Multiframe Assignment Tracker for MSTWG Data

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1 th International Conference on Information Fusion Seattle, WA, USA, July 6-9, 9 Multiframe Assignment Tracker for MSTWG Data R. Tharmarasa, S. Sutharsan and T. Kirubarajan ECE Dept., McMaster University Hamilton, ON, Canada tharman@mail.ece.mcmaster.ca, suthar@grad.ece.mcmaster.ca, kiruba@mcmaster.ca Thomas Lang General Dynamics Canada Limited Ottawa, Ontario, Canada tom.lang@gdcanada.com Abstract In this paper, a multiframe assignment tracker is applied to the simulated data sets provided by the Multistatic Tracking Working Group (MSTWG). The multiframe assignment tracker solves the data association problem as a constrained optimization for fusing multiple sets of data to the tracks with an Interacting Multiple Model (IMM) estimator. The challenges with these data sets are high false alarm rate, low probability of detection and multiple synchronous/asynchronous sensors. Multiframe data association is used to perform data association, which is the crucial part of thetracking. Centralized trackingisused to optimally fuse the information from multiple sensors. A track s status is updated using an m out of n logic rather than the track quality based logic that requires moreaccurateprobability ofdetection values, which are not available and vary with time and geometry in the MSTWG data sets. The resultsobtained with the multiframe assignment tracker for all the data setsare given in the form of MSTWG performance metrics. Keywords: multitarget tracking, multistatic sensors, multiframe assignment, interacting multiple model, nonlinear filtering. Introduction ISIF 87 The Multistatic Tracking Working Group (MSTWG) was formed to share the scientific and technical ideas, problems, and solutions related to multistatic tracking for sonar and radar []. Multistatic sensors have many advantages over passive/active monostatic sensors including better area coverage and high probability of detection due to geometrical diversity. In addition, multistatic systems are resilient to target countermeasure due to unknown receiver locations even though transmitter location can be estimated by the target. Although multistatic sensors have many advantages, tracking with these sensors poses some additional challenges. Geometrical diversity is an advantage, however it results in inconsistent detections over all the receivertransmitter pairs. That is, it is possible for a target to get measurements only from few of the transmitterreceiver pairs and even the pairs that give the measurements will change with time due to target, receiver and transmitter movements. In addition, high clutter with low Probability of Detection (PD) will make the problem even more difficult. Hence, these problems must be handled carefully by the tracking algorithm. In this paper, a trackerdevelopedatmcmaster University for multisensor multitarget tracking is used to analyze the MSTWG data sets. The tracker was developed to handle several data sets obtained from different sensorsystems (e.g., passive coherentlocation, perimeter surveillance radar, multistatic sensors). In this tracker, data association is performed using the multiframe assignment technique [][], target maneuvers are handled by Interacting Multiple Model (IMM) [] and track maintenance is performed based on either measurement association logic or track quality. Converted Measurement Kalman Filter (CMKF), Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) are incorporated to handle measurement nonlinearity. In addition, the tracker can handle constraints on state values (e.g., maximum speed). The remainder of the paper is structured as follows. Sectiondescribes the configurationandmeasurement model of multistatic sensor networks. Section describes the tracker details including track maintenance, filtering and data association. The results for all the MSTWG data sets are given in Section. Conclusions are then given in Section 5. Multistatic Sensor Network In a multistatic sensor network, there are multiple transmitters and multiple receivers. A sample scenario with two transmitters and two receivers is shown in

2 Figure. According to the transmitter-receiver pair, each pair will act as a monostatic or bistatic sensor. The main advantage of the multistatic sensor network over the monostatic sensors is better target detection probability due to geometric diversity. Transmitter θ d r Target d t Receiver Receiver Figure. Multistatic sensor network Transmitter In the MSTWG data sets, measurements are bistatic range (r b ) and bearing (θ), and the j-th measurement at the sensor s at time k is given by [ ] rb (j, k) z s (j, k) = () θ(j, k) where = [ dr (k) + d t (k) atan ( x(k) xr(k) y(k) y r(k) ) ] + ω s (j, k) () d r (k) = (x(k) x r (k)) + (y(k) y r (k)) () d t (k) = (x(k) x t (k)) + (y(k) y t (k)) () and [x, y], [x r, y r ] and [x t, y t ] are the x and y coordinates of the target, receiver