QADA-PDA versus JPDA for Multi-Target Tracking in Clutter

Transcription

1 QADA-PDA versus JPDA for Multi-Target Tracking in Clutter Jean Dezert 1, Albena Tchamova 2, Pavlina Konstantinova 3 1 ONERA - The French Aerospace Lab, F Palaiseau, France. jean.dezert@onera.fr 2 Inst. for Information and Communication Technologies, Bulgarian Academy of Sciences, "Acad.G.Bonchev" Str., bl.25a, 1113 Sofia, Bulgaria. tchamova@bas.bg 3 European Polytechnical University Pernik, Bulgaria. pavlina.konstantinova@gmail.com July 10th, 2017 J. Dezert, A. Tchamova, P. Konstantinova YBS Tribute Workshop, Xi an, China July 10th, / 27

2 Outline 1 Introduction 2 Joint Probabilistic Data Association Filter 3 Data Association in Multi Target Tracking 4 Presentation of QADA method Choice of DA matrix for QADA Derivation of DA quality in QADA method QADA-PDA Kalman Filter for MTT 5 Measures of performances 6 Scenario 1 - Targets merging in a close formation 7 Scenario 2 - Targets merging in a close formation and then splitting 8 Scenario 3 - Two crossing targets 9 Conclusions 10 References J. Dezert, A. Tchamova, P. Konstantinova YBS Tribute Workshop, Xi an, China July 10th, / 27

3 Introduction (1) QADA = Quality Assessment of Data Association This presentation is an extension/improvement of the Fusion 2017 paper [1] J. Dezert, A. Tchamova, P. Konstantinova, E. Blasch, A Comparative Analysis of QADA-KF with JPDAF for Multi-Target Tracking in Clutter, in Proc. of Fusion 2017 int. Conference This QADA-PDA method for MTT has been published very recently (June 2017) in [2] J. Dezert, A. Tchamova, P. Konstantinova, Performance Evaluation of improved QADA-KF and JPDAF for Multitarget Tracking in Clutter, Proc of the annual international scientific conf. "Education, Science, Innovations", European Polytechnical Univ., Pernik, Bulgaria, June 9-10, J. Dezert, A. Tchamova, P. Konstantinova YBS Tribute Workshop, Xi an, China July 10th, / 27

4 Introduction (2) Multi-Target Tracking (MTT) ñ Data Association + Tracking Filter 1 Data Association (DA) - important task of MTT [Bar-Shalom 1990] DA purpose is to find the assignment matrix with most likely observation-to-track associations to keep and improve target tracks maintenance performance Classical DA approach: -Use all observations-to-tracks pairings selected in the 1st optimal global DA solution to update tracks,... even if some pairings solutions are doubtful (have poor quality) Sophisticate approaches: - Use all possible joint DA solutions and their a posteriori probas ñ Joint Probabilistic Data Association Filter (JPDAF) [Bar-Shalom Fortmann Scheffe 1980] - Use the 1st best global DA solution, evaluate its quality and modify the tracking filter accordingly ñ Quality Assessment of Data Association (QADA) approach introduced in [Dezert Benameur 2014] 2 Tracking filters The CMKF (Converted Measurement Kalman Filter) [Lerro Bar-Shalom 1993] and JPDAF are used in this work 3 In this presentation We compare performances of QADA-PDA KF based MTT (QADA using PDA matrix and min dist. decision strategy) JPDAF based MTT. J. Dezert, A. Tchamova, P. Konstantinova YBS Tribute Workshop, Xi an, China July 10th, / 27

