高斯过程认知学习的多机动目标泊松多伯努利混合滤波器

赵子文; 陈辉; 连峰; 张光华; 张文旭

doi:10.11999/JEIT241139

高斯过程认知学习的多机动目标泊松多伯努利混合滤波器

doi: 10.11999/JEIT241139 cstr: 32379.14.JEIT241139

1.
兰州理工大学自动化与电气工程学院兰州 730050
2.
西安交通大学自动化科学与工程学院西安 710049

基金项目: 国家自然科学基金 (62163023, 61873116, 62366031, 62363023)，甘肃省基础研究创新群体(25JRRA058)，中央引导地方科技发展资金项目(25ZYJA040)，甘肃省重点人才项目(2024RCXM86)，甘肃省军民融合发展专项资金(本基金无项目编号)

详细信息

作者简介:
赵子文：男，博士生，研究方向为多目标跟踪技术

陈辉：男，教授，博士生导师，博士，研究方向为多目标跟踪、数据融合、最优控制等

连峰：男，教授，博士生导师，博士，研究方向为目标跟踪、信息融合与传感器管理

张光华：男，副教授，博士生导师，博士，研究方向为信息融合与目标跟踪

张文旭：男，副教授，硕士生导师，博士，研究方向为深度强化学习、智能决策与数据挖掘和机器人技术

通讯作者:
陈辉　chenh@lut.edu.cn

中图分类号: TN911.7; TP274
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- 文章访问数: 127
- HTML全文浏览量: 66
- PDF下载量: 9
- 被引次数: 0
出版历程
- 收稿日期: 2024-12-27
- 修回日期: 2025-07-11
- 网络出版日期: 2025-07-25
- 刊出日期: 2025-08-27

Multiple Maneuvering Target Poisson Multi-Bernoulli Mixture Filter for Gaussian Process Cognitive Learning

1.
School of Automation and Electrical Engineering, Lanzhou University of Technology, Lanzhou 730050, China
2.
School of Automation Science and Engineering, Xi’an Jiaotong University, Xi’an 710049, China

Funds: The National Natural Science Foundation of China (62163023, 61873116, 62366031, 62363023), Gansu Provincial Basic Research Innovation Group of China (25JRRA058), The Central Government’s Funds for Guiding Local Science and Technology Development of China (25ZYJA040), Gansu Provincial Key Talent Project of China (2024RCXM86), Gansu Provincial Special Fund for Military-Civilian Integration Development of China