and transmitter, respectively, atan( ) is the four-quadrant arctangent and ω s (j, k) is a zero-mean Gaussian random variable with covariance Q s (j, k). If a measurement is a false alarm, then it is assumed to be uniformly distributed across the surveillance region. Note that monostatic measurement can also be considered as a special case of bistatic with transmitter and receiver at the same location. Even if the Time-Difference-of-Arrivals (TDOAs) are given instead of bistatic range, they can be converted to the bistatic range by multiplying by speed of the signal in the given medium and then adding the distance between the receiver and the transmitter. Tracker Multisensor-multitarget tracking tracker developed at McMaster University for several real data sets, including the MSTWG data, is used to analyze and perform the tracking with the multistatic data sets. The tracker is capable of handling multiple sensors, monostatic/bistatic measurements, asynchronous measurements, nonlinear measurements and target maneuvers. In some cases, bistatic Doppler is also available. However, they are not used in this data processing. The multiframe assignment tracker is capable of handling Doppler data. 88. Filtering In order to handle the nonlinearity in the measurements, the extended Kalman filter [], Unscented Kalman filter [8] and the converted measurement Kalman filter [] are included in the tracker. The user has the option to choose one of the above three filters. An IMM estimator with two constant velocity models of different process noises is used to handle the target maneuvers in the MSTWG data sets []. The state dynamic equation for constant velocity model is given by [] X(k) = T T X(k ) + T T T T where X(k) (= [x(k), ẋ(k), y(k), ẏ(k)]) is the target s state and υ(k) is a zero-mean Gaussian white noise, whose covariance varies for different IMM models. The maximum speed of the target, which is a prior information, is imposed byadding a pseudo-measurement to keep the speed below the maximum limit when the estimated speed exceeds threshold []. This will help to reduce the false tracks and to avoid associating wrong measurements to target originated tracks, especially when targetoriginatedmeasurements are missing. The state update using a speed pseudo-measurement is performed using EKF with the following models: z v (k) = (6) ẑ v (k) = ẋ(k) + ẏ (k) (7) H v (k) = [ ẋ(k)/ẑ v (k) ẏ(k)/ẑ v (k) ] (8) R v (k) = H v (k)p(k)h v (k) ( V max ) (V max ẑ v (k)) υ(k) (5) (9) where z v (k) is the speed pseudo measurement, ẑ v (k) is the predicted speed measurement, H v (k) is the measurement matrix, R v (k) is the pseudo measurement s variance, P(k) is the updated state covariance and V max is the maximum speed. The pseudo measurement update is performed sequentially after updating the target state with the associated measurements, and it is performed only if the updated target state s speed is above the maximum limit. This pseudo measurement update is repeated for few iterations until the updated speed is below or close to the maximum speed []. A more flexible framework for incorporating constraints is under development.. Track maintenance The tracks are classified into two categories: ) Tentative tracks and ) Confirmed tracks. Tentative tracks are the ones formed with fewer initial measurement associations than required for confirmation tracks within

3 a certain time limit. Upon obtaining more measurements, the tentative tracks are promoted as the Confirmed tracks. If not enough measurements are associated with a tentative track, then the tentative tracks are deleted. In this tracker, the user has the option to choose either logic (m out of n) or quality based track maintenance []. The track quality is updated using the measurement likelihood, probability of detection and false alarm rate []. For MSTWG data sets, logic based track maintenance was found to be more applicable since the exactprobabilityofdetection, whichis requiredfor track quality calculation, is not known. The logic based track maintenance is done as follows: For track initialization: out of M init measurement frames determines the dimension (D) of the optimization problem. This assignment can be done in two ways. The first one, called S-D + -D assignment, is a two-step approach in which measurements from all the sensors are grouped together first and then the grouped measurements are associated to the tracks []. The second approach called (S + )-D assignment is a one-step algorithm in which measurements are directly assigned to the tracks []. In the (S + )-D formulation, if S is equal to one then it will be same as -D. In this tracker, (S + )-D assignment is used since it does not require a maximum likelihood (ML) estimate, which is used in measurement-to-measurement association in S-D. A sample assignment tree for (S+)-D is shown in Figure. Track Dummy track Sensor Sensor Sensor S Dummy measurement if at least N init measurements are