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

ZHAO Ziwen; CHEN Hui; LIAN Feng; ZHANG Guanghua; ZHANG Wenxu

doi:10.11999/JEIT241139

Volume 47 Issue 8

Aug. 2025

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Article Navigation > Journal of Electronics & Information Technology > 2025 > 47(8): 2724-2735

ZHAO Ziwen, CHEN Hui, LIAN Feng, ZHANG Guanghua, ZHANG Wenxu. Multiple Maneuvering Target Poisson Multi-Bernoulli Mixture Filter for Gaussian Process Cognitive Learning[J]. Journal of Electronics & Information Technology, 2025, 47(8): 2724-2735. doi: 10.11999/JEIT241139

Citation:

ZHAO Ziwen, CHEN Hui, LIAN Feng, ZHANG Guanghua, ZHANG Wenxu. Multiple Maneuvering Target Poisson Multi-Bernoulli Mixture Filter for Gaussian Process Cognitive Learning[J]. Journal of Electronics & Information Technology, 2025, 47(8): 2724-2735. doi: 10.11999/JEIT241139

Citation:

ZHAO Ziwen, CHEN Hui, LIAN Feng, ZHANG Guanghua, ZHANG Wenxu. Multiple Maneuvering Target Poisson Multi-Bernoulli Mixture Filter for Gaussian Process Cognitive Learning[J]. Journal of Electronics & Information Technology, 2025, 47(8): 2724-2735. doi: 10.11999/JEIT241139

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

doi: 10.11999/JEIT241139 cstr: 32379.14.JEIT241139

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

Received Date: 2024-12-27
Rev Recd Date: 2025-07-11

Available Online: 2025-07-25

Publish Date: 2025-08-27

Abstract

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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References(38)

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