Optimal federated fusion of multiple maneuvering targets based on multi-Bernoulli filters

Yu XUE; Xi'an FENG

doi:10.1631/FITEE.2400598

Your Location：

Home >

Browse articles >

Optimal federated fusion of multiple maneuvering targets based on multi-Bernoulli filters

Regular Papers | Updated：2025-06-09

- Optimal federated fusion of multiple maneuvering targets based on multi-Bernoulli filters
- 基于多伯努利滤波器的多机动目标最优联邦融合
- Frontiers of Information Technology & Electronic Engineering Vol. 26, Issue 5, Pages: 753-769(2025)
- Affiliations：
  
  School of Marine Science and Technology, Northwestern Polytechnical University, Xi'an 710072, China
- Author bio：
  
  E-mail: 18829236362@163.com
  ‡ Corresponding authors
- Funds：
- DOI：10.1631/FITEE.2400598
  CLC： TP273.5
- Received：17 July 2024，
  
  Revised：01 December 2024，
  
  Published Online：02 May 2025，
  
  Published：2025-05
- Accepted：
Scan QR Code
Yu XUE, Xi'an FENG. Optimal federated fusion of multiple maneuvering targets based on multi-Bernoulli filters[J]. Frontiers of information technology & electronic engineering, 2025, 26(5): 753-769.
DOI：

Yu XUE, Xi'an FENG. Optimal federated fusion of multiple maneuvering targets based on multi-Bernoulli filters[J]. Frontiers of information technology & electronic engineering, 2025, 26(5): 753-769. DOI： 10.1631/FITEE.2400598.

摘要

为实现多个不确定机动目标的最优融合跟踪，提出一种具有分层结构的联合多高斯混合多伯努利（JMGM-MB）滤波器的联邦融合算法。JMGM-MB滤波器以交互多模型（IMM）滤波形式传递每个潜在目标的状态密度，因此精度高于多模型高斯混合多伯努利（MM-GM-MB）滤波器。在分层结构中，每个传感器节点执行局域JMGM-MB滤波器来捕获存活目标、新生目标和消亡目标。所提算法的一个显著特点是在融合节点运行一个主滤波器，以帮助判断状态估计的来源和补充漏检。所有滤波器的输出被关联为多组单目标估计。严格推导了IMM滤波器的最优融合，并将其用于合并关联的单目标估计。引入协方差上界技术以真正消除滤波器间的相关性，进而保证了算法的最优性。仿真结果表明，所提算法在线性和异类场景中均优于现有的集中式和分布式融合算法，且允许灵活调整主滤波器和局域滤波器的相对权重。

Abstract

A federated fusion algorithm of joint multi-Gaussian mixture multi-Bernoulli (JMGM-MB) filters is proposed to achieve optimal fusion tracking of multiple uncertain maneuvering targets in a hierarchical structure. The JMGM-MB filter achieves a higher level of accuracy than the multi-model Gaussian mixture MB (MM-GM-MB) filter by propagating the state density of each potential target in the interactive multi-model (IMM) filtering manner. Within the hierarchical structure

each sensor node performs a local JMGM-MB filter to capture survival

newborn

and vanishing targets. A notable characteristic of our algorithm is a master filter running on the fusion node

which can help identify the origins of state estimates and supplement missed detections. The outputs of all filters are associated into multiple groups of single-target estimates. We rigorously derive the optimal fusion of IMM filters and apply it to merge associated single-target estimates. This optimality is guaranteed by the covariance upper-bounding technique

which can truly eliminate correlations among filters. Simulation results demonstrate that the proposed algorithm outperforms the existing centralized and distributed fusion algorithms in linear and heterogeneous scenarios

and the relative weights of the master and local filters can be adjusted flexibly.

关键词

Keywords

references

Balenzuela MP , Wills AG , Renton C , et al. , 2022 . Parameter estimation for jump Markov linear systems . Automatica , 135 : 109949 . https://doi.org/10.1016/j.automatica.2021.109949 https://doi.org/10.1016/j.automatica.2021.109949

Carlson NA , 1990 . Federated square root filter for decentralized parallel processors . IEEE Trans Aerosp Electron Syst , 26 ( 3 ): 517 - 525 . https://doi.org/10.1109/7.106130 https://doi.org/10.1109/7.106130

Chang CB , Athans M , 1978 . State estimation for discrete systems with switching parameters . IEEE Trans Aerosp Electron Syst , AES-14 ( 3 ): 418 - 425 . https://doi.org/10.1109/TAES.1978.308603 https://doi.org/10.1109/TAES.1978.308603

Da K , Li TC , Zhu YF , et al. , 2020a . Gaussian mixture particle jump-Markov-CPHD fusion for multitarget tracking using sensors with limited views . IEEE Trans Signal Inform Process Netw , 6 : 605 - 616 . https://doi.org/10.1109/TSIPN.2020.3016478 https://doi.org/10.1109/TSIPN.2020.3016478