5 Joint Probabilistic Data Association Filter Ñ proposed in [Bar-Shalom Fortmann Scheffe 1980] as an extension of PDAF for MTT Main idea: The meas.-to-target association probas β t i pkq ř Θpkq PtΘpkq Zk u ˆω it pθpkqq and β t 0pkq 1 řm k i 1 βt ipkq are computed jointly across the targets from the joint posteriori probas PpΘpkq Z k q and only for the latest set of measurements. The target track updates are done for t 1,..., N T by mÿ k ˆx t pk kq ˆx t pk k 1q ` K t pkq β t ipkq z t ipkq i 1 P t pk kq β t 0pkqP t pk k 1q ` `1 β t 0pkq P t cpkq ` P t pkq Assumptions of JPDAF the number N T of targets is known and tracks have been initialized; ppx t pkq Z k q Npx t pkq; ˆx t pk kq, P t pk kqq, for t 1,..., N T each target generates at most one meas. at each scan and there are no merged meas.; each target is detected with some known detection probability Pd t ď 1; false alarms (FA) are uniformly distributed with known FA density λ FA (Poisson pmf). Advantages very good theoretical framework, and 0-scan-back filter (memoryless filter) work well with moderate FA densities and non persisting interferences Drawbacks often intractable for complex dense MTT scenarios track coalescence effects in difficult scenarios J. Dezert, A. Tchamova, P. Konstantinova YBS Tribute Workshop, Xi an, China July 10th, / 27

6 Data Association (DA) Problem Data Association in Multi Target Tracking Find the global optimal assignments of measurements z j, j 1,..., N available at time k to targets T i, i 1,..., N T by maximizing the overall gain (rewards): RpΩ, Aq fi Nÿ T i 1 j 1 Nÿ ωpi, jqapi, jq. Ω rωpi, jqs is the DA matrix representing the gain of the associations of target T i with the measurement z j (usually homogeneous to the likelihood). Assignment solution: N T ˆ N binary matrix A rapi, jqs with api, jq P t0, 1u # 1, if z j is associated to track T i api, jq 0, otherwise. How to get the optimal solution(s) by Kuhn-Munkres/Hungarian algorithm (1955/1957) by Bourgeois and Lassalle (1971) for rectangular DA matrix. by Murty s method (1968) which gives the m-best assignments in order of increasing cost ñ used in QADA method J. Dezert, A. Tchamova, P. Konstantinova YBS Tribute Workshop, Xi an, China July 10th, / 27

7 The QADA method Main Idea behind QADA method [Dezert Benameur 2014] compare pz j, T i q in the 1st-best DA solution with pz j, T i q in the 2nd-best DA solution establish a quality indicator, associated with pairing in 1st-best DA solution, based on belief functions, PCR6 fusion rule [DSmT Books], and some decision strategy. QADA assumes the DA (reward) matrix is known, regardless of the manner in which it is obtained. ñ Several QADA-based MTT are possible depending of the choice of DA matrix construction The QADA method 1 based on a (modified) Basic Belief Assignment (BBA) modeling 2 the computation of quality of DA (i.e. confidence) qpi, jq P r0, 1s of pairings pt i, z j q, i 1,.., N T ; j 1,.., N chosen in the 1st-best DA solution is based on its stability in the 2nd best DA solution and a belief Interval distance decision strategy 1 1 In our Fusion 2017 paper, it is based on Pignistic Probability transformation decision strategy, which is a lossy transformation. J. Dezert, A. Tchamova, P. Konstantinova YBS Tribute Workshop, Xi an, China July 10th, / 27

8 Choice of DA matrix for QADA Two choices of DA matrix Ω for QADA-KF have been tested 1 QADA-GNN ñ DA matrix Ω is based on distances (as used in Global Nearest Neighbours (GNN) approach) Elements ω ij are the normalized distances dpi, jq s.t. d 2 pi, jq ď γ given by ωpi, jq dpi, jq fi rpz j pkq ẑ i pk k 1qq 1 S 1 pkqpz j pkq ẑ i pk k 1qqs 1{2 2 QADA-PDA ñ DA matrix Ω is based on Posterior Data Association (PDA) probas as given in PDAF Elements ω ij of Ω are the posterior DA probas p ij given by PDAF $ b for j 0 (no valid observ.) & b`řn l 1 α il p ij α % ij for 1 ď j ď N b`řn l 1 α il where b fi p1 P g P d qλ FA p2πq M{2a S ij and α ij fi P d e d2 ij 2 The pn ` 1qth column of Ω will include the values p i0 associated with H 0 pkq DA hypothesis (i.e. no one of the validated measurements originated from the target T i at time k). J. Dezert, A. Tchamova, P. Konstantinova YBS Tribute Workshop, Xi an, China July 10th, / 27

