Poisson Multi-Bernoulli Mixture Filter for Heavy-tailed Process and Measurement Noises

ZHU Jiangbo; XIE Wexin; LIU Zongxiang; WANG Xiaoli

doi:10.23919/cje.2022.00.325

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Jiangbo ZHU, Wexin XIE, Zongxiang LIU, et al., “Poisson Multi-Bernoulli Mixture Filter for Heavy-tailed Process and Measurement Noises,” Chinese Journal of Electronics, vol. x, no. x, pp. 1–11, xxxx doi: 10.23919/cje.2022.00.325

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Jiangbo ZHU, Wexin XIE, Zongxiang LIU, et al., “Poisson Multi-Bernoulli Mixture Filter for Heavy-tailed Process and Measurement Noises,” Chinese Journal of Electronics, vol. x, no. x, pp. 1–11, xxxx doi: 10.23919/cje.2022.00.325

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Poisson Multi-Bernoulli Mixture Filter for Heavy-tailed Process and Measurement Noises

doi: 10.23919/cje.2022.00.325

ZHU Jiangbo^{1, 2
,},
XIE Wexin^{1, 2
,},
LIU Zongxiang^{1, 2
,
,},
WANG Xiaoli^3
,

1.
College of Electronics and Information Engineering, Shenzhen University, Shenzhen 518060, China
2.
Guangdong Key Laboratory of Intelligent Information Processing, Shenzhen University, Shenzhen 518060, China
3.
School of Electronics and Information, Guangdong Polytechnic Normal University, Guangzhou 510660, China

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Author Bio:
Jiangbo ZHU was born in 1986. He received his B.S. degree in communication engineering from Information Engineering University, Zhengzhou, China, in 2009, and an M.S. degree in signal and information processing from Zhongyuan University of Technology, Zhengzhou, in 2012. He is currently pursuing a Ph.D. degree with the Guangdong Key Laboratory of Intelligent Information Processing, College of Electronic and Information Engineering, Shenzhen University. His research interests include signal processing and target tracking. (Email: jbzhu@email.szu.edu.cn)

Wexin XIE graduated from Xidian University and joined the faculty in 1965. From 1981 to 1983, he was a visiting scholar with the University of Pennsylvania, USA. In 1989, he was invited to University of Pennsylvania as a visiting professor. He is currently a professor with Shenzhen University. His research interests include intelligent information processing, fuzzy information processing, image processing and pattern recognition. (Email: wxxie@szu.edu.cn)

Zongxiang LIU was born in 1965. He received his B.S. and M.S. degrees from the Department of Precision Instrument Engineering, Tianjin University, Tianjin, China, in 1985 and 1988, respectively, and the Ph.D. degree from the School of Electronic Engineering, Xidian University, Xi’an, China, in 2005. He is currently a Professor with the Guangdong Key Laboratory of Intelligent Information Processing, Shenzhen University, Shenzhen, China. His research interests include multi-sensor data fusion, intelligent information processing, and fuzzy information processing. (Email: liuzx@szu.edu.cn)

Xiaoli WANG was born in 1992. She received her Ph.D. degree from the College of Electronic and Information Engineering, Shenzhen University, Shenzhen, China, in 2021. She is currently a lecturer in the College of Electronics and Information, Guangdong Polytechnic Normal University, Guangzhou, China. Her research interests include multi-sensor information fusion, fuzzy information processing and target tracking. (Email:xlwang@gpnu.edu.cn)
Corresponding author: Email: liuzx@szu.edu.cn
Received Date: 2022-09-24
Accepted Date: 2023-10-27

Available Online: 2023-11-22

Abstract

Abstract

A novel Poisson multi-Bernoulli mixture (PMBM) filter is proposed to track multiple targets in the presence of heavy-tailed process and measurement noises. Unlike the standard PMBM filter that requires the Gaussian process and measurement noises, the proposed filter uses the Student’s t distribution to model the heavy-tailed noise feature. It propagates Student’s t-based PMBM posterior in the closed-form recursion. The introduction of the moment matching method enables the proposed filter to deal with the process and measurement noises with different heavy-tailed degrees to some extent. Simulation results demonstrate that the overall performance of the proposed filter is better than the existing heavy-tailed noise filters in various scenarios.
- Heavy-tailed noise,
- Multi-target tracking,
- Student’s t distribution,
- Poisson multi-Bernoulli mixture

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References(36)

