 1 } 1 P {χ Z 1 = } [ ][ P {χ 1 Z 1 } P {χ 1 Z 1 } with initial probability of P {χ 0 Z 0 } = P {χ 0 } = 0.1 used in the two-stage trac initialization run at each scan. State and covariance estimates ˆx and ˆP are given by the standard PDA algorithm: m ˆx = β i ()ˆx i (18) i=0 m ˆP = β i ()( ) ˆP i + (ˆx i ˆx )(ˆx i ˆx ) T (19) i=0 where ˆx 0 = ˆx 1, ˆP 0 = ˆP 1 and data association probabilities are given by: β 0 () = 1 P G P d 1 δ (0) β i () = P GP d (z i ) p d (z i ) 1 δ ˆρ i, i = 1,.., m (1) { PG Pd : m = 0 δ = m P G Pd P G i=1 P d(z i ) p d(z i ) : m ˆρ i 0 () p d (z) i = Λ i := 1 N (z P ; i ẑ 1, Ŝ), i = 0,.., m (3) { G 0 : m = 0 ˆm = m P d P G P {χ Z 1 (4) } : m 0 m i=0 P d = P d (z)p d (z)dz P d(z i )Λi m (5) V i=0 Λi with z 0 = ẑ 1 where m is the number of validated observations z i ; P d (.) and P G are the probabilities of detection as a function of space and gating validation, respectively. p d (z) is the measurement lielyhood in the gating window, assumed to be Gaussian. The approximation in (5) may be seen as a crude but fast quadrature integral-lie evaluation. In IPDA-MAP ˆρ i is the estimated clutter density at the i-th observation z i at time and simplifies in the standard IPDA algorithm to ˆρ i = ˆm V, i = 1,.., m. The probability of target existence update is determined by: P {χ Z } = 1 δ 1 δ P {χ Z 1 } P {χ Z 1 } (6) in conjunction with the Marov update (17). Estimation and prediction are obtained by the standard Kalman filter: Ŝ = H ˆP 1 H T + R (7) K = ˆP 1 H T Ŝ 1 (8) ˆx i ( ) = ˆx 1 + K z i H ˆx 1 (9) ˆP 1 = (I K H) ˆP 1 (30) ˆx +1 = F ˆx (31) ˆP +1 = F ˆP F T + Q (3).3.1 Spatial Clutter-Map Estimation ] In [7] it was shown that an efficient non-biased estimator of the inverse clutter measurement density (17) is

5 the averaged distance N 1 (c) from resolution cell center to the nearest Poisson measurement point. This is a direct property of the Poisson distributed measurements, as then the mathematical distance ξ between two Poisson measurements has exponential distribution (33) and expectation (35), [16, 17, 18]. The averaging process N (c) can be done either according to a moving average (36) or by autoregressive filter (37), where µ (c) is the inverse clutter density measurement at cell c at time. p ξ (ξ) = ξ U(ξ), ρe { with (33) U(ξ) = 1 : ξ 0, 0 : ξ < 0. (34) E(ξ) = 1 ρ N (c) = 1 L α = j= L+1 (35) µ j (c), moving average, or,(36) = α N 1 (c) + (1 α )µ (c), auto regressive with (37) { 1 : < L, L 1 L : L. The averaged measurements have zero bias because the sum y = L l=1 ξ l of L independent, exponentially distributed random variables ξ l have a Gamma distribution (38) with mean (39) and variance (41). A crucial property is that the relative variance of the estimator is given by (4), which means it converges asymptotically with 1 L to the true value of y and simulations have shown that estimates become reasonable for L as small as, in other words after only scans a useable clutter density estimate is available. However, as the analysis is done for Poisson distributed clutter, real clutter densities with discontinuities, e.g. different areas with different mean values of poisson distributed clutters, again will have bias and a transition between these regions. For further details see [7]. p y (y) = ρ L (L 1)!y L 1 e ρy U(y) (38) Ey = L ρ (39) Ey = L(L + 1) ρ (40) σ (y) = Ey E y = L ρ (41) σ (y) E y = 1 L (4) For the spatial inverse clutter map estimator, N (c), ξ (c) is the mathematical distance and is determined by the size µ (c) = min i=1,..,m A i (c) of a fixed - dimensional shape (e.g. circle or square), centered at resolution cell c, just touching the nearest observed clutter measurement z i and is clipped outside the surveillance area, see figure.3.1. As the measurement generation process has measurements from targets as well as of clutter, the fol- Figure 5: Spatial clutter map estimator. lowing size measure is used: m µ (c) = A I(i) (c)p t (i)p c (z I(i) ), where (43) i=1 { 1, i = 1, P t (i) = ( ) P t (i 1) 1 P c (z I(j) (44) ), i =,.., m Where I(.) is an index (sorting) function such that A I(i) A I(i+1), i = 1,.., m 1, P c (z i ) is the probability of z i to be a clutter measurement and P t(i > 1) is the probability that all i 1 previous measurements z I(j), j = 1,.., i 1, were from targets and not clutter. Let χ and χ,i be the events that the target exists, and, that of target existence and measurement z i is a target measurement, respectively. Then P {χ, χ,i Z } denotes the probability of target existence and measurement z i is from the target given all previous and current observations. Therefore P c (z i ) = 1 P {χ, χ,i Z } (45) P {χ, χ,i Z } = P G P d (z i ) p d(z i ) ˆρ i 1 δ P {χ Z 1 } P {χ Z 1 } (46) where i = 1,.., m. Remar: The data association probabilities given before are related as β,i P {χ,i χ, Z } = P {χ,χ,i Z } P {χ. Equation (45) is valid Z } for single target tracing. For multi-target tracing, P c is the product of (45) across all tracs τ = 1,.., T (z i ) which select z i, i.e. P c(z i ) = T (z i ) τ=1 P c τ (z i )..3. Updates of P d -MAP For a real system the detection thresholds are needed which are determined based on P fa, P d and SNR, all of which may vary spatially and even slowly temporarily. The actual threshold γ used in the thresholding unit to generate measurements is determined by P fa and P d, see figure.1. P fa = V rc ˆρ fa is estimated by the spatial clutter density estimator. For a chosen spatially varying P d, the signal to noise ratio could be estimated and based on (47) and the optimal values for a given SNR can be obtained from [1]. However, this may lead to instabilities and an autoregressive filter for P d with a