9 Derivation of DA quality in QADA method 1 Build DA matrix Ω and find 1st-best and 2nd-best global DA solutions A 1 and A 2 using Murty s algo. 2 Compare a 1 pi, jq in A 1 (1st best solution) with a 2 pi, jq value in A 2 (2nd best sol.). 3 Establish a quality indicator qpi, jq P r0, 1s for each optimal pairing pt i, z j q. Several cases are possible Case 1: a 1 pi, jq a 2 pi, jq 0 ñ Agreement on non-association of T i with z j A useless stable case. We set qpi, jq 0. Case 2: a 1 pi, jq a 2 pi, jq 1 ñ Agreement on association pt i, z j q Stable case with different impacts on R 1 pω, A 1 q and R 2 pω, A 2 q. BBAs construction on frame Θ tx pt i, z j q, Xu done as follows for s 1, 2 m s pxq a s pi, jq ωpi, jq{r s pω, A s q and m s px Y Xq 1 m s pxq Conjunctive rule of combination (here no conflict occurs) # m 12 pxq m 1 pxqm 2 pxq ` m 1 pxqm 2 px Y Xq ` m 1 px Y Xqm 2 pxq m 12 px Y Xq m 1 px Y Xqm 2 px Y Xq In [1], QADA quality/confidence indicator is based on lossy pignistic proba transf. qpi, jq fi BetPpXq m 12 pxq ` 1 2 m 12pX Y Xq In [2] and here, QADA quality/confidence indicator is based on min distance strategy J. Dezert, A. Tchamova, P. Konstantinova YBS Tribute Workshop, Xi an, China July 10th, / 27

10 Principle of QADA method (cont d) Case 3: a 1 pi, jq 1 and a 2 pi, jq 0 ñ conflict in solutions between A 1 and A 2 find index j 2, such that a 2 pi, j 2 q 1 BBAs construction on frame Θ tx fi pt i, z j q, Y fi pt i, z j2 qu Basic Belief Assignment (BBA) modeling # m 1 pxq a 1 pi, jq m 1 px Y Yq 1 m 1 pxq ωpi,jq R 1 pω,a 1 q`r 2 pω,a 2 q # m 2 pyq a 2 pi, j 2 q m 2 px Y Yq 1 m 2 pyq BBAs fusion with PCR6 fusion rule $ & mpxq m 1 pxqm 2 px Y Yq ` m 1 pxq mpyq m 1 px Y Yqm 2 pyq ` m 2 pyq % mpx Y Yq m 1 px Y Yqm 2 px Y Yq ωpi,j 2 q R 1 pω,a 1 q`r 2 pω,a 2 q m 1 pxqm 2 pyq m 1 pxq`m 2 pyq m 1 pxqm 2 pyq m 1 pxq`m 2 pyq In [1], QADA quality/confidence indicator is based on lossy pignistic proba transf. qpi, jq fi BetPpXq m 12 pxq ` 1 2 m 12pX Y Yq In [2] and here, QADA quality/confidence indicator is based on min distance strategy J. Dezert, A. Tchamova, P. Konstantinova YBS Tribute Workshop, Xi an, China July 10th, / 27

11 Decision-Making from a BBA with min distance strategy Belief interval of A BIpAq fi rbelpaq, PlpAqs r ÿ BP2 Θ BĎA mpbq, ÿ BP2 Θ BXA H Euclidean belief interval based distance [Han Dezert Yang 2014] d 1 d E BIpm 1, m 2 q fi 2 ÿ d I pbi Θ 1 1 paq, BI 2 paqq 2 AP2 Θ d I pra 1, b 1 s, ra 2, b 2 sq Decision-making from a BBA d a1 ` b 1 2 a2 ` b 2 2 δ ˆX arg min XPΘ dpm, m Xq Quality of the decision qp ˆXq 1 Higher is qp ˆXq more trustable is the decision δ ˆX mpbqs j 2 ` 1 j 2 b1 a 1 b2 a d BI pm, m ˆX q řxpθ d P r0, 1s BIpm, m X q J. Dezert, A. Tchamova, P. Konstantinova YBS Tribute Workshop, Xi an, China July 10th, / 27

