重尾噪声环境下的自适应TPMBM滤波器

doi:10.12305/j.issn.1001-506X.2025.09.04

摘要/Abstract

摘要：

针对未知重尾噪声统计特性的目标跟踪问题，提出基于伽马学生t分布逆威舍特的轨迹泊松多伯努利混合（trajectory Poisson multi-Bernoulli mixture，TPMBM）滤波算法。该算法利用学生t分布和逆威舍特分布对噪声和扩展目标扩展状态进行建模，并将多元多重滤波器（multivariate multiple filter，MMF）嵌入到TPMBM滤波器中以估计新息特征、自适应调整噪声自由度和尺度矩阵；并采用多窗口融合技术进一步提高MMF的自适应估计能力。仿真结果表明，与现有算法相比所提算法的跟踪精度、质心误差和交并比（intersection over union，IOU）形状拟合度均表现最佳，质心误差降低了15%，IOU形状拟合度提升了10%。在重尾噪声环境下具有更高的估计精度和鲁棒性。

关键词: 重尾噪声, 学生t分布, 扩展目标跟踪, 轨迹泊松多伯努利混合滤波

Abstract:

To address the target tracking problem of unknown heavy-tailed noise statistical characteristics, the trajectory Poisson multi-Bernoulli mixture filtering （TPMBM） algorithm based on Gamma student’s t-distribution inverse Wishar is proposed. The algorithm uses student’s t-distribution and inverse Wishart distribution to model the extended state of noise and extended target, and embeds multivariate multiple filter （MMF） into the TPMBM filter to estimate innovative characteristics, adaptively adjusts the noise degree of freedom and scale matrix. Multi window fusion technology is used to further improve the adaptive estimation ability of MMF. The simulation results demonstrate that, compared with existing algorithms, the proposed algorithm exhibits the best performance in tracking accuracy, centroid error, and intersection over union （IOU） shape fitting. The proposed algorithm reduces the centroid error by 15% and improves the IOU shape fitting by 10%. It also demonstrates higher estimation accuracy and robustness in the influence of noise in heavy-tailed noise environments.

Key words: heavy-tail noise, student’s t-distribution, extended target tracking, trajectory Poisson multi-Bernoulli mixture （TPMBM） filtering

中图分类号:

TN 953

李翠芸, 赵泽宇, 张双武. 重尾噪声环境下的自适应TPMBM滤波器[J]. 系统工程与电子技术, 2025, 47(9): 2808-2817.

Cuiyun LI, Zeyu ZHAO, Shuangwu ZHANG. Adaptive TPMBM filter in heavy-tailed noise environment[J]. Systems Engineering and Electronics, 2025, 47(9): 2808-2817.

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目标	目标初始运动状态	存活时间/s
1	$ {{\boldsymbol{x}}_1} = {[ - 200\;{\mathrm{m}}, - 200\;{\mathrm{m}},5.2\;{\mathrm{m/s}},4.87\;{\mathrm{m/s}}]^{\mathrm{T}}} $	$ {t_1} \in [5,80] $
2	$ {{\boldsymbol{x}}_2} = {[ - 200\;{\mathrm{m}},200\;{\mathrm{m}},6.2\;{\mathrm{m/s}}, - 5.38\;{\mathrm{m/s}}]^{\mathrm{T}}} $	$ {t_2} \in [15,65] $
3	$ {{\boldsymbol{x}}_3} = {[200\;{\mathrm{m}}, - 200\;{\mathrm{m}}, - 6.82\;{\mathrm{m/s}},6.2\;{\mathrm{m/s}}]^{\mathrm{T}}} $	$ {t_3} \in [15,70] $
4	$ {{\boldsymbol{x}}_4} = {[200\;{\mathrm{m}},200\;{\mathrm{m}}, - 5.63\;{\mathrm{m/s}}, - 6.32\;{\mathrm{m/s}}]^{\mathrm{T}}} $	$ {t_4} \in [20,60] $
5	$ {{\boldsymbol{x}}_5} = {[ - 300\;{\mathrm{m}},175\;{\mathrm{m}},7\;{\mathrm{m/s}}, - 6.32\;{\mathrm{m/s}}]^{\mathrm{T}}} $	$ {t_5} \in [25,80] $

噪声类型	噪声特性
$ {w}_i$	$\begin{gathered}{\mathrm{N}}\left(0,\left\|\sin (k) \boldsymbol{R}_k\right\|\right) \\p_{{\mathrm{m o}}}=0.05\end{gathered}$
$ v_i$	$\begin{gathered}N\left(0,4 k \boldsymbol{R}_k\right) \\p_{{\mathrm{m o}}}=0.05\end{gathered}$

滤波器	平均误差/m
GGIW-TPMBM	10.906 9
GSTIW-TPMBM	6.966 9
MMF-GSTIW-TPMBM	5.028 4

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