Multiple-model GLMB filter based on track-before-detect for tracking multiple maneuvering targets

doi:10.23919/JSEE.2024.000040

Abstract

Abstract:

A generalized labeled multi-Bernoulli (GLMB) filter with motion mode label based on the track-before-detect (TBD) strategy for maneuvering targets in sea clutter with heavy tail, in which the transitions of the mode of target motions are modeled by using jump Markovian system (JMS), is presented in this paper. The close-form solution is derived for sequential Monte Carlo implementation of the GLMB filter based on the TBD model. In update, we derive a tractable GLMB density, which preserves the cardinality distribution and first-order moment of the labeled multi-target distribution of interest as well as minimizes the Kullback-Leibler divergence (KLD), to enable the next recursive cycle. The relevant simulation results prove that the proposed multiple-model GLMB-TBD (MM-GLMB-TBD) algorithm based on K-distributed clutter model can improve the detecting and tracking performance in both estimation error and robustness compared with state-of-the-art algorithms for sea clutter background. Additionally, the simulations show that the proposed MM-GLMB-TBD algorithm can accurately output the multitarget trajectories with considerably less computational complexity compared with the adapted dynamic programming based TBD (DP-TBD) algorithm. Meanwhile, the simulation results also indicate that the proposed MM-GLMB-TBD filter slightly outperforms the JMS particle filter based TBD (JMS-MeMBer-TBD) filter in estimation error with the basically same computational cost. Finally, the impact of the mismatches on the clutter model and clutter parameter is investigated for the performance of the MM-GLMB-TBD filter.

Key words: generalized labeled multi-Bernoulli (GLMB), track-before-detect (TBD), jump Markovian system (JMS), K-distribution, Kullback-Leibler divergence (KLD)

Chenghu CAO, Yongbo ZHAO. Multiple-model GLMB filter based on track-before-detect for tracking multiple maneuvering targets[J]. Journal of Systems Engineering and Electronics, 2024, 35(5): 1109-1121.