12 QADA-PDA Kalman Filter for MTT Classical Kalman Filter (KF) state estimate with Kalman filter gain matrix ˆxpk kq ˆxpk k 1q ` Kpkqpzpkq ẑpk k 1q Kpkq Ppk k 1qH T pkqrhpkqppk k 1qH T pkq ` Rs 1 In KF, zpkq is assumed to be correct with the measurement noise characterized by the given covariance matrix R If R decreases ñ zpkq is more precise ñ Gain Kpkq increases If R increases ñ zpkq is less precise ñ Gain Kpkq decreases Improved KF with QADA quality factor The quality factor qpi, jq qpt i, z j q expresses the confidence in the association pt i, z j q If qpt i, z j q Ñ 0 ñ we don t trust pt i, z j q ñ z j is incorrect and so we increase R If qpt i, z j q Ñ 1 ñ we trust pt i, z j q ñ z j is correct and we keep R as it is KF gain adjustment with QADA R QADA 1 qpt i, z j q R ñ Kpkq Ppk k 1qHT pkqrhpkqppk k 1qH T pkq ` R QADA s 1 J. Dezert, A. Tchamova, P. Konstantinova YBS Tribute Workshop, Xi an, China July 10th, / 27

13 Measures of performances We compare the performances several MTT algorithms (using Monte Carlo simul.) KDA-GNN KF based MTT (GNN matrix based on Kinematic meas.) QADA-GNN KF based MTT (QADA using GNN matrix) QADA-PDA KF based MTT (QADA using PDA matrix) JPDAF Criteria for MTT performance evaluation 1 TL = Track Life Ñ average number of track updates before track deletion A track is removed after 3 successive incorrect associations, or missed detections With JPDAF, a track is removed if the true measurement is out of the gate during 3 successive scans 2 pmc = Percentage of miscorrelation Ñ Percentage of incorrect measurement-to-track association during the scans Ñ for JPDAF, pmc = % of time the true measurement is outside its target gate pmc for JPDAF is not equivalent to pmc for other algos It does reflect only partially the performances of JPDAF 3 Number of correct associations TP = Track purity TP Total number of associations 4 PPI = Probabilistic Purity Index Ñ used only with JPDAF PPI % of correctness of measurement having the highest proba J. Dezert, A. Tchamova, P. Konstantinova YBS Tribute Workshop, Xi an, China July 10th, / 27

14 Scenario 1 - Targets merging in a close formation Targets T 1, T 2, T 3, T 4 move from West to East with constant velocity 100m{sec during 30 scans. The stationary sensor is located at the origin with range 10000m. The sampling period is T scan 5sec Measurement precision: Azimuth Ñ σ Az 0.2 deg and range Ñ σ D 40 m. From scans 15 to 30, targets move in parallel with inter distance of 150 m FA are uniformly distributed in the surveillance region with know density P d is associated with the sensor. J. Dezert, A. Tchamova, P. Konstantinova YBS Tribute Workshop, Xi an, China July 10th, / 27

15 Simulation results for scenario 1 Monte Carlo results based on 200 runs (in %) QADA-PDA QADA-GNN JPDAF KDA-GNN Average TL (88.12) (84.31) Average pmc 2.45 (2.67) 2.39 (3.28) Average TP (84.54) (79.86) PPI= Performance results for 0.15 FA per gate on average Note: JPDAF requires almost 3 times more computational time than other methods because an exponential growing of number of joint association hypotheses. J. Dezert, A. Tchamova, P. Konstantinova YBS Tribute Workshop, Xi an, China July 10th, / 27

16 Results with 0.15 FA per gate on average Simulation results for scenario 1 Averaged RMSE on X for track 1 with the tracking methods. Averaged RMSE on Y for track 1 with the tracking methods. J. Dezert, A. Tchamova, P. Konstantinova YBS Tribute Workshop, Xi an, China July 10th, / 27

