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，提出了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(Interactive Multiple Model Gamma Box Particle δ- Generalized Labeled Multi-Bernoulli, 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 have similar motion patterns and exhibit certain collective motion characteristics are often referred to as group targets. Dense group targets, characterized by a large number of closely spaced individuals, suffer from poor measurement resolvability, severe measurement overlap, and frequent target disappearance and reappearance, making it difficult to establish stable tracks for individual targets within the group. Therefore, such groups are typically treated as a whole to jointly estimate the kinematic state of their centroid and their extended shape. To enhance the tracking accuracy and computational efficiency for multiple maneuvering group targets under nonlinear measurements, an interacting multiple model group box-particle δ-generalized labeled multi-Bernoulli (IMM-GBP-δ-GLMB) algorithm is proposed. The tracking efficiency under nonlinear measurements is improved through the box particle filter (BPF) method. By improving the likelihood function of the GPB algorithm and introducing the IMM algorithm, the tracking capability for the extended shape and the centroid kinematic state of group targets is respectively enhanced, and the tracking accuracy of the algorithm is improved. Finally, by integrating with the GLMB filter, the tracking of multiple maneuvering group targets with unknown number is achieved. Methods To address the limitation of existing algorithms, which primarily capture the area-based overlap relationship between the predicted extended state of group targets and the measurement distribution while neglecting shape similarity, the likelihood function of the BPF is modified. The improved algorithm achieves higher prediction accuracy by incorporating geometric parameters — such as the semi-major axis, semi-minor axis, and inclination angle — into the likelihood function, thereby enhancing the modeling of similarity between the predicted extended state and the measurement distribution. This is particularly beneficial in scenarios involving maneuvering group targets, where the inclination angle of the extended shape changes frequently as the group maneuvers. Based on modeling group motion with the IMM, a model index is appended to the kinematic state of each box particle’s centroid. By jointly estimating the model index and the centroid kinematic state in each iteration of the algorithm, we realize tracking of the mode transitions of individual box particles, which further improves tracking accuracy. Finally, we embed the improved IMM-GBP filter into the labeled random finite set framework and derive the IMM-GBP-δ-GLMB algorithm, which enables effective tracking of multiple maneuvering group targets. Results and Discussions Simulation experiments are conducted to compare the proposed algorithm (IMM-GBP-δ-GLMB) with the IMM sequential Monte Carlo δ-GLMB (IMM-SMC-δ-GLMB) filter. While comparable estimation accuracy in terms of centroid state, extended state, measurement rate, and target number for multiple group targets is maintained, emphasis is placed on computational efficiency. In the given simulation scenario, the proposed algorithm achieves a 3.8-fold improvement in timeliness, at the cost of a loss of about 8.5% in tracking accuracy. For the 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, showing good temporal robustness to increasing group target numbers. Hence, the proposed algorithm has strong practical value. Conclusions This paper addresses the tracking problem of multiple maneuvering group targets under nonlinear measurement conditions by proposing the IMM-GBP-δ-GLMB algorithm. The main contributions are as follows: (1) By improving the likelihood function of the BPF, we enhance the algorithm's ability to measure the similarity between the target's extended shape and the measurement distribution, which in turn improves the tracking accuracy of the group target state. (2) By labeling the motion model for each box particle, we track the transition of the target's motion state during the filtering process. This allows the filter to achieve higher tracking accuracy with fewer box particles, thereby improving computational efficiency. (3) Integrating the IMM-GBP method into the δ-GLMB framework yields the final IMM-GBP-δ-GLMB filter and realizes effective tracking of multiple maneuvering group targets. -
表 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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