Multi-target Tracking Algorithm Based on Information Association and Weighting

doi:10.3969/j.issn.1009-086x.2025.01.003

Abstract

Abstract:

A probability hypothesis density filtering algorithm based on information association weighting is proposed to address the two issues of decreased accuracy in multi-target state estimation and overestimation of the number of multi-targets， which are caused by asynchronicity and high-density clutter aliasing in passive and active radar detection information across multiple platforms. Firstly， a multi-target tracking model is constructed， and the mechanism of why existing algorithms are susceptible to clutter is analyzed. Secondly， a multi-target tracking algorithm based on information association weighting is derived. The tolerance time parameter is set according to the target speed and tolerable error， and the detection information with a short asynchronous time is approximated as synchronous information. The association algorithm is used to select passive and active radar information from the same target， and the minimum variance weighted fusion is used to improve detection accuracy. The randomly distributed clutter is filtered out， due to its association difficulties caused by large differences in angle values. Finally， simulation analysis shows that the proposed algorithm improves the accuracy of multi-target state estimation and reduces the overestimation of the number of multi-targets compared to existing algorithms.

Key words: multi-target tracking, cooperative detection, probability hypothesis density（PHD）, information association, minimum variance weighting

摘要：

针对多平台被动、主动雷达探测信息异步和高密度杂波混叠导致多目标状态估计精度下降与多目标数量过度估计的问题，提出基于信息关联加权的概率假设密度滤波算法。构建多目标跟踪模型，并分析了现有算法易受杂波影响的机理。推导了基于信息关联加权的多目标跟踪算法，根据目标速度和可容忍误差设置容忍时间参数，将异步时间较短的探测信息近似为同步，利用关联算法筛选来源于同一目标的被动、主动雷达信息，利用最小方差加权融合提升探测精度，而随机分布的杂波由于角度数值差距较大导致难以关联而被剔除。仿真分析表明，所提算法相比于现有算法提升了多目标状态估计精度，减少多目标数量过度估计情况。

关键词: 多目标跟踪, 协同探测, 概率假设密度滤波, 信息关联, 最小方差加权

CLC Number:

TJ76

Yongzheng YU, Wei WANG, Zhiwei PU. Multi-target Tracking Algorithm Based on Information Association and Weighting[J]. Modern Defense Technology, 2025, 53(1): 23-36.

于勇政, 王伟, 蒲治伟. 基于信息关联加权的多目标跟踪算法[J]. 现代防御技术, 2025, 53(1): 23-36.

Figures/Tables 29

Fig. 1 Illustration of multi-target tracking model

Fig. 2 Illustration of multi-target tracking algorithm

Fig. 3 Flowsheet of IAW algorithm

Fig. 4 Real trajectory of multi-target

Fig. 5 Detection information with P(10)

Fig. 6 Multi-target position states estimation under P（10）

Fig. 7 Multi-target speed states estimation under P（10）

Fig. 8 OSPA under P（10）

Fig. 9 Multi-target quantity estimation under P（10）

Fig. 10 Detection information under P(40)

Fig. 11 Multi-target position states estimation under P（40）

Fig. 12 Multi-target speed states estimation under P（40）

Fig. 13 OSPA under P（40）

Fig. 14 Multi-target quantity estimation under P（40）

Fig. 15 Comparison of OSPA with different algorithms under P（10）

Fig. 16 Comparison of multi-target quantity with different algorithms under P（10）

Fig. 17 Comparison of OSPA with different algorithms under P（40）

Fig. 18 Comparison of multi-target quantity with different algorithms under P（40）

Fig. 19 Correct estimation weight test results

Fig. 20 Comparison between correct estimation target state values and true values

Fig. 21 Conservative failure estimation weight test results

Fig. 22 Comparison between conservative failure estimation target state values and true values

Fig. 23 Conservative loss estimation weight test results

Fig. 24 Comparison between conservative loss estimation target state values and true values

Fig. 25 Excessive error estimation weight test results

Fig. 26 Comparison between excessive error estimation target state values and true values

Fig. 27 Excessive repeated estimation weight test results

Fig. 28 Comparison between excessive repeated estimation target state values and true values

Table 1 Computational complexity and time of different algorithms

计算结果	SP	FTP	IAW
计算复杂度	—	O（N²）	N²·O（mn²）
P（0）计算时间/s	145.254 7	40.849 2	153.628 3
P（10）计算时间/s	194.110 0	82.050 9	211.257 7
P（20）计算时间/s	270.940 1	204.400 0	348.798 7
P（40）计算时间/s	421.762 9	632.969 2	960.758 4