associated together, then form a track and marked as tentative. otherwise, do nothing. For tentative track: out of M tent measurement frames if at least N tent measurements are associated to the track, then promote the track as confirmed. otherwise, delete the track. For confirmed track: out of last M conf measurement frames if at least N conf measurements are associated to the track, then do nothing. otherwise, delete the track. In the above, measurement frames include the time steps and the sensors. In order to get better association results, the measurements are first associated to the confirmed tracks. Then, the unassociated measurements are used to update the tentative tracks. Finally, the measurements that are not associated to the confirmed or tentative tracks are used to initialize new tracks. Multiframe association ((S+)-D, S-D or -D) is used for data associationand they are explained in detail in section. and... Multiframe assignment for existing tracks In multiframe assignment, measurements from multiple (say, S) sensors are matched to the tracks in the track list. That is, elements of (S +) lists are matched together through a optimization algorithm to solve the data association. The number of lists in the assignment 89 Figure. Assignment tree for (S + )-D. The cost of assigning measurements i, i,..., i S to track t is given by ( ) p(zii c tii...,i S = log...,i S X t ) () p(z ii...,i S ) where p(z ii...,i S X t ) = p(z ii...,i S ) = S ( P D ) u(is) s= S s= (P D p(z is X t )) u(is) () ψ s () where u(i s ) takes value if i s = and otherwise, P D is the probability of detection and ψ s is the volume of the measurement space of sensor s. The (S +)-D assignment formulation finds the most likely hypothesis by solving the following constrained optimization: min χ ti i...i S subject to T T N N t= i = i = N i = N t= i = N S i S= N S i S= N S i S= c tii...i S χ tii...i S () χ tii...i S =, t =,...,T () χ tjii...i S =, j =,...,N (5)

4 T N t= i = N S i S =. χ tii...i S j =, j =,...,N S (6) where χ tii...i S is a binary variable such that { Zii χ tii...i S =...,i S is from target t otherwise (7) In the above, i s = indicates the dummy measurement, t = indicates the dummy track, T is the total number of tracks and N s is the number of measurements from sensor s. Lagrangian relaxation, as described in [], followed by the auction algorithm [] is used to solve the assignment problem in quasi-polynomial time. Computational load of the (S + )-D assignment can be reduced by approximately decomposing the (S +)- D assignment into S individual -D assignments. That is, each sensor s measurements are associated to the tracks separately. Even though this is an approximation, tracker performance will not be affected significantly in most cases, especially when target maneuvers are not high.. Initializing New Tracks New tracks are formed using the measurements that are not associated to already existing tracks from all the transmitter-receiver pairs. If the probabilities of detections of the targets are high for all the transmitterreceiverpairs, then the measurements atone time step from all the transmitter-receiver pairs can be used to initialize new tracks using the logic of at least n measurements from m transmitter-receiverpairs. However, this approach will fail in low probability of detection cases. Hence, measurements over multiple time steps must be considered in track initialization, as shown in Figure. TR Dummy TR TR Time step k TR TR TR Time step k + Figure. Assignment tree with multiple transmitterreceiver pairs and time steps. Even though the above approach is optimal, it will be computationallydemanding evenwith few transmitterreceiver pairs. A suboptimal approach, in which first new tracks are formed for eachtransmitter-receiverpair separately by considering multiple time steps and then the new tracks from all the transmitter-receiver pairs 8 are fused together, can be used to reduce the computational load so that track initialization can be done in real-time. That is, in this tracker, distributed tracking is used for track initialization and centralized tracking is used to update the already initialized tracks. The distributed tracking for initialization might result in slight performance degradation compared to the centralized tracking. However, the advantage of diversity of sensor field is not totally lost. It is reasonable to assume that target-sensor geometry will not change significantly in two or three measurement time steps. Hence, even if only one sensor has better detections of a target due to target-sensor geometry, a track will be initialized at least by that sensor. After initializing, the measurements from all the sensors will be used in the following time steps to confirm the track. Track-to-track association, which is needed to fuse the initial tracks from all the sensors, is also performed using the multiframe assignment under the assumption that the track errors are independent, which