Da K , Li TC , Zhu YF , et al. , 2020b . Kullback‍–Leibler averaging for multitarget density fusion . Proc 16 th Int Symp on Distributed Computing and Artificial Intelligence , p. 253 - 261 . https://doi.org/10.1007/978-3-030-23887-2_29 https://doi.org/10.1007/978-3-030-23887-2_29

Dong XD , Zhang XF , Zhao J , et al. , 2021 . Multi-maneuvering sources DOA tracking with improved interactive multi-model multi-Bernoulli filter for acoustic vector sensor (AVS) array . IEEE Trans Veh Technol , 70 ( 8 ): 7825 - 7838 . https://doi.org/10.1109/TVT.2021.3093063 https://doi.org/10.1109/TVT.2021.3093063

Dunne D , Kirubarajan T , 2013 . Multiple model multi-Bernoulli filters for manoeuvering targets . IEEE Trans Aerosp Electron Syst , 49 ( 4 ): 2679 - 2692 . https://doi.org/10.1109/TAES.2013.6621845 https://doi.org/10.1109/TAES.2013.6621845

Gao L , Battistelli G , Chisci L , 2020 . Multiobject fusion with minimum information loss . IEEE Signal Process Lett , 27 : 201 - 205 . https://doi.org/10.1109/LSP.2019.2963817 https://doi.org/10.1109/LSP.2019.2963817

Georgescu R , Willett P , 2012 . The multiple model CPHD tracker . IEEE Trans Signal Process , 60 ( 4 ): 1741 - 1751 . https://doi.org/10.1109/TSP.2012.2183128 https://doi.org/10.1109/TSP.2012.2183128

Gunay M , Orguner U , Demirekler M , 2016 . Chernoff fusion of Gaussian mixtures based on sigma-point approximation . IEEE Trans Aerosp Electron Syst , 52 ( 6 ): 2732 - 2746 . https://doi.org/10.1109/TAES.2016.150403 https://doi.org/10.1109/TAES.2016.150403

Hu GG , Xu LY , Gao BB , et al. , 2023 . Robust unscented Kalman filter-based decentralized multisensor information fusion for INS/GNSS/CNS integration in hypersonic vehicle navigation . IEEE Trans Instrum Meas , 72 : 8504011 . https://doi.org/10.1109/TIM.2023.3281565 https://doi.org/10.1109/TIM.2023.3281565

Hu XL , Zhang Q , Song BJ , et al. , 2022 . σ -threshold Bayes filter in unknown birth background with multi-Bernoulli finite sets . Proc IEEE Int Conf on Signal Processing, Communications and Computing , p. 1 - 4 . https://doi.org/10.1109/ICSPCC55723.2022.9984566 https://doi.org/10.1109/ICSPCC55723.2022.9984566

Julier SJ , Uhlmann JK , 1997 . A non-divergent estimation algorithm in the presence of unknown correlations . Proc American Control Conf , p. 2369 - 2373 . https://doi.org/10.1109/ACC.1997.609105 https://doi.org/10.1109/ACC.1997.609105

Li GY , Battistelli G , Chisci L , et al. , 2024 . Distributed joint detection, tracking, and classification via labeled multi-Bernoulli filtering . IEEE Trans Cybern , 54 ( 3 ): 1429 - 1441 . https://doi.org/10.1109/TCYB.2022.3208038 https://doi.org/10.1109/TCYB.2022.3208038

Li TC , 2024 . Arithmetic average density fusion—part II: unified derivation for unlabeled and labeled RFS fusion . IEEE Trans Aerosp Electron Syst , 60 ( 3 ): 3255 - 3268 . https://doi.org/10.1109/TAES.2024.3359592 https://doi.org/10.1109/TAES.2024.3359592

Li TC , Corchado JM , Chen HM , 2018 . Distributed flooding-then-clustering: a lazy networking approach for distributed multiple target tracking . Proc 21 st Int Conf on Information Fusion , p. 2415 - 2422 . https://doi.org/10.23919/ICIF.2018.8455759 https://doi.org/10.23919/ICIF.2018.8455759

Li TC , Corchado JM , Sun SD , 2019a . Partial consensus and conservative fusion of Gaussian mixtures for distributed PHD fusion . IEEE Trans Aerosp Electron Syst , 55 ( 5 ):‍ 2150 - 2163 . https://doi.org/10.1109/TAES.2018.2882960 https://doi.org/10.1109/TAES.2018.2882960

Li TC , Fan HQ , García J , et al. , 2019b . Second-order statistics analysis and comparison between arithmetic and geometric average fusion: application to multi-sensor target tracking . Inform Fus , 51 : 233 - 243 . https://doi.org/10.1016/j.inffus.2019.02.009 https://doi.org/10.1016/j.inffus.2019.02.009