6 longer time constant may be a better way. This is currently under investigation and will be published later. Another way is to use an independent estimate of the SNR, as given in [13]. Therefore, for the experiments 1 to 4, a nown SNR is assumed. 3 Experiments The objective of is to experimentally confirm an improvement in the tracing performance when spatial clutter density estimation by the IPDA-MAP algorithm is used to build a spatial probability of detection map (Pd-MAP). As mentioned before five experiments are designed. In the first and second experiment the clutter densities are high ( m ) and low ( 5 m ), respectively, and uniform over the whole surveillance area. The probabilities of detection are selected as P d = 0.9 and P d = Pd = 0.74, respectively. The signal to noise ratio is chosen to be 1dB, such that the second experiment has roughly optimal probability of detection and optimal clutter density (taen from [1]), where as the first one only matches the Swerling model I relation ( ) 1+SNR ρ fa = ρ Pd fa (47) P d In the third and forth experiment an optimal and a non-uniform clutter with low and high-clutter density areas are used, respectively, as shown in figure 3. For the third experiment, ideal feedbac, that is the optimal probabilities of detection are used, where as in the forth experiment a constant probability of detection of 0.9 for the whole surveillance area is assumed. In the fifth experiment, which will be done as part of further research, the same parameters as in experiment four are used initially but then the clutter density is estimated, using the spatial clutter map estimator (36,43). As the IPDA algorithm with two-point differencing initialization needs roughly P d 0.7 to reliably initialize tracs the estimated Pd-MAP is thresheld and ept at 0.7 for lower estimates. Table 1 gives the values used in experiments three, four and the initial values for experiment five. Experiment Exp. 3 Exp. 4 and 5 (init.) ρ 1 5 m 0 P d SNR 1 1dB 1dB ρ 5 m m P d SNR 1dB 1dB Table 1: Parameters for experiments three, four and five (initially). To determine the performance confirmed true tracs over 50 scans are measured while eeping the confirmed false trac statistics constant at a rate of 1 in 50. An automatic initialization of tracs is used that is based on two successive scans (two point differencing). At every scan new tracs are initialized for all possible measurement combinations of any two measurements from Figure 6: Surveillance area with high clutter density areas and trajectory (blue) starting at scan 1 and ending at scan 50. In experiment 1 and : ρ 1 = ρ, P d1 = P d and SNR 1 = SNR. For experiment 3 and 4 see table 1. In experiment 5 the spatial clutter map estimate is used and with no access to true probability of detection and clutter density and only uses the non-optimal initial guesses given in the table. different scans, if the absolute measurement differences of such a combination fall below a certain threshold (maximum target speed). All of these tracs are assigned an initial probability of target existence. During a simulation run this probability is normally increased for true tracs by the validation of later measurements, while for false tracs it will decrease on average. If it drops below a termination threshold the trac will be terminated. If the probability of target existence exceeds a confirmation threshold, the trac becomes a confirmed trac. Depending on whether a trac follows a target or not, they are classified as true or false tracs, respectively. This leaves four possibilities, confirmed true and false tracs (CTT and CFT) and terminated true and false tracs (TTT and TFT). Naturally, the goal is to have as many confirmed true tracs with a low limited number (ideally zero) of confirmed false tracs and no terminated true tracs. Because of the stochastic nature of the measurements, the associated pdfs on the numbers of true and false tracs have some variance, are overlapping and are functions of underlying parameters. The initial target existence probability, P {χ 0 } = 0.1, and the termination threshold, T t = 0.0, were chosen to be of reasonable value from experience based on experimental optimization [6] but held constant here and only the confirmation threshold T c is adapted to eep the confirmed false trac rate roughly constant. 4 Results The results of experiments 1 and, given by figure 4, show that feedbac for an adaptive probability of detection can improve performance drastically by raising the detection threshold to have an optimal clutter

