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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2022, Vol. 56 Issue (5): 967-976    DOI: 10.3785/j.issn.1008-973X.2022.05.014
    
Robust cooperative target tracking under heavy-tailed non-Gaussian localization noise
Xiao-bo CHEN(),Ling CHEN,Shu-rong LIANG,Yu HU
Automotive Engineering Research Institute, Jiangsu University, Zhenjiang 212013, China
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Abstract  

The statistical properties of the localization data are unknown and the localization data are susceptible to outlier interference, which affects the cooperative target tracking performance. Aiming at the problem, a robust cooperative target tracking method for heavy-tailed non-Gaussian localization noise was proposed. It was assumed that the localization noise followed multivariate Student’s t-distribution and a joint Bayesian estimation model of target state and localization noise parameters was constructed. To overcome the difficulty of computing joint posterior distribution owing to the coupling of target state and noise distribution parameters, the variational Bayesian inference and the mean-field theory were applied to decouple the joint posterior distribution and convert the problem of joint estimation of target state and localization noise parameters into a optimization problem. Alternative optimization was implemented to achieve recursive estimation of system parameters. The proposed cooperative target tracking method was evaluated experimentally. Simulation results showed that when unknown outliers exist in localization data, the proposed algorithm has better tracking robustness.

Key words： cooperative target tracking      Student’s t-distribution      variational Bayesian inference      outlier noise      robustness     
Received: 05 June 2021      Published: 31 May 2022
CLC:  TP 301.6  
Fund:  国家自然科学基金资助项目(61773184)；国家重点研发计划资助项目(2018YFB0105000)；江苏省六大人才高峰高层次人才资助项目(JXQC-007)
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Xiao-bo CHEN
Ling CHEN
Shu-rong LIANG
Yu HU
Cite this article:

Xiao-bo CHEN,Ling CHEN,Shu-rong LIANG,Yu HU. Robust cooperative target tracking under heavy-tailed non-Gaussian localization noise. Journal of ZheJiang University (Engineering Science), 2022, 56(5): 967-976.

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https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2022.05.014     OR     https://www.zjujournals.com/eng/Y2022/V56/I5/967


重尾非高斯定位噪声下鲁棒协同目标跟踪

针对定位数据的统计特性未知且易受异常值干扰而影响协同目标跟踪性能的问题，提出一种重尾非高斯定位噪声下的鲁棒协同目标跟踪方法. 该方法假设定位噪声服从多元学生t-分布，建立联合估计目标状态与定位噪声参数的贝叶斯模型. 针对目标状态与噪声分布参数相互耦合而难以计算联合后验分布的问题，应用变分贝叶斯推断原理和平均场理论对后验分布进行解耦，将目标状态与定位噪声参数的联合后验分布估计问题转化为最优化问题，以交替优化的方式实现系统参数的在线递推估计. 对提出的协同目标跟踪方法进行测试. 仿真结果表明，当定位数据中存在未知的野值噪声时，提出的协同跟踪算法具有较好的鲁棒性.


关键词： 协同目标跟踪,  学生t-分布,  变分贝叶斯推断,  野值噪声,  鲁棒性 
Fig.1 Probability density function of Student’s t-distribution for different $ \lambda $ values
Fig.2 Illustration of translation and rotation of coordinate system
Fig.3 Probabilistic graph model of cooperative target tracking
Fig.4 Illustration of cooperative target tracking
Fig.5 Error comparison of different online tracking algorithms
算法 ARMSE
$ {\varphi _1} $/m $ {\chi _1} $/% $ {\varphi _2} $/(m·s?1) $ {\chi _2} $/%
KF-ST 0.185 01 ? 0.097 41 ?
EKF-CT 0.171 99 7.0 0.093 06 4.5
VB-CT 0.160 40 13.3 0.087 43 10.2
VB-RCT 0.152 80 17.4 0.083 61 14.2
Tab.1 Performance analysis of tracking error obtained by different algorithms
Fig.6 Position ARMSE in different outlier ratios
Fig.7 Schematic diagram of non-Gaussian distribution location noise of CV in different degrees of anomaly
Fig.8 Tracking errors of different algorithms when sampling outliers from different distributions
分布 异常程度 pARMSE/m
KF EKF-CT VB-CT VB-RCT
$S\left( { {\boldsymbol{v} }_k^2;{\boldsymbol{0}},{\boldsymbol A},15} \right)$ $ {\boldsymbol A} = 15{\boldsymbol{R}} $ 0.185 01 0.166 35 0.151 25 0.153 42
$ {\boldsymbol A} = 25{\boldsymbol{R}} $ 0.185 01 0.171 99 0.160 40 0.152 80
$ {\boldsymbol A} = 35{\boldsymbol{R}} $ 0.185 01 0.175 22 0.169 33 0.152 39
$U\left( { {\boldsymbol{v} }_k^2; - {\boldsymbol{a}},{\boldsymbol{a}}} \right)$ ${\boldsymbol{a}} = 15{\boldsymbol{R} }$ 0.187 60 0.167 49 0.148 83 0.155 28
${\boldsymbol{a}} = 30{\boldsymbol{R} }$ 0.187 60 0.174 86 0.158 82 0.154 78
${\boldsymbol{a}} = 45{\boldsymbol{R} }$ 0.187 60 0.178 31 0.164 19 0.154 12
$L\left( { {\boldsymbol{v} }_k^2;{\boldsymbol{0}},{\boldsymbol{b}}} \right)$ ${\boldsymbol{ b}} = 10{\boldsymbol{R} }$ 0.187 60 0.163 32 0.153 40 0.155 02
${\boldsymbol{b}} = 15{\boldsymbol{R} }$ 0.187 60 0.168 40 0.156 86 0.154 72
${\boldsymbol{b}} = 20{\boldsymbol{R} }$ 0.187 60 0.171 82 0.160 33 0.154 44
Tab.2 ARMSE of different algorithms when sampling outliers from different distributions
Fig.9 Position ARMSE under different forgetting factors
Fig.10 Variation of tracking errors with number of variational iterations
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