Box Particle Filter δ-GLMB Algorithm for Multiple Maneuvering Group Targets Tracking
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摘要: 针对非线性量测条件下的多机动群目标跟踪问题，该文提出一种基于交互式多模型的伽马箱粒子δ-广义标签多伯努利(IMM-GBP-δ-GLMB)算法。基于箱粒子滤波框架和区间分析理论，以区间覆盖代替多点概率近似，实现对量测不确定性和扩展状态的高效表示；通过改进似然函数和引入交互式多模型分别增强对群目标扩展外形和质心运动状态的跟踪能力，提升了算法的跟踪精度。最后，结合随机有限集理论推导了算法的δ-GLMB形式。仿真结果表明，所提算法以8.5%左右的跟踪精度代价，获得了3.8倍的时效性提升；对3个群目标和2个群目标的平均跟踪时间增长速度为原算法的96%，对群目标数量增加具有较好的时间鲁棒性，所提算法具有较好的实用价值。Abstract:
Objective Targets that move in a coordinated manner or show similar motion patterns are commonly referred to as group targets. Dense group targets contain many closely spaced individuals and often suffer from poor measurement resolvability, severe measurement overlap, and frequent target disappearance and reappearance. These factors make it difficult to establish stable tracks for individual targets within the group. Such groups are therefore usually treated as a whole to jointly estimate the kinematic state of the centroid and the extended shape. To improve tracking accuracy and computational efficiency for multiple maneuvering group targets under nonlinear measurements, an Interacting Multiple Model Gamma Box Particle δ-Generalized Labeled Multi-Bernoulli (IMM-GBP-δ-GLMB) algorithm is proposed. Tracking efficiency under nonlinear measurements is improved using the Box Particle Filter (BPF). The likelihood function of the GBP algorithm is improved, and the IMM algorithm is introduced to enhance tracking of the extended shape and centroid kinematic state of group targets. Finally, the method is integrated with the GLMB filter to track an unknown number of multiple maneuvering group targets. Methods Existing algorithms mainly describe the area-based overlap between the predicted extended state of group targets and the measurement distribution, but they do not fully capture shape similarity. To address this limitation, the likelihood function of the BPF is modified. Geometric parameters, including the semi-major axis, semi-minor axis, and inclination angle, are incorporated into the likelihood function. This improves the modeling of similarity between the predicted extended state and the measurement distribution. The modification is particularly useful for maneuvering group targets, because the inclination angle of the extended shape changes frequently during maneuvering. Based on IMM modeling of group motion, a model index is added to the centroid kinematic state of each box particle. The model index and centroid kinematic state are jointly estimated in each iteration, allowing mode transitions of individual box particles to be tracked and further improving tracking accuracy. The improved IMM-GBP filter is then embedded into the labeled random finite set framework, and the IMM-GBP-δ-GLMB algorithm is derived for effective tracking of multiple maneuvering group targets. Results and Discussions Simulation experiments are conducted to compare the proposed IMM-GBP-δ-GLMB algorithm with the IMM Sequential Monte Carlo δ-GLMB (IMM-SMC-δ-GLMB) filter. The proposed algorithm maintains comparable estimation accuracy for the centroid state, extended state, measurement rate, and number of targets, while improving computational efficiency. In the given simulation scenario, the proposed algorithm achieves a 3.8-fold improvement in timeliness, with an approximately 8.5% reduction in tracking accuracy. In scenarios with two and three group targets, the average tracking time growth rate of the proposed algorithm is 96% of that of the IMM-SMC-δ-GLMB filter. This result indicates good temporal robustness as the number of group targets increases. Therefore, the proposed algorithm has strong practical value. Conclusions This paper addresses the tracking of multiple maneuvering group targets under nonlinear measurement conditions by proposing the IMM-GBP-δ-GLMB algorithm. The main contributions are as follows: (1) The likelihood function of the BPF is improved to strengthen the measurement of similarity between the target extended shape and the measurement distribution, improving the tracking accuracy of group target states. (2) A motion model label is assigned to each box particle, and transitions in the target motion state are tracked during filtering. This allows the filter to achieve higher tracking accuracy with fewer box particles and improves computational efficiency. (3) The IMM-GBP method is integrated into the δ-GLMB framework to obtain the final IMM-GBP-δ-GLMB filter, which realizes effective tracking of multiple maneuvering group targets. -
1 群目标预测概率密度的主要计算流程
输入：$ \left\{{\varPi }\left({r}_{+}|r\right),{p}^{\left(\varsigma \right)}\left(\xi ,r,\ell\right),{p}_{\text{S}}\left(\cdot ,r,\ell\right)，\left[f\right]\left({\xi }_{+}|\cdot ,{r}_{+},\ell\right)\right\} $ 1. 输入交互 ①求解模型的预测概率密度 $ p_{\text{S}}^{(\varsigma )}\left({r}_{+},\ell\right)=\displaystyle\sum \limits_{r\in \mathcal{R}}{\varPi }\left({r}_{+}|r\right){p}^{\left(\varsigma \right)}\left(r,\ell\right) $ (56) ②模型的条件概率密度 $ p_{\text{S}}^{(\varsigma )}\left({r}_{+}|r,\ell\right)={\varPi }\left({r}_{+}|r\right){p}^{\left(\varsigma \right)}\left(r,\ell\right)/p_{\text{S}}^{(\varsigma )}\left({r}_{+},\ell\right) $ (57) ③混合估计 $ p_{}^{(\varsigma )}\left({\xi }_{0}|{r}_{+},\ell\right)=\displaystyle\sum \limits_{r\in \mathcal{R}}{p}^{\left(\varsigma \right)}\left(\xi |r,\ell\right)p_{\text{S}}^{(\varsigma )}\left({r}_{+}|r,\ell\right) $ (58) 2. 滤波器预测 $ \begin{aligned}p_{\text{S}}^{(\varsigma )}\left({\xi }_{+},{r}_{+},{\ell}_{+}\right)&=\frac{\left\langle {p}_{\text{S}}\left(\cdot ,r,\ell\right)\left[f\right]\left({\xi }_{+}|\cdot ,{r}_{+},\ell\right),p_{}^{(\varsigma )}\left(\cdot |{r}_{+},\ell\right)\right\rangle }{\left\langle {p}_{\text{S}}\left(\cdot ,r,\ell\right),p_{}^{(\varsigma )}\left(\cdot |{r}_{+},\ell\right)\right\rangle }\\&={\delta }_{\ell}\left({\ell}_{+}\right)p_{\text{S}}^{(\varsigma )}\left({r}_{+},{\ell}_{+}\right)p_{\text{S}}^{(\varsigma )}\left({\xi }_{+}|{r}_{+},{\ell}_{+}\right)\\&\approx{\delta }_{\ell}\left({\ell}_{+}\right)p_{\text{S}}^{(\varsigma )}\left({r}_{+},{\ell}_{+}\right)\displaystyle\sum \limits_{i=1}^{N\left({r}_{+},{\ell}_{+}\right)}\omega _{\text{S}}^{\left({r}_{+},{\ell}_{+},i\right)}{U}_{\left[\left.\xi _{\text{S} ,+}^{\left({\ell}_{+},i\right)}\right| {r}_{+}\right]}\left(\xi |r\right)\end{aligned} $ (59) 输出：联合新生目标的概率密度$ p_{\text{B}}^{(\varsigma )}\left({\xi }_{+},{r}_{+},{\ell}_{+}\right) $，得到$ p_{+}^{(\varsigma )}\left({\xi }_{+},{r}_{+},{\ell}_{+}\right) $。 
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