is a reasonable assumption for new tracks. The associated measurements for the fused tracks must be counted correctly to confirm or delete the tentative tracks as soon as possible. For example, if four transmitter-receiver pairs are available and only three tracks, which are created using two consecutive measurements, are fused together, then the update history for the fused track is associations out of measurements frames. When the bistatic range and bearing are available, target s initial state is obtained by converting the measurement to Cartesian coordinates by removing any possible bias [] as follows: where β(k) r(k) = = atan ( xt (k) x r (k) y t (k) y r (k) (r b (k) L(k) ) (r b (k) L(k)cos(β(k))) ) θ(k) (8) (9) x(k) = x r (k) + e σ θ / r(k)sin(θ(k)) () y(k) = y r (k) + e σ θ / r(k)cos(θ(k)) () L = (x t (k) x r (k)) + (y t (k) y r (k)) ().5 Performance evaluation The tracker performance is evaluated using the metrics track probability of detection (T-PD), track falsealarm rate (T-FAR), track-localization error (T-LE), track fragmentation rate (T-FR), latency (L) and execution rate (ER) that are defined by MSTWG []. The new definition of track fragmentation rate from [7] is used instead of the older one defined in []. Two values of T-PD are given for all the data sets in order to avoid any confusion in the T-PD definition. In the first one, the time steps from the first measurement association, i.e., including the time steps before confirmation,

5 are used. T-PD values calculated by considering the time steps only after confirmation are given inside the bracket with. The execution rates correspond to the MATLAB implementation of the tracker on a. GHz Core Duo processor with GB of RAM. Results In this section, the tracking results for NATO Undersea Research Centre (NURC), the Netherlands Organization for Applied Scientific Research (TNO) and TNOblind data sets using the proposed tracker are presented. In addition to the above three data sets, one more data set from Applied Research Laboratory, University of Texas (ARL-UT) is available for processing. However, the plots of the measurements of this data set look different from those of others and this could be due to a problem in measurement extraction form the given data format. Hence, the results of ARL-UT data set are not given here.. NURC Data Inthe NURC data, ascenariowithfourtransmitterreceiver pairs and one target is considered [6]. The scenario is shown in Figure, where indicates the starting point of the target and indicates the staring point of the ship. There are three ships, and ship has a transmitter and receiver, ship has a receiver and ship has a transmitter. There is only one target and it is moving in a straight line. Scenario duration is 8 minutes with sampling interval of minute. Y (m) x R/T R T Target 6 x Figure. NURC scenario In the tracker, the EKF is used for filtering with out of logic to initialize new tracks, out of logic for tentative track maintenance and out of logic to delete the confirmed tracks. Since there are four transmitter-receiver pairs, three time steps will be required for track confirmation or deletion. For.5 db threshold, out of 8 logic is used for tentative track 8 maintenance since the probability of detection is low with high threshold. A maximum speed of5 m/s, which is used for track velocity covariance initialization and limit the target speed, and process noise standard deviation of.5 m/s are assumed. The tracking results for full data ingestion and.5 db threshold are shown in Tables and, respectively. In both cases, no false tracks are reported and target is detected from the first time step and confirmed after three time steps with full data ingestion, while it is confirmed only after time steps with.5 db threshold. However, track is never lost/dropped after confirmation. As a result, T-FR is equal to and track PD is one for full data set and.89 for.5 db threshold. Table. Results of NURC data with full data ingestion Metric Tracker Evaluation T-PD (.99 ) T-FAR (hour ) T-LE (m) 7. T-FR L (min) ER.. TNO Data Three targets with four transmitter-receiverpairs are considered in TNO data set [5]. Only one target is moving with a zig-zagtrajectory, and other two targets are stationary. Two ships are moving from west to east in straight lines, and each has a transmitter and a receiver. The scenario duration is 8 minutes with a sampling time of minute. The scenario is shown in Figure 5, where indicates the moving target s starting point, indicates the stationary target and indicates the staring point of the ship. Each measurement has a ghost with mirrored bearing, which could introduce mirror tracks. Removing the mirror tracks is an important task for this data set. Tracker parameter settings are: tentative track formation logic is out of, tentative track maintenance Table. Results of NURC data with.5 db threshold Metric Tracker Evaluation T-PD.89 (.88 ) T-FAR (hour ) T-LE (m).5 T-FR L (min) ER.