7 density. Figure 4 shows the maximal performance gain in terms of the temporal behavior of the true trac statistics. While experiment 1 has a high, non-optimal P d = 0.9 and a resulting high clutter density, the performance lacs far behind the one of experiment, which has optimal probability of detection and clutter density for the given signal to noise ratio. The comparison between the IPDA-MAP which uses a clutter map and the standard non-parametric IPDA algorithm shows a clear advantage for the former with the biggest gain stemming from the optimal signal detection. Fig. 4 shows the results of experiment 3 and 4 with the setting given in figure 3 and table 1. Clearly, using the optimal probability of detection for ideal thresholding increases the performance significantly. The vertical dashed lines show the area boundaries in x-direction in which the target is moving. Interestingly, the difference in performance is increased when the clutter density of the areas are swapped, i.e. ρ 1 ρ. Then the trac starts in a high clutter area, followed by low, then high and finally low clutter again. In this case (red lines), a non-optimal probability of detection corresponding to a higher clutter density, yields significantly worse results for non-optimal selection. Also, in the second high clutter area the non-optimal selection starts loosing tracs, as seen in the enlarged plot area in figure 4. This shows that the optimal probability of detection and corresponding clutter density are crucial to initialize new tracs. A second observation is that the IPDA algorithm maintains tracs very well, once they are confirmed, even in the case of nonoptimal selection of the detection probability. Nevertheless, true/false-trac discrimination performance can still be improved by the use of the optimal probability of detection. Fig. 4 shows the estimated clutter density of the spatial estimator after only 50 scans and a time constant of scans for the autoregressive filter. This would be the initial clutter density for experiment 5 before feedbac is turned on. Fig. 4 shows the estimated clutter density when feedbac is used to bring the the clutter density to the optimal density of 5 m. Further investigations on necessary time constants in the feedbac loop will be done in future research. Furthermore, a crucial side effect of performing spatially adaptive detection thresholding is that the algorithm s running time can be reduced drastically. This is due to the fact the number of false tracs is proportional to the square of the number of clutter measurements received, which influences the total run time. Running times are given in table. 5 Conclusions In this paper the effect of spatially optimal probability of detection via feedbac has been investigated. Experiments 1 to 4 looed at ideal feedbac with exactly nown clutter densities and probabilities of detection. The results are very promising and show a large potential of performance improvements in terms of the number of confirmed true tracs within 500 runs Confirmed true tracs Exp. 1 map : Pd = Exp. map : Pd*=0.74 Exp. 1 nonpar: Pd =0.90 Exp. nonpar: Pd*= Scans Figure 7: Results of experiments 1(non-optimal) and (ideal feedbac) in homogenous clutter for the IPDA- MAP(blue) and the non-parametric standard IPDA algorithm (green). Experiment Running Time per Confirmation second for 500 runs threshold T c Exp (58074) ( ) Exp. 557 (436) ( ) Exp Exp. 3swap Exp Exp. 4swap Table : Running times and confirmation thresholds for the experiments. The impact of the low clutter density is evident from experiments 1 and. The performance of the ideal feedbac depends very much on the clutter density where a trac gets initiated. In high clutter performance is severely impaired as experiments 3 and 4 and their counterparts with swapped clutter densities (ρ 1 ρ ) show. Values in bracets are for the standard IPDA algorithm as shown in figure 4. number of confirmed true tracs and in the actual runtime performance. The use of the spatial clutter density estimator with its low time constant is crucial for tracing slowly varying clutter, without loosing a lot of accuracy. Thus, it is very reasonable to expect good performance of a completely closed loop with adaptive probability of detection and clutter density estimation. From a radar operators point of view, this could remove the CFAR unit for the thresholding unit and thus remove manual interaction of setting threshold parameters. References [1] T. Hanselmann and D. Mušici. Optimal signal detection for false trac discrimination. In The Eight International Conference on Information Fusion, Philadelphia, PA, USA, July [] D. Mušici, R.J. Evans, and S. Stanović. Integrated probabilistic data association (ipda). IEEE Transactions on Automatic Control, 39(6): , 1994.