References 19

1	LEE S， HONG D， KIM J， et al. Congestion-Aware Multi-Drone Delivery Routing Framework［J］. IEEE Transactions on Vehicular Technology， 2022， 71（9）： 9384-9396.
2	隋鑫，柳直. 无人机群出动，俄对乌展开报复［N］. 环球时报， 2023-08-03（016）.
	SUI Xin， LIU Zhi. Drone Swarm Deployed， Russia Retaliates Against Ukraine［N］. Global Times， 2023-08-03（016）.
3	于勇政，邵学辉，高仕博，等. 多平台协同跟踪最优构型设计［J］. 现代防御技术， 2023， 51（3）： 107-119.
	YU Yongzheng， SHAO Xuehui， GAO Shibo， et al. Optimal Configuration Design for Multi-Platform Collaborative Target Tracking［J］. Modern Defence Technology， 2023， 51（3）： 107-119.
4	LIU Yang， KILIÇ V， GUAN Jian， et al. Audio-Visual Particle Flow SMC-PHD Filtering for Multi-Speaker Tracking［J］. IEEE Transactions on Multimedia， 2020， 22（4）： 934-948.
5	KROPFREITER T， MEYER F， HLAWATSCH F. An Efficient Labeled/Unlabeled Random Finite Set Algorithm for Multiobject Tracking［J］. IEEE Transactions on Aerospace and Electronic Systems， 2022， 58（6）： 5256-5275.
6	VO B N， MA W K. The Gaussian Mixture Probability Hypothesis Density Filter［J］. IEEE Transactions on Signal Processing， 2006， 54（11）： 4091-4104.
7	YI Wei， LI Guchong， BATTISTELLI G. Distributed Multi-Sensor Fusion of PHD Filters with Different Sensor Fields of View［J］. IEEE Transactions on Signal Processing， 2020， 68： 5204-5218.
8	LIU Ben， THARMARASA R， JASSEMI R， et al. RFS-Based Multiple Extended Target Tracking with Resolved Multipath Detections in Clutter［J］. IEEE Transactions on Intelligent Transportation Systems， 2023， 24（10）： 10400-10409.
9	JAVAID S， SAEED N， QADIR Z， et al. Communication and Control in Collaborative UAVs： Recent Advances and Future Trends［J］. IEEE Transactions on Intelligent Transportation Systems， 2023， 24（6）： 5719-5739.
10	CORMACK D， HOPGOOD J R. Message Passing and Hierarchical Models for Simultaneous Tracking and Registration［J］. IEEE Transactions on Aerospace and Electronic Systems， 2021， 57（3）： 1524-1537.
11	MUNOZ-MARTIN J F， BOSCH-LLUIS X， RODRIGUEZ-ALVAREZ N， et al. Calibration Strategy for Compact Polarimetric GNSS-R Instruments［J］. IEEE Transactions on Geoscience and Remote Sensing， 2023， 61： 1-13.
12	LI Guchong， YI Wei， LI Suqi， et al. Asynchronous Multi-Rate Multi-Sensor Fusion Based on Random Finite Set［J］. Signal Processing， 2019， 160： 113-126.
13	LI Ruoyun， ZHANG Yuxi， SUN Jinping. Active and Passive Radar Target Fusion Recognition Method Based on Bayesian Network［C］∥2022 15th International Congress on Image and Signal Processing， BioMedical Engineering and Informatics （CISP-BMEI）. Piscataway： IEEE， 2022： 1-5.
14	QIU Lei， YANG Jun， FAN Yize. A Monopulse Radar Anti-Jamming Method Based on Labeled GM-PHD［C］∥2022 IEEE 2nd International Conference on Power， Electronics and Computer Applications （ICPECA）. Piscataway： IEEE， 2022： 98-101.
15	YANG Jiaye， LI Wenxin， MALLICK M， et al. Fusion of Asynchronous Radar and Infrared Sensors Data on a Moving Platform Using the PHD Filter［C］∥2023 IEEE Radar Conference. Piscataway： IEEE， 2023： 1-6.
16	HAN Xiaofei， HE Huafeng， ZHANG Qi， et al. Suppression of Deception-False-Target Jamming for Active/Passive Netted Radar Based on Position Error［J］. IEEE Sensors Journal， 2022， 22（8）： 7902-7912.
17	刘树东，梁婷蓉，王燕，等. 基于多模态信息融合的水下移动目标定位［J］. 导航定位学报， 2022， 10（3）： 14-24.
	LIU Shudong， LIANG Tingrong， WANG Yan， et al. Underwater Moving Target Localization Based on Multi-Modal Information Fusion［J］. Journal of Navigation and Positioning， 2022， 10（3）： 14-24.
18	卢锦，马令坤，吕春玲，等. 基于代价参考粒子滤波器组的多目标检测前跟踪算法［J］. 自动化学报， 2024， 50（4）： 851-861.
	LU Jin， MA Lingkun， Chunling LÜ， et al. A Multi-Target Track-Before-Detect Algorithm Based on Cost-Reference Particle Filter Bank［J］. Acta Automatica Sinica， 2024， 50（4）： 851-861.
19	袁溆东，雒梅逸香，王智超，等. 无人机载MiniSAR实时成像处理GPU异步优化［J］. 上海航天（中英文）， 2023， 40（4）： 15-24.
	YUAN Xudong， yixiang LUOMEI， WANG Zhichao， et al. GPU Asynchronous Optimization for UAV-Borne MiniSAR Real-Time Imaging Processing［J］. Aerospace Shanghai（Chinese & English）， 2023， 40（4）： 15-24.