6 x Table. Results of TNO data with db threshold Y (m) R/T R/T Target Target Target x Figure 5. TNO scenario logic is 6 out of 8 and confirmed track deletion logic is out of 5. That is, two time steps will be required for track confirmation. A maximum speed of m/s and process noise standard deviation of.5 m/s are assumed. The tracking results with db threshold are shown in Table. The track PD is only.5. This is mainly due to missing the stationary targets and can be understood from the T-PD, which is.989, calculated by considering only the moving target. It is observed that out of four transmitter-receiver pairs only two of them give the correct measurements for stationary targets and other two measurement sets have some offset from the possible actual measurements. This can be observed in Figure 6, which shows the measurements above db and confirmed tracks that are obtained using measurements above db. Since moving target measurements from all transmitter-receiver pairs matched well with the target location, it is very unlikely to encounter problems in measurement conversion. Hence, it is concluded that there is a problem with stationary target measurements for two of the transmitter-receiverpairs. However, tracking those stationary targets using only the measurements from two pairs of sensors is possible by relaxing the confirmation logic to out of 8 instead of 6 out of 8. However, it will introduce false tracks including the mirror tracks. Note that no false tracks including the mirror tracks are formed with 6 out of 8 confirmation logic. Since the receiver locations are different, the mirror measurements from all the transmitter-receiver pairs will not fall in same place in the state space. As a result, the 6 out of 8 logic will not be satisfied for mirror tracks and they are not confirmed. This is the advantage of the centralized tracking over distributed tracking for this scenario. However, it is possible to remove the mirror tracks even in distributed tracking by using a similar logic in track fusion stage. 8 Metric Tracker Evaluation all targets only moving target T-PD.5 (.8 ).989 (.97 ) T-FAR (hour ) T-LE (m) 97 9 T-FR L (min) 7 ER.9.9 Y (m) x Receiver Transmitter Measurement Confirmed track Truth x Figure 6. Tracks of TNO data with measurements above db. Unlike in the NURC data set, track breakages are observed here when the target changes the direction suddenly. Even though IMM estimator can handle target maneuvers, modeling the sharp turns is very hard. It is possible to reduce the track breakage by increasing the process noise, however it will result in large T-LE and false tracks.. TNOblind Data In the TNOblind data set, there are three transmitter-receiver pairs and four targets. The scenario is shown in Figure 7, where * indicate the target s starting position, indicate the receiver s starting position and indicates the transmitter s starting position. The receiver receives the measurement from transmitter only, similarly receiver and receive the measurement only from transmitter and, respectively. Measurements with db threshold are considered with out of logic for initialization, 8 out of logic for tentative track maintenance and out of 8 logic for confirmed track maintenance. In order to handle the target maneuvers, an IMM estimator with two constant

7 Y (m) x T R T/R T R Target 5 x Figure 7. TNOblind scenario Y (m) 5 x Confirmed track Truth 6 8 x 8 Figure 8. Tracks of TNOblind data with db threshold and given measurement variances. velocity models with process noise standard deviations.5 m/s and.5 m/s is used with maximum speed of m/s. The tracks obtained by the tracker with the given measurementvariances are shownin Figure 8. Different transmitter-receiver pairs have different measurement accuracies depending on which signal (FM or CW) is used. The standard deviations of the bistatic range measurements are in the range of to m for FM and 7 to m for CW. The tracker performance metrics are shown in Table. Altogether nine tracks are formed, however few of them are the broken tracks of same target. By observing the target originated measurements and the target trajectory, anomalies are suspected in the measurements or in the measurement variances. Then, the tracker performance with bistatic range variance of m for both FM and CW was analyzed. The results with the above increased variance are shown in Figure 9 and Table. Instead of nine tracks that are formed with given variances, only five tracks are formed now. New results seem better in all aspects compared to the results with the given variances. The targets are detected well in advance and track breakages are also reduced. Only one track breakage is observed for the second target, which is at south-east corner. This could not be avoided since there are no measurements for few time steps. Targets one and four are detected from the beginning, while targets two and four are detected only after few minutes. Hence, T-PD is one for targets one and two and the overall T-PD is.9. No false tracks are reported. 