Li TC , Wang XX , Liang Y , et al. , 2020 . On arithmetic average fusion and its application for distributed multi-Bernoulli multitarget tracking . IEEE Trans Signal Process , 68 :‍ 2883 - 2896 . https://doi.org/10.1109/TSP.2020.2985643 https://doi.org/10.1109/TSP.2020.2985643

Li TC , Song Y , Song EB , et al. , 2024a . Arithmetic average density fusion—part I: some statistic and information-theoretic results . Inform Fus , 104 : 102199 . https://doi.org/10.1016/j.inffus.2023.102199 https://doi.org/10.1016/j.inffus.2023.102199

Li TC , Yan RB , Da K , et al. , 2024b . Arithmetic average density fusion—part III: heterogeneous unlabeled and labeled RFS filter fusion . IEEE Trans Aerosp Electron Syst , 60 ( 1 ):‍‍‍ 1023 - 1034 . https://doi.org/10.1109/TAES.2023.3334223 https://doi.org/10.1109/TAES.2023.3334223

Li WL , Jia YM , 2011 . Gaussian mixture PHD filter for jump Markov models based on best-fitting Gaussian approximation . Signal Process , 91 ( 4 ): 1036 - 1042 . https://doi.org/10.1016/j.sigpro.2010.08.004 https://doi.org/10.1016/j.sigpro.2010.08.004

Mahler R , 2014 . Advances in Statistical Multisource-Multitarget Information Fusion . Artech House , Norwood, USA .

Ouyang C , Ji HB , Guo ZQ , 2012 . Extensions of the SMC-PHD filters for jump Markov systems . Signal Process , 92 ( 6 ): 1422 - 1430 . https://doi.org/10.1016/j.sigpro.2011.11.032 https://doi.org/10.1016/j.sigpro.2011.11.032

Peng C , Chai L , Yi W , et al. , 2021 . Distributed multi-sensor multi-view fusion of PHD filter for maneuvering targets . Proc CIE Int Conf on Radar , p. 1182 - 1187 . https://doi.org/10.1109/Radar53847.2021.10028507 https://doi.org/10.1109/Radar53847.2021.10028507

Punithakumar K , Kirubarajan T , Sinha A , 2008 . Multiple-model probability hypothesis density filter for tracking maneuvering targets . IEEE Trans Aerosp Electron Syst , 44 ( 1 ): 87 - 98 . https://doi.org/10.1109/TAES.2008.4516991 https://doi.org/10.1109/TAES.2008.4516991

Schuhmacher D , Vo BT , Vo BN , 2008 . A consistent metric for performance evaluation of multi-object filters . IEEE Trans Signal Process , 56 ( 8 ): 3447 - 3457 . https://doi.org/10.1109/TSP.2008.920469 https://doi.org/10.1109/TSP.2008.920469

Shen-Tu H , Lin RF , Shen WC , et al. , 2024 . An arithmetic geometric mixed average GM-PHD algorithm for decentralized sensor network with limited field of view . IEEE Sens J , 24 ( 12 ): 19995 - 20008 . https://doi.org/10.1109/JSEN.2024.3392891 https://doi.org/10.1109/JSEN.2024.3392891

Sun SL , 2020 . Distributed optimal linear fusion estimators . Inform Fus , 63 : 56 - 73 . https://doi.org/10.1016/j.inffus.2020.05.006 https://doi.org/10.1016/j.inffus.2020.05.006

Sun YC , Kim D , Hwang I , 2022 . Multiple-model Gaussian mixture probability hypothesis density filter based on jump Markov system with state-dependent probabilities . IET Radar Sonar Navig , 16 ( 11 ): 1881 - 1894 . https://doi.org/10.1049/rsn2.12304 https://doi.org/10.1049/rsn2.12304

Üney M , Clark DE , Julier SJ , 2013 . Distributed fusion of PHD filters via exponential mixture densities . IEEE J Sel Top Signal Process , 7 ( 3 ): 521 - 531 . https://doi.org/10.1109/JSTSP.2013.2257162 https://doi.org/10.1109/JSTSP.2013.2257162

Üney M , Houssineau J , Delande E , et al. , 2019 . Fusion of finite-set distributions: pointwise consistency and global cardinality . IEEE Trans Aerosp Electron Syst , 55 ( 6 ): 2759 - 2773 . https://doi.org/10.1109/TAES.2019.2893083 https://doi.org/10.1109/TAES.2019.2893083

Vo BT , Vo BN , Cantoni A , 2009 . The cardinality balanced multi-target multi-Bernoulli filter and its implementations . IEEE Trans Signal Process , 57 ( 2 ): 409 - 423 . https://doi.org/10.1109/TSP.2008.2007924 https://doi.org/10.1109/TSP.2008.2007924