References

[1]	Y. Bar-Shalom, Multitarget-Multisensor Tracking: Advanced Applications. Artech House, Norwood, MA, USA, 1990.
[2]	Y. Bar-Shalom, T. E. Fortmann, and P. G. Cable, “Tracking and data association,” The Journal of the Acoustical Society of America, vol. 87, no. 2, pp. 918–919, 1990. doi: 10.1121/1.398863
[3]	J. D. Fan, W. X. Xie, and Z. X. Liu, “A low complexity distributed multitarget detection and tracking algorithm,” Chinese Journal of Electronics, vol. 32, no. 3, pp. 429–437, 2023. doi: 10.23919/cje.2021.00.282
[4]	S. S. Blackman, “Multiple hypothesis tracking for multiple target tracking,” IEEE Aerospace and Electronic Systems Magazine, vol. 19, no. 1, pp. 5–18, 2004. doi: 10.1109/MAES.2004.1263228
[5]	S. Puranik and J. Tugnait, “Tracking of multiple maneuvering targets using multiscan JPDA and IMM filtering,” IEEE Transactions on Aerospace and Electronic Systems, vol. 43, no. 1, pp. 23–35, 2007. doi: 10.1109/TAES.2007.357152
[6]	R. P. S. Mahler, Statistical Multisource-Multitarget Information Fusion. Artech House, Boston, MA, USA, 2007.
[7]	R. P. S. Mahler, “Multitarget Bayes filtering via first-order multitarget moments,” IEEE Transactions on Aerospace and Electronic Systems, vol. 39, no. 4, pp. 1152–1178, 2003. doi: 10.1109/TAES.2003.1261119
[8]	B. N. Vo and W. K. Ma, “The Gaussian mixture probability hypothesis density filter,” IEEE Transactions on Signal Processing, vol. 54, no. 11, pp. 4091–4104, 2006. doi: 10.1109/TSP.2006.881190
[9]	B. T. Vo, B. N. Vo, and A. Cantoni, “Analytic implementations of the cardinalized probability hypothesis density filter,” IEEE Transactions on Signal Processing, vol. 55, no. 7, pp. 3553–3567, 2007. doi: 10.1109/TSP.2007.894241
[10]	P. Dong, Z. L. Jing, H. Leung, et al., “Student- t mixture labeled multi-Bernoulli filter for multi-target tracking with heavy-tailed noise,” Signal Processing, vol. 152 pp. 331–339, 2018. doi: 10.1016/j.sigpro.2018.06.014
[11]	B. T. Vo, B. N. Vo, and A. Cantoni, “The cardinality balanced multi-target multi-Bernoulli filter and its implementations,” IEEE Transactions on Signal Processing, vol. 57, no. 2, pp. 409–423, 2009. doi: 10.1109/TSP.2008.2007924
[12]	B. N. Vo, B. T. Vo, and H. G. Hoang, “An efficient implementation of the generalized labeled multi-Bernoulli filter,” IEEE Transactions on Signal Processing, vol. 65, no. 8, pp. 1975–1987, 2017. doi: 10.1109/TSP.2016.2641392
[13]	B. T. Vo and B. N. Vo, “Labeled random finite sets and multi-object conjugate priors,” IEEE Transactions on Signal Processing, vol. 61, no. 13, pp. 3460–3475, 2013. doi: 10.1109/TSP.2013.2259822
[14]	S. Reuter, B. T. Vo, B. N. Vo, et al., “The labeled multi-Bernoulli filter,” IEEE Transactions on Signal Processing, vol. 62, no. 12, pp. 3246–3260, 2014. doi: 10.1109/TSP.2014.2323064
[15]	Á. F. García-Fernández, J. L. Williams, K. Granstrom, et al., “Poisson multi-Bernoulli mixture filter: Direct derivation and implementation,” IEEE Transactions on Aerospace and Electronic Systems, vol. 54, no. 4, pp. 1883–1901, 2018. doi: 10.1109/TAES.2018.2805153
[16]	Q. Dong, J. W. Hu, and B. Ji, “Multi-target tracking algorithms based on random finite set: A survey,” Aerospace Technology, no. 3, pp. 79–83,94, 2019. doi: 10.16338/j.issn.1009-1319.20180234
[17]	Y. X. Xia, K. Granstrcom, L. Svensson, et al., “Performance evaluation of multi-Bernoulli conjugate priors for multi-target filtering,” in Proceedings of the 20th International Conference on Information Fusion (FUSION), Xi’an, China, pp. 1–8, 2017.
[18]	J. L. Williams, “Marginal multi-Bernoulli filters: RFS derivation of MHT, JIPDA, and association-based member,” IEEE Transactions on Aerospace and Electronic Systems, vol. 51, no. 3, pp. 1664–1687, 2015. doi: 10.1109/TAES.2015.130550
[19]	H. C. Du and W. X. Xie, “Extended target marginal distribution Poisson multi-Bernoulli mixture filter,” Sensors, vol. 20, no. 18, article no. 5387, 2020. doi: 10.3390/s20185387