17 Simulation results for scenario 1 (cont d) Results with 0.15 FA per gate on average Averaged RMSE on X for track 3 with the tracking methods. Averaged RMSE on Y for track 3 with the tracking methods. J. Dezert, A. Tchamova, P. Konstantinova YBS Tribute Workshop, Xi an, China July 10th, / 27

18 Scenario 2 - Targets merging in a close formation and then splitting Simulation of groups of target for scenario 2 Five air targets (T 1, T 2, T 3, T 4, T 5 ) moving from Norht-West to South-East with constant velocity 100m{sec during 65 scans. The stationary sensor is located at the origin with range 20000m. The sampling period is T scan 5sec Measurement precision: Azimuth Ñ σ Az 0.35 deg and range Ñ σ D 25 m. Targets move in three groups: Group1 T 1, Group2 pt 2, T 3, T 4 ), Group3 T 5 The number of false alarms (FA) follows a Poisson distribution. FA are uniformly distributed in the surveillance region. P d is associated with the sensor. J. Dezert, A. Tchamova, P. Konstantinova YBS Tribute Workshop, Xi an, China July 10th, / 27

19 Simulation results for scenario 2 Monte Carlo results based on 300 runs Performances of QADA KF methods with 0.2 FA per gate J. Dezert, A. Tchamova, P. Konstantinova YBS Tribute Workshop, Xi an, China July 10th, / 27

20 Simulation results for scenario 2 (cont d) Results with 0.2 FA per gate on average Group of Targets Scenario rmse X filtered for track sensor error along X 160 rmse X filtered KDA rmse X filtered QADA GNN 140 rmse X filtered QADA PDA 120 rmse X filtered JPDAF [m] FA in gate= scans Averaged RMSE on X for track 1 with the four tracking methods. Group of Targets Scenario rmse Y filtered for track sensor error along Y 120 rmse Y filtered KDA rmse Y filtered QADA GNN 100 rmse Y filtered QADA PDA rmse Y filtered JPDAF 80 FA in gate=0.2 [m] scans Averaged RMSE on Y for track 1 with the four tracking methods. J. Dezert, A. Tchamova, P. Konstantinova YBS Tribute Workshop, Xi an, China July 10th, / 27

21 Simulation results for scenario 2 (cont d) Results with 0.2 FA per gate on average [m] Group of Targets Scenario rmse X filtered for track sensor error along X rmse X filtered KDA rmse X filtered QADA GNN rmse X filtered QADA PDA rmse X filtered JPDAF FA in gate= scans Averaged RMSE on X for track 3 with the four tracking methods. Groups of Targets Scenario rmse Y filtered for track FA in gate= [m] sensor error along Y rmse Y filtered KDA rmse Y filtered QADA GNN rmse Y filtered QADA PDA rmse Y filtered JPDAF scans Averaged RMSE on Y for track 3 with the four tracking methods. J. Dezert, A. Tchamova, P. Konstantinova YBS Tribute Workshop, Xi an, China July 10th, / 27

22 Scenario 3 : Two crossing targets Scenario 3 - Two crossing targets Y[m] X[m] Two maneuvering targets moving from West to East with constant velocity 38m{sec during 65 scans. The stationary sensor is located at the origin with range 1200m. The sampling period is T scan 1sec. σ Az 0.25 deg and σ D 25 m for azimuth and range respectively. P d is associated with the sensor. J. Dezert, A. Tchamova, P. Konstantinova YBS Tribute Workshop, Xi an, China July 10th, / 27

23 Monte Carlo results based on 300 runs Simulation results for scenario 3 Performances of QADA-PDA versus JPDA for 0.2 FA per gate Performances of QADA-PDA versus JPDA for 0.4 FA per gate J. Dezert, A. Tchamova, P. Konstantinova YBS Tribute Workshop, Xi an, China July 10th, / 27