Wang KW , Zhang Q , Hu XL , 2024 . Multisensor multitarget tracking arithmetic average fusion method based on probabilistic time window . IEEE Sens J , 24 ( 3 ): 3583 - 3593 . https://doi.org/10.1109/JSEN.2023.3337267 https://doi.org/10.1109/JSEN.2023.3337267

Wei JX , Luo F , Chen SC , et al. , 2023 . Robust fusion of GM-PHD filters based on geometric average . Signal Process , 206 : 108912 . https://doi.org/10.1016/j.sigpro.2022.108912 https://doi.org/10.1016/j.sigpro.2022.108912

Wu SY , Dong XD , Zhao J , et al. , 2019 . A fast implementation of interactive-model generalized labeled multi-Bernoulli filter for interval measurements . Signal Process , 164 :‍ 345 - 353 . https://doi.org/10.1016/j.sigpro.2019.05.028 https://doi.org/10.1016/j.sigpro.2019.05.028

Wu WH , Cai YC , Jin HB , et al. , 2021a . Derivation of the multi-model generalized labeled multi-Bernoulli filter: a solution to multi-target hybrid systems . Front Inform Technol Electron Eng , 22 ( 1 ): 79 - 87 . https://doi.org/10.1631/FITEE.2000105 https://doi.org/10.1631/FITEE.2000105

Wu WH , Sun HM , Huang ZL , et al. , 2021b . Multi-GMTI fusion for Doppler blind zone suppression using PHD fusion . Signal Process , 183 : 108024 . https://doi.org/10.1016/j.sigpro.2021.108024 https://doi.org/10.1016/j.sigpro.2021.108024

Xie X , Sun HM , Wu WH , et al. , 2019 . Multi-UAV multi-target tracking in the presence of Doppler blind zone . Proc IEEE Int Conf on Unmanned Systems , p. 438 - 442 . https://doi.org/10.1109/ICUS48101.2019.8996083 https://doi.org/10.1109/ICUS48101.2019.8996083

Xie XX , Wang Y , Guo JQ , et al. , 2023 . The multiple model Poisson multi-Bernoulli mixture filter for extended target tracking . IEEE Sens J , 23 ( 13 ): 14304 - 14314 . https://doi.org/10.1109/JSEN.2023.3270272 https://doi.org/10.1109/JSEN.2023.3270272

Xue Y , Feng XA , 2024 . Joint multi-Gaussian mixture model and its application to multi-model multi-Bernoulli filter . Dig Signal Process , 153 : 104616 . https://doi.org/10.1016/j.dsp.2024.104616 https://doi.org/10.1016/j.dsp.2024.104616

Yang H , Li TC , Yan JK , et al. , 2024 . Hierarchical average fusion with GM-PHD filters against FDI and DoS attacks . IEEE Signal Process Lett , 31 : 934 - 938 . https://doi.org/10.1109/LSP.2024.3356823 https://doi.org/10.1109/LSP.2024.3356823

Yi W , Li SQ , Wang BL , et al. , 2020 . Computationally efficient distributed multi-sensor fusion with multi-Bernoulli filter . IEEE Trans Signal Process , 68 : 241 - 256 . https://doi.org/10.1109/TSP.2019.2957638 https://doi.org/10.1109/TSP.2019.2957638

Zhao BF , 2024 . Multisensor maneuvering target fusion tracking using interacting multiple model . Autom Contr Comput Sci , 58 ( 3 ): 303 - 312 . https://doi.org/10.3103/S0146411624700184 https://doi.org/10.3103/S0146411624700184

Zhou YQ , Yan LP , Li H , et al. , 2024 . The multiple pairwise Markov chain model-based labeled multi-Bernoulli filter . J Franklin Inst , 361 ( 10 ): 106939 . https://doi.org/10.1016/j.jfranklin.2024.106939 https://doi.org/10.1016/j.jfranklin.2024.106939

Views

Downloads

CSCD

Alert me when the article has been cited

Submit

Tools

Publicity Resources

Recent advances in multisensor multitarget tracking using random finite set

Related Author

Kai DA

Yongfeng ZHU

Hongqi FAN

Qiang FU

Tiancheng LI

Related Institution

The National Key Laboratory of Science and Technology on ATR, National University of Defense Technology

MOE Key Laboratory of Information Fusion Technology, School of Automation, Northwestern Polytechnical University

Map

Chat

Address：Zhejiang University Press, 148 Tianmushan Road, Hangzhou, China Postal code：310028
Tel：+86-571-88273162 Email：fitee@zju.edu.cn
It is recommended to read the content of this site in Chrome&IE9+. Please switch to extreme mode in browser 360.
Cookies We use cookies to help provide and enhance our service and tailor content. By continuing, you agree to the use of cookies.

⁰