8 number of confirmed true tracs within 500 runs Confirmed true tracs 0 Exp. 3 : Pd*=[ ] Exp. 4 : Pd = Exp. 3swap: Pd*=[ ] Exp. 4swap: Pd = Scans x ClutterMap ρ fa (1./ cluttermap.densityinv) Scans Figure 8: Results of experiments 3(non-optimal) and 4(ideal feedbac) in non-homogenous clutter. If the high and low clutter density areas are swapped (ρ 1 ρ ), the differences between experiments 3swap and 4swap are even more evident. The lower subplot is a magnification of the above one and the vertical dashed lines indicate the clutter area boundaries in the horizontal direction, compare figure x 4 15 ClutterMap ρ fa (cluttermap.clmap/vrc) 5 Figure 9: The spatial clutter density estimator with ARMA filter is already fairly accurate after only 50 scans and a time constant of scans. [3] S. B. Colegrove, A. W. Davis, and J. K. Ayliffe. Trac initiation and nearest neighbours incorporated into probabilistic data association. Journal of Electrical Electronics Engineering - Australia, 6, [4] Y. Bar-Shalom, Y. Chang, and H. A. P. Blom. Automatic trac formation in clutter with a recursive algorithm. In Y. Bar-Shalom, editor, Multitarget- Mulitsensor Tracing: Principles and Techniques, volume 1. Artech House, Norwood, MA, [5] Yaaov Bar-Shalom and Xiao-Rong Li. Multitarget- Mulitsensor Tracing: Principles and Techniques. YBS, Box U-157, Storrs, CT , 3 edition, [6] D. Mušici and R. Evans. Clutter map information for data association and trac initialization. IEEE Transactions on Aerospace and Electronic Systems, 40(): , April 004. [7] D. Mušici, Sofia Suvarova, Mar Morelande, and Bill Moran. Clutter map and target tracing. In The Figure : Preliminary experiment 5 shows that it is possible to drive the clutter density towards the optimal density around 5 m. However, some oscillations may occur but performance will be far better than in experiment 4, much closer to experiment 3. Eight International Conference on Information Fusion, Philadelphia, PA, USA, July [8] X. R. Li and Y. Bar-Shalom. Detection threshold selection for tracing performance optimization. IEEE Transactions on Aerospace and Electronic Systems, 30(3):74 749, July [9] Sun-Mog Hong and R. Evans. Optimization of waveform and detection threshold for range and range-rate tracing in clutter. IEEE Transactions on Aerospace and Electronic Systems, 41(1):17 33, January 005. [] Peter Willett, Ruixin Niu, and Yaaov Bar-Shalom. Integration of bayesian detection with target tracing. IEEE Transactions on Signal Processing, 49(1):17 9, January 001. [11] Thomas E. Fortmann, Yaaov Bar-Shalom, Molly Scheffe, and Saul Gelfand. Detection thresholds for tracing in clutter - a connection between estimation and signal processing. IEEE Transactions on Automatic Control, 30(3):1 9, March [1] Saul B. Gelfand, Thomas E. Fortmann, and Yaaov Bar-Shalom. Adaptive detection threshold optimization for tracing in clutter. IEEE Transactions on Aerospace and Electronic Systems, 3():514 53, [13] Abdlla Abdljalell, Brano D. Kovačević, and Željo M. Djurović. Adaptive cfar detection of radar target in non-gaussian clutter. Journal of Aut. Control, University of Belgrade, (87-4), 000. [14] C. Rago, P. Willett, and Y. Bar-Shalom. Detectiontracing performance with combined waveforms. IEEE Transactions on Aerospace and Electronic Systems, 34():61 64, April [15] H.L. Van Trees. Detection, Estimation and Modulation Theory, Part III. John Wiley, John Wiley, New Yor, [16] Donald Lee Snyder. Random Point Processes. Wiley, New Yor, [17] John Fran Charles Kingman. Poisson Processes. Oxford University Press, New Yor, 199. [18] Sheldon Mar Ross. Introduction to Probability Models. Academic Press, London,