[20]	K. Granström, L. Svensson, Y. X. Xia, et al., “Poisson multi-Bernoulli mixture trackers: Continuity through random finite sets of trajectories,” in Proceedings of the 21st International Conference on Information Fusion (FUSION), Cambridge, UK, pp. 1–5, 2018.
[21]	A. F. Garcia-Fernandez, L. Svensson, J. L. Williams, et al., “Trajectory Poisson multi-Bernoulli filters,” IEEE Transactions on Signal Processing, vol. 68 pp. 4933–4945, 2020. doi: 10.1109/TSP.2020.3017046
[22]	F. Meyer, A. Tesei, and M. Z. Win, “Localization of multiple sources using time-difference of arrival measurements,” in Proceedings of International Conference on Acoustics, Speech and Signal Processing (ICASSP), New Orleans, LA, USA, pp. 3151–3155, 2017.
[23]	J. Christmas and R. Everson, “Robust autoregression: Student-t innovations using variational Bayes,” IEEE Transactions on Signal Processing, vol. 59, no. 1, pp. 48–57, 2011. doi: 10.1109/TSP.2010.2080271
[24]	R. Piché, S. Särkkä, and J. Hartikainen, “Recursive outlier-robust filtering and smoothing for nonlinear systems using the multivariate student-t distribution,” in Proceedings of International Workshop on Machine Learning for Signal Processing, Santander, Spain, pp. 1–6, 2012.
[25]	Y. L. Huang, Y. G. Zhang, N. Li, et al., “A robust Gaussian approximate filter for nonlinear systems with heavy tailed measurement noises,” in Proceedings of International Conference on Acoustics, Speech and Signal Processing (ICASSP), Shanghai, China, pp. 4209–4213, 2016.
[26]	W. L. Li, Y. M. Jia, J. P. Du, et al., “PHD filter for multi-target tracking with glint noise,” Signal Processing, vol. 94 pp. 48–56, 2014. doi: 10.1016/j.sigpro.2013.06.012
[27]	C. Y. Li, R. Wang, and H. B. Ji, “Multiple extended-target tracking based on variational Bayesian cardinality-balanced multi-target multi-Bernoulli,” Control Theory & Applications, vol. 32, no. 2, pp. 187–195, 2015. doi: 10.7641/CTA.2015.40454
[28]	N. J. Gordon and A. F. M. Smith, “Approximate non-Gaussian Bayesian estimation and modal consistency,” Journal of the Royal Statistical Society:Series B (Methodological), vol. 55, no. 4, pp. 913–918, 1993. doi: 10.1111/j.2517-6161.1993.tb01949.x
[29]	I. Bilik and J. Tabrikian, “Maneuvering target tracking in the presence of glint using the nonlinear Gaussian mixture kalman filter,” IEEE Transactions on Aerospace and Electronic Systems, vol. 46, no. 1, pp. 246–262, 2010. doi: 10.1109/TAES.2010.5417160
[30]	M. Roth, E. Özkan, and F. Gustafsson, “A student’s t filter for heavy tailed process and measurement noise,” in Proceedings of International Conference on Acoustics, Speech and Signal Processing (ICASSP), Vancouver, BC, Canada, pp. 5770–5774, 2013.
[31]	M. J. Wang, H. B. Ji, Y. Q. Zhang, et al., “A student’s T mixture cardinality-balanced multi-target multi-Bernoulli filter with heavy-tailed process and measurement noises,” IEEE Access, vol. 6 pp. 51098–51109, 2018. doi: 10.1109/ACCESS.2018.2869419
[32]	G. C. Li, L. J. Kong, W. Yi, et al., “Multiple model Poisson multi-Bernoulli mixture filter for maneuvering targets,” IEEE Sensors Journal, vol. 21, no. 3, pp. 3143–3154, 2021. doi: 10.1109/JSEN.2020.3022669
[33]	K. G. Murty, “Letter to the editor—An algorithm for ranking all the assignments in order of increasing costs,” Operations Research, vol. 16, no. 3, pp. 682–687, 1968. doi: 10.1287/opre.16.3.682
[34]	D. Schuhmacher, B. T. Vo, and B. N. Vo, “A consistent metric for performance evaluation of multi-object filters,” IEEE Transactions on Signal Processing, vol. 56, no. 8, pp. 3447–3457, 2008. doi: 10.1109/TSP.2008.920469
[35]	Y. G. Punchihewa, B. T. Vo, B. N. Vo, et al., “Multiple object tracking in unknown backgrounds with labeled random finite sets,” IEEE Transactions on Signal Processing, vol. 66, no. 11, pp. 3040–3055, 2018. doi: 10.1109/TSP.2018.2821650
[36]	Z. Z. Su, H. B. Ji, and Y. Q. Zhang, “A Poisson multi-Bernoulli mixture filter with spawning based on Kullback-Leibler divergence minimization,” Chinese Journal of Aeronautics, vol. 34, no. 11, pp. 154–168, 2021. doi: 10.1016/j.cja.2020.11.015