5 Conclusions A multisensor-multitarget tracking tracker developed by McMaster University was applied to MSTWG data sets to analyze and show the effectiveness of the tracker 8 Table. Results of TNOblind data with db threshold. Metric Tracker Evaluation Given variance σ rb = m T-PD.66 (.6 ).9 (.89 ) T-FAR (hour ) T-LE (m) T-FR.5.5 L (min) 99 6 ER.. for multistatic synchronous/asynchronous sensor networks. Except for the ARL-UT data set, all other data sets are processed and complete tracking results are obtained. Results on the NURC data set need no further improvement. A few problems were observed with TNO and TNOblind data sets on the measurement and tracker sides. For TNO data, the tracker must be modified to handle the sharp turns and the problem with stationary targets measurements from two of the transmitter-receiver pairs, which lead to track miss, must be resolved. For TNOblind data, better results are obtained with larger measurement variance for bistatic range than the given ones. References [] Y. Bar-Shalom and X. R. Li, Multitarget- Multisensor Tracking: Principles and Techniques, YBS Publishing, Connecticut, 995. [] Y. Bar-Shalom, X. Li and T. Kirubarajan, Estimation with Applications to Tracking and Navigation, Wiley, New York,.

8 Y (m) 5 x 8 Confirmed track Truth 6 8 x Figure 9. Tracks of TNOblind data with db threshold and bistatic range variance m. [] D. P. Bertsekas, The Auction Algorithm: A Distributed Relaxation Method for the Assignment Problem, Annals of Operations Research, Vol., pp. 5, June 988. [] S. Coraluppi, D. Grimmett and P. de Theije, Benchmark Evaluation of Multistatic Trackers, Proceedings of the 9th International Conference on Information Fusion, Florence, Italy, July 6. 5 [] K. R. Pattipati, T. Kirubarajan and R. L. Popp, Survey of Assignment Techniques for Multitarget Tracking, Proceedingsof theworkshop on Estimation, Tracking, and Fusion: A Tribute to Yaakov Bar-Shalom, Monterey, CA, May. [] P. W. Richards, Constrained Kalman Filtering Using Pseudo-Measurements, Proceedings of the IEE Colloquium on Algorithms for Target Tracking London, UK, May 995. [] T. Sathyan, A. Sinha and T. Kirubarajan, Computationally Efficient Assignment-Based Algorithms for Data Association for Tracking with Angle-Only Sensors, Proceedings ofthespie Conference on Signal and Data Processing of Small Targets, San Diego, CA, August 7. [] A. Sinha, Z. J. Ding, T. Kirubarajan and M. Farooq, Track Quality Based Multitarget Tracking Algorithm, Proceedings of the SPIE Conference on Signal and Data Processing of Small Targets, Orlando, FL, April 6. [] S-W. Yeom, T. Kirubarajan and Y. Bar-Shalom, Track Segment Association, Fine-Step IMM and Initialization with Doppler for Improved Track Performance, IEEE Transactions on Aerospace and Electronic Systems, Vol., No., pp. 9 9, January. [5] P. de Theije and H. Groen, Multistatic Sonar Simulations with SIMONA, Proceedings of the 9th International Conference on Information Fusion, Florence, Italy, July 6. [6] D. Grimmett and S. Coraluppi, Contact-Level Multistatic Sonar Data Simulator for Tracker Performance Assessment, Proceedings of the 9th International Conference on Information Fusion, Florence, Italy, July 6. [7] D. Grimmett, S. Coraluppi, B. R. La Cour, C. G. Hempel, T. Lang and P. A. M. de Theije, MSTWG Multistatic Tracker Evaluation Using Simulated Scenario Data Sets, Proceedings of the th International Conference on Information Fusion, Cologne, Germany, July 8. [8] S. J. Julier and J. K. Uhlmann, A New Extension of the Kalman Filter to Nonlinear Systems, Proceedings of the SPIE Conference on Signal Processing, Sensor Fusion and Target Recognition VI, Orlando, FL, April 997. [9] B. La Cour, C. Collins and J. Landry, Multieverything Sonar Simulator (MESS), Proceedings of the 9th International Conference on Information Fusion, Florence, Italy, July 6. 8