A Multiple Extended Target Generalized Labeled Multi-Bernoulli Filter Based on Joint Likelihood Function
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摘要: 高分辨率雷达监视系统可观测到区域内不同形状的多个扩展目标，可靠的形状估计有利于提高扩展目标跟踪性能，并可作为战场态势评估的重要依据。该文针对不同形状多扩展目标跟踪问题，提出一种基于联合似然函数的广义标签多伯努利(JL-GLMB)滤波器，可实现目标数目、航迹以及形状的精确估计。首先，将目标形状建模为星凸集，并利用非线性量测变换滤波器更新GLMB分布中的高斯分量，有效提高扩展目标状态估计精度。然后，通过对数加权融合策略，构造联合似然函数，综合衡量扩展目标和量测单元之间的相似程度。最后，基于吉布斯采样，提出快速计算扩展目标状态后验概率密度的方法，有效提高数据关联的准确率和计算效率。仿真实验结果表明，所提滤波器能够有效估计不同形状的多扩展目标状态，且在杂波环境下具有稳定的势估计。Abstract: High-resolution radar systems monitor multiple extended targets with different shapes in a surveillance area. Reliable shapes estimation can effectively improve tracking performance and are crucial to battle-field situation evaluations. In this paper, a Joint Likelihood based Generalized Labeled Multi-Bernoulli (JL-GLMB) filter is proposed to estimate accurately the number of targets, target tracks, and target shapes. Firstly, the extended target is modeled as a star-convex set, and Gaussian components in the GLMB density are updated by the measurement transformation filter to improve the accuracy of state estimation. Then, a joint likelihood function is constructed by log-weighted fusion strategy to measure comprehensively the similarity between extended target and measurement cell. Finally, a fast approximation method for posterior probability density is proposed based on Gibbs sampling, which improves the accuracy and efficiency of the data association. Simulation results show that the proposed algorithm can effectively estimate multiple extended target states of different shapes, and provide stable cardinality estimation in the clutter environment compared to traditional multiple extended target tracking.
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算法1 吉布斯采样算法 输入：$ {\gamma ^{(1)}},{T_{\text{G}}},\eta ({\gamma _i}) $ 输出：$ {\gamma ^{(1)}},{\gamma ^{(2)}}, \cdots ,{\gamma ^{({T_{\text{G}}})}} $ 初始化：$ c = [ - 1,0, \cdots ,|{\mathcal{U}}({{\mathbf{Z}}_k})|] $; $ \hat \eta = [\eta ( - 1),\eta (0), \cdots ,\eta (|{\mathcal{U}}({{\mathbf{Z}}_k})|)] $; for $ t = 2,3, \cdots ,{T_{\text{G}}} $ do $ {\gamma ^{(t)}} = [{\text{ }}] $; for $m = 1,2, \cdots ,|{{\boldsymbol{\varXi}} _{k - 1} }| + |{ {\mathbf{B} }_k}|$ do for $ j = 1,2, \cdots ,|{\mathcal{U}}({{\mathbf{Z}}_k})| $ do $ {\hat \eta _m}(j) = {\eta _m}(j) $$(1 - {1_{\{ \gamma _{1:m - 1}^{(t)},\gamma _{m + 1:|{{\boldsymbol{\varXi}} _{k - 1} }| + |{ {\mathbf{B} }_k}|}^{(t - 1)}\} } }(j))$; end for $ \gamma _m^{(t)} \sim {\text{Categorical}}(c,{\hat \eta _m}) $; end for ${\gamma ^{(t)} } = [\gamma _1^{(t)},\gamma _2^{(t)}, \cdots ,\gamma _{|{\varXi _{k - 1} }| + |{ {\mathbf{B} }_k}|}^{(t)}]$; end for 
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表 1 不同杂波数目下，GPR-GLMB和JL-GLMB滤波器跟踪性能对比(GPR-GLMB/JL-GLMB)
杂波数目 0 50 100 150 200 OSPA距离 14.096 8/4.335 7 16.660 1/4.459 5 19.272 8/4.594 5 21.759 7/4.701 5 24.350 1/4.830 6 位置误差 6.965 0/0.012 8 7.568 7/0.013 2 8.179 7/0.013 3 8.756 7/0.014 0 9.340 3/0.014 6 形状误差 10.807 8/8.154 2 11.091 9/8.181 5 11.255 9/8.210 8 11.435 0/8.278 2 11.644 1/8.297 5 势误差 1.290 0/0.186 0 3.365 8/0.327 5 5.421 5/0.469 0 7.493 6/0.604 2 9.553 0/0.842 0
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