Figures/Tables 11

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References 49

1	LI T C Arithmetic average density fusion-Part II: unified derivation for unlabeled and labeled RFS fusion. IEEE Trans. on Aerospace and Electronic Systems, 2024, 60 (3): 3255- 3268. doi: 10.1109/TAES.2024.3359592
2	ZHU Y, WANG J, LIANG S Efficient joint probabilistic data association filter based on Kullback-Leibler divergence for multi-target tracking. IET Radar, Sonar and Navigation, 2017, 11 (10): 1540- 1548. doi: 10.1049/iet-rsn.2017.0102
3	ALLICK M, CORALUPPI S, CARTHEL C. Multitarget tracking using multiple hypothesis tracking. Hoboken: Wiley, 165−201.
4	KOCH W, KEUK G V Multiple hypothesis track maintenance with possibly unresovled measurements. IEEE Trans. on Aerospace and Electronic System, 1997, 33 (3): 883- 892. doi: 10.1109/7.599263
5	CHEUNG B, DAVEY S, GRAY D Probabilistic multi-hypothesis tracker for multiple platform path planning. IET Radar, Sonar and Navigation, 2015, 9 (3): 255- 265. doi: 10.1049/iet-rsn.2014.0089
6	VO B N, VO B T, PHAM N T, et al Joint detection and estimation of multiple objects from image observations. IEEE Trans. on Signal Processing, 2010, 58 (10): 5129- 5241. doi: 10.1109/TSP.2010.2050482
7	LI S Q, YI W, HOSEINNEZHAD R, et al Multi-objection tracking for generic observation model using labeled random finite sets. IEEE Trans. on Signal Processing, 2018, 66 (2): 368- 383. doi: 10.1109/TSP.2017.2764864
8	LI G, LI G C, HE Y Distributed GGIW-CPHD-based extended target tracking over a sensor network. IEEE Signal Processing, 2022, 29, 842- 846. doi: 10.1109/LSP.2022.3158589
9	ÁNGEL F, FERNANDEZ G, MASKELL S Continuous-discrete multiple target filtering: PMBM, PHD and CPHD filter implementations. IEEE Trans. on Signal Processing, 2020, 68, 1300- 1314. doi: 10.1109/TSP.2020.2968247
10	LI C, WANG W G, KIRUBARAJAN T, et al PHD and CPHD filtering with unknown detection probability. IEEE Trans. on Signal Processing, 2018, 66 (14): 3784- 3798. doi: 10.1109/TSP.2018.2835398
11	DA K, LI T C, ZHU Y F, et al Gaussian mixture particle jump-Markov-CPHD fusion for multitarget tracking using sensors with limited views. IEEE Trans. on Signal and Information Processing over Networks, 2020, 6, 605- 616. doi: 10.1109/TSIPN.2020.3016478
12	LI T C, JUAN M, SUN S Partial consensus and conservative fusion of gaussian mixtures for distributed PHD fusion. IEEE Trans. on Aerospace and Electronic System, 2019, 55 (5): 2150- 2163. doi: 10.1109/TAES.2018.2882960
13	JONES B A CPHD Filter birth modeling using the probabilistic admissible region. IEEE Trans. on Aerospace and Electronic System, 2018, 54 (3): 1456- 1469. doi: 10.1109/TAES.2018.2793378
14	YU B R, LI T C, GE S J, et al Robust CPHD fusion for distributed multitarget tracking using asynchronous sensors. IEEE Sensor Journal, 2021, 22 (1): 1030- 1040.
15	NANNURU S, BLOUIN S, COATES M, et al Multi-sensor CPHD filter. IEEE Trans. on Aerospace and Electronic System, 2016, 52 (4): 1834- 1854. doi: 10.1109/TAES.2016.150265
16	YI W, LI G C, BATTISTELLI G Distributed multi-sensor fusion of PHD filters with different sensor fields of view. IEEE Trans. on Signal Processing, 2020, 68, 5204- 5218. doi: 10.1109/TSP.2020.3021834
17	BRYANT D S, DELANDE E D, GEHLY S, et al The CPHD filter with target spawning. IEEE Trans. on Signal Processing, 2017, 65 (5): 1324- 1338.
18	YI W, CHAI L Heterogeneous multi-sensor fusion with random finite set multi-object densities. IEEE Trans. on Signal Processing, 2021, 69, 3399- 3414. doi: 10.1109/TSP.2021.3087033
19	BRYANT D S, VO B T, VO B N, et al A generalized labeled multi-Bernoulli filter with object spawning. IEEE Trans. on Signal Processing, 2018, 66 (23): 6177- 6189. doi: 10.1109/TSP.2018.2872856
20	PAPI F, KIM D A particle multi-target tracker for superpositional measurements using labeled random finite sets. IEEE Trans. on Signal Processing, 2015, 63 (16): 4348- 4358.
21	VO B N, VO B T, HOANG H G An efficient implementation of the generalized labeled multi-Bernoulli filter. IEEE Trans. on Signal Processing, 2017, 65 (8): 1975- 1987. doi: 10.1109/TSP.2016.2641392
22	BEARD M, VO B T, VO B N Bayesian multi-target tracking with merged measurements using labeled random finite sets. IEEE Trans. on Signal Processing, 2015, 63 (6): 1433- 1447.
23	GOSTAR A K, HOSEINNEZHAD R, RATHNAVAKE T, et al. Constrained sensor control for labeled multi-Bernoulli filter using Cauchy-Schwarz divergence. IEEE Trans. on Signal Processing, 2017, 24(9): 1313−1317.
24	PAPI F, VO B N, VO B T, et al Generalized labeled multi-Bernoulli approximation of multi-object densities. IEEE Trans. on Signal Processing, 2015, 63 (20): 5487- 5497.
25	LI S Q, BATTISTELLI G, CHISCI L, et al Computationally efficient multi-agent multi-object tracking with labeled random finite sets. IEEE Trans. on Signal Processing, 2019, 67 (1): 260- 275. doi: 10.1109/TSP.2018.2880704
26	WIEN T, MEYER F, HLAWATSCH F A fast labeled multi-Bernoulli filter using belief propagation. IEEE Trans. on Aerospace and Electronic System, 2020, 56 (3): 2478- 2488. doi: 10.1109/TAES.2019.2941104