摘要

摘要: 针对复杂不确定环境下的多机动目标跟踪(MMTT)问题，该文提出一种基于高斯过程(GP)数据驱动的多目标跟踪方法。GP作为一种非参数贝叶斯方法，可通过有限样本灵活推断无限维函数，更能够灵活地自适应复杂多变的目标机动模式。通过GP算法学习多机动目标不确定的运动与观测模型，能有效克服传统多模型(MM)方法中因预设模型过多或模型失配所导致的性能退化问题。然后，利用泊松多伯努利混合(PMBM)建立多目标跟踪滤波的共轭先验递推结构，并使用GP学习未知的多目标动力学和观测模型，从而最终提出高斯过程多机动目标PMBM滤波器。仿真结果表明，该方法在复杂多变的MMTT任务中展现出较高的跟踪精度，验证了其在处理MMTT问题上的有效性和鲁棒性。
- 多机动目标跟踪 /
- 数据驱动 /
- 高斯过程 /
- 泊松多伯努利混合
Abstract: Objective Multiple Maneuvering Target Tracking (MMTT) remains a critical yet challenging problem in radar signal processing and sensor fusion, particularly under complex and uncertain conditions. The primary difficulty arises from the unpredictable or highly dynamic nature of target motion. Conventional model-based methods, especially Multiple Model (MM) approaches, rely on predefined motion models to accommodate varying target behaviors. However, these methods face limitations, including sensitivity to initial parameter settings, high computational cost due to model switching, and degraded performance when actual target behavior deviates from the assumed model set. To address these limitations, this study proposes a data-driven MMTT method that combines Gaussian Process (GP) learning with the Poisson Multi-Bernoulli Mixture (PMBM) filter to improve robustness and tracking accuracy in dynamic environments without requiring extensive model assumptions. Methods The proposed method exploits the data-driven modeling capability of GP, a non-parametric Bayesian inference approach that learns high-dimensional, nonlinear function mappings from limited historical data without specifying explicit functional forms. In this study, GP models both the state transition and observation processes of multi-target systems, reducing the dependence on predefined motion models. During the offline phase, historical target trajectories and sensor measurements are collected to build a training dataset. The squared exponential kernel is selected for its smoothness and infinite differentiability, which effectively captures the continuity and dynamic characteristics of target state evolution. GP hyperparameters, including length scale, signal variance, and observation noise variance, are jointly optimized by maximizing the log-marginal likelihood, ensuring generalization and expressiveness in complex environments. In the online filtering phase, the trained GP models are incorporated into the PMBM filter, forming a recursive GP-PMBM filtering structure. Within this framework, the PMBM filter employs a Poisson point process to represent undetected targets and a multi-Bernoulli mixture to characterize the posterior state distribution of detected targets. During the prediction step, the GP-derived nonlinear state transition model is propagated using the Cubature Kalman Filter (CKF). In the update step, the GP-learned observation model refines state estimates, enhancing both tracking accuracy and robustness. Results and Discussions Extensive simulation experiments under two different MMTT scenarios validate the effectiveness and performance advantages of the proposed method. In Scenario 1, a moderate 2D surveillance environment with clutter and a varying number of targets is constructed. The GP-PMBM filter significantly outperforms existing methods, including LSTM-PMBM, MM-PMBM, MM-GLMB, and MM-PHD filters, based on the Generalized Optimal Sub-Pattern Assignment (GOSPA) metric (Fig. 3). In addition, the GP-PMBM filter achieves the lowest standard deviation in cardinality estimation, demonstrating high accuracy and stability (Fig. 4). Further experiments under different monitoring conditions confirm the robustness of GP-PMBM. When clutter rates vary, the GP-PMBM filter consistently achieves the lowest average GOSPA error, reflecting strong stability under interference (Fig. 5). As detection probability decreases, most algorithms show significant degradation in accuracy. However, GP-PMBM maintains superior tracking performance, achieving the lowest GOSPA distance across all detection conditions (Fig. 6). In Scenario 2, target motion becomes more complex, with increased maneuverability and higher–frequency birth–death dynamics. Despite these challenges, the GP-PMBM filter maintains superior tracking performance, even under highly maneuverable conditions and frequent target appearance and disappearance (Fig. 9, Fig. 10). Conclusions This study proposes a novel GP-PMBM filtering framework for MMTT in complex environments. By integrating the data-driven learning capability of the GP with the PMBM filter, the proposed method addresses the limitations of conventional model-based tracking approaches. The GP-PMBM filter automatically learns unknown motion and observation models from historical data, eliminating the dependence on predefined model sets and significantly improving adaptability. Simulation results confirm that the GP-PMBM filter achieves superior tracking accuracy, improved cardinality estimation, and enhanced robustness under varying clutter levels and detection conditions. These results indicate that the proposed method is well-suited for environments characterized by frequent maneuvering changes and uncertain target behavior. Future work will focus on extending the GP-PMBM framework to multi-maneuvering extended target tracking tasks to address more challenging scenarios.
- Multi-maneuvering target tracking /
- Data-driven /
- Gaussian Process (GP) /
- Poisson Multi-Bernoulli Mixture (PMBM)

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图 2 跟踪结果

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图 1 多机动目标真实轨迹

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图 3 GOSPA堆叠面积

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图 4 多机动目标势估计

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图 5 不同杂波条件下的平均GOSPA

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图 6 不同检测概率条件下的平均GOSPA

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图 7 场景2中多机动目标真实轨迹

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图 8 场景2中跟踪结果

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图 9 场景2中势估计分条热度

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图 10 场景2中GOSPA误差

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表 1 目标初始状态和存活时间

目标	初始状态 (m, v/s, m, v/s)	存活时间 (s)
1	$ {\left[ {\begin{array}{*{20}{c}} { - 300}&0&{100}&0 \end{array}} \right]^{\rm T}} $	1～20
2	$ {\left[ {\begin{array}{*{20}{c}} {500}&0&{400}&0 \end{array}} \right]^{\rm T}} $	3～30
3	$ {\left[ {\begin{array}{*{20}{c}} {50}&0&{ - 600}&0 \end{array}} \right]^{\rm T}} $	5～30
4	$ {\left[ {\begin{array}{*{20}{c}} { - 800}&0&{ - 400}&0 \end{array}} \right]^{\rm T}} $	10～35
5	$ {\left[ {\begin{array}{*{20}{c}} {400}&0&{500}&0 \end{array}} \right]^{\rm T}} $	15～65
6	$ {\left[ {\begin{array}{*{20}{c}} { - 500}&0&{600}&0 \end{array}} \right]^{\rm T}} $	18～65
7	$ {\left[ {\begin{array}{*{20}{c}} {100}&0&{200}&0 \end{array}} \right]^{\rm T}} $	50～70
8	$ {\left[ {\begin{array}{*{20}{c}} {300}&0&{ - 350}&0 \end{array}} \right]^{\rm T}} $	55～75
9	$ {\left[ {\begin{array}{*{20}{c}} {700}&0&{ - 800}&0 \end{array}} \right]^{\rm T}} $	60～80

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