24 Simulation results for scenario 3 (cont d) Results with 0.2 FA per gate on average Crossing Targets Scenario rmse X filtered for track [m] 10 5 FA in gate= scans sensor error along X rmse X filtered KDA rmse X filtered QADA GNN rmse X filtered QADA PDA rmse X filtered JPDAF Averaged RMSE on X for track 1 with the four tracking methods. Crossing Targets Scenario rmse Y filtered for track 1 18 sensor error along X 16 FA in gate=0.2 rmse X filtered KDA rmse X filtered QADA GNN 14 rmse X filtered QADA PDA 12 rmse X filtered JPDAF 10 [m] scans Averaged RMSE on Y for track 1 with the four tracking methods. J. Dezert, A. Tchamova, P. Konstantinova YBS Tribute Workshop, Xi an, China July 10th, / 27

25 Simulation results for scenario 3 (cont d) Results with 0.2 FA per gate on average Crossing Targets Scenario rmse X filtered for track [m] FA in gate= scans sensor error along X rmse X filtered KDA rmse X filtered QADA GNN rmse X filtered QADA PDA rmse X filtered JPDAF Averaged RMSE on X for track 2 with the four tracking methods. Crossing Targets Scenario rmse Y filtered for track 1 18 sensor error along X 16 FA in gate=0.2 rmse X filtered KDA rmse X filtered QADA GNN 14 rmse X filtered QADA PDA 12 rmse X filtered JPDAF 10 [m] scans Averaged RMSE on Y for track 2 with the four tracking methods. J. Dezert, A. Tchamova, P. Konstantinova YBS Tribute Workshop, Xi an, China July 10th, / 27

26 Conclusions 1 QADA-PDA is a zero-scan back method 2 QADA-PDA is quite simple to implement (mix of PDAF calculus and Optimal assignment search) 3 QADA-PDA is a good compromise between strict hard-assignment (GNN) and full soft-assignment (JPDA) 4 QADA-PDA avoids JPDA combinatorics/complexity 5 QADA-PDA works better than QADA-GNN, KDA-GNN and JPDA in difficult scenarios 6 QADA-PDA is a new and interesting practical method for MTT in clutter Perspectives 1 making more precise evaluations of QADA-PDA method 2 development and test of better quality evaluation models (if any) 3 improvement of MTT performances using attribute information J. Dezert, A. Tchamova, P. Konstantinova YBS Tribute Workshop, Xi an, China July 10th, / 27

27 References Y. Bar-Shalom (Ed.), Multitarget-Multisensor Tracking: Advanced Applications, Artech House, J. Dezert, K. Benameur, On the Quality of Optimal Assignment for Data Association, Proc. of Belief 2014, Oxford, UK, Sept J. Dezert et al., On the Quality Estimation of Optimal Multiple Criteria Data Association Solutions, Proc. of Fusion, J. Dezert, et al., Multitarget Tracking Performance based on the Quality Assessment of Data Association, Proc. of Fusion 2016, July Y. Bar-Shalom, T.E. Fortmann, M. Scheffe, JPDA for Multiple Targets in Clutter, Proc. Conf. on Inf. Sci. and Syst., Princeton, March D. Lerro, Y. Bar-Shalom, Tracking with debiased consistent Converted Measurement versus EKF, IEEE Trans on AES, R.J. Fitzgerald, Track Biases and Coalescence with Probabilistic Data Association, IEEE Trans. on AES, Vol. 21, F. Smarandache, J. Dezert (Editors), Advances and Applications of DSmT for Information Fusion, Volumes 1, 2, 3 & 4, ARP, J. Dezert et al., The Impact of the Quality Assessment of Optimal Assignment for Data Association in Multitarget Tracking Context, Cybernetics and Inf. Techn. J., Vol.15, No.7, pp , J. Dezert et al., Performance Evaluation of improved QADA-KF and JPDAF for Multitarget Tracking in Clutter, Proc of the annual international scientific conference " Education, Science, Innovations", EPU, Pernik, Bulgaria, June D. Han, J. Dezert, Y. Yang, New Distance Measures of Evidence based on Belief Intervals, Proc. of Belief 2014, Oxford, D. Han, J. Dezert, Y. Yang, Belief interval Based Distances Measures in the Theory of Belief Functions, IEEE Trans. on SMC, J. Dezert, A. Tchamova, P. Konstantinova YBS Tribute Workshop, Xi an, China July 10th, / 27