27	VO B T, VO B N A multi-scan labeled random finite set model for multi-object state estimation. IEEE Trans. on Signal Processing, 2019, 67 (19): 4948- 4963. doi: 10.1109/TSP.2019.2928953
28	BEARD M, REUTER S, GRANSTROM K, et al Multiple extended target tracking with labeled random finite sets. IEEE Trans. on Signal Processing, 2016, 64 (7): 1638- 1653. doi: 10.1109/TSP.2015.2505683
29	LIN S F Robust pitch estimation and tracking for speakers based on sub-band encoding and the generalized labeled multi-bernoulli filter. IEEE Trans. on Audio, Speech, and Language Processing, 2019, 27 (4): 827- 841. doi: 10.1109/TASLP.2019.2898818
30	VO B N, VO B T, BEARD M Multi-sensor multi-object tracking with the generalized labeled multi-Bernoulli filter. IEEE Trans. on Signal Processing, 2019, 67 (23): 5951- 5967.
31	PASHA S A, VO B N, TUAN H D, et al A Gaussian mixture PHD filter for jump Markov system models. IEEE Trans. on Aerospace and Electronic System, 2009, 45 (3): 919- 936. doi: 10.1109/TAES.2009.5259174
32	WOOD T M Interacting methods for maneuver handling in the GM-PHD filter. IEEE Trans. on Aerospace and Electronic System, 2011, 47 (4): 3021- 3025. doi: 10.1109/TAES.2011.6034685
33	DUNNE D, KIRUBARAJAN T Multiple model multi-Bernoulli filters for maneuvering targets. IEEE Trans. on Aerospace and Electronic System, 2013, 49 (4): 2679- 2692. doi: 10.1109/TAES.2013.6621845
34	PUNITHAKUMAR K, KIRUBARAJAN T Multiple models probability hypothesis density filter for tracking maneuvering targets. IEEE Trans. on Aerospace and Electronic System, 2008, 44 (1): 87- 98. doi: 10.1109/TAES.2008.4516991
35	GEORGESCU R, WILLETT P The multiple model CPHD tracker. IEEE Trans. on Signal Processing, 2012, 60 (4): 1741- 1751. doi: 10.1109/TSP.2012.2183128
36	YI W, JIANG M, HOSEINNEZHAD R The multiple model Vo-Vo filter. IEEE Trans. on Aerospace and Electronic System, 2017, 53 (2): 1045- 1054. doi: 10.1109/TAES.2017.2667300
37	CAO C H, ZHAO Y B An efficient implementation of the multiple-model generalized labeled multi-Bernoulli filter for track-before-detect of point targets using image sensor. IEEE Trans. on Aerospace and Electronic Systems, 2021, 57 (6): 4416- 4432. doi: 10.1109/TAES.2021.3091756
38	CAO C H, ZHAO Y B A multiple-model generalized labeled multi-Bernoulli filter based on blocked Gibbs sampling for tracking maneuvering targets. Signal Processing, 2021, 186, 108119.
39	JIANG H C, YI W, CUI G L Knowledge-based track-before-detect strategies for fluctuating targets in K-distributed clutter. IEEE Sensors Journal, 2016, 16 (19): 7124- 7132. doi: 10.1109/JSEN.2016.2597320
40	YI W, JIANG H C, KIRUBARAJAN T Track-before-detect strategies for radar detection in G0-distributed clutter. IEEE Trans. on Aerospace and Electronic Systems, 2017, 53 (5): 2516- 2533. doi: 10.1109/TAES.2017.2702259
41	JIANG H C, YI W, CUI G L Track-before-detect strategies for range distributed target detection in compound-Gaussian clutter. Signal Processing, 2016, 120, 462- 467. doi: 10.1016/j.sigpro.2015.09.034
42	WEI L, ZHANG X, FAN L. TBD algorithm based on improved randomized hough transfer for dim target detection. Proc. of the 2nd International Conference on Signal Processing Systems, 2000. DOI: 10.1109/ICSPS.2010.5555508.
43	CAO C H, ZHAO Y B, PANG X J, et al Sequential Monte Carlo cardinalized probability hypothesized density filter based on track-before-detect for fluctuating targets in heavy-tailed clutter. Signal Processing, 2019, 169, 107367.
44	MCDONALD M, BALAJI B Impact of measurement model mismatch on nonlinear track-before-detect performance for maritime radar surveillance. IEEE of Ocean Engineering, 2011, 36 (4): 602- 614.
45	BREKKE E, HALLINGSTAD O, GLATTETRE J Tracking small targets in heavy-tailed clutter using amplitude information. IEEE Journal of Ocean Engineering, 2010, 35 (2): 314- 329. doi: 10.1109/JOE.2010.2044670
46	LI S Q, YI W, KONG L J, et al. Multi-Bernoulli filter based track-before-detect for jump Markov models. Proc. of the IEEE Radar Conference, 2014: 1257−1261.
47	WANG Z Q, SUN J. Maneuvering target tracking via dynamic-programming based track-before-detect algorithm. Proc. of the CIE International Conference on Radar, 2016. DOI: 10.1109/RADAR.2016.8059558.
48	LI X Z, WANG S Y, ZHENG D K. A DP-TBD algorithm with adaptive state transition set for maneuvering targets. Proc. of the CIE International Conference on Radar, 2016: 64−68.
49	BARDEL N, ABBASSI N, DEBOUVRIES F. A Bayesian filtering algorithm in jump Markov systems with application to track-before-detect. Proc. of the IEEE Radar Conference, 2010: 1397−1402.

Symbol	Parameter	Value
$ \delta _b^2 $	Blurring factor	1
$ {\sigma _T} $	Source intensity	1
$ {T_s} $	Sampling time interval/s	1
$ {P_S} $	Survival probability	0.98
SCR	SCR/dB	{8,9,10,12,13}
$ {\lambda _c} $	Intensity of the clutter	{60,90,120,150}
$ {\delta _x},{\delta _y} $	Cell side length	$ {\delta _x} = {\delta _y} = 1 $
$ \mathcal{C}\left( x \right) $	Illustrating template	$ 3{\text{ pixel}} \times 3{\text{ pixel}} $
$ \alpha ,\beta $	Shape and scale parameter	$ \alpha = 0.5,\beta = 2 $

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