基于轨迹测量的多目标滤波器，可精确跟踪多个目标运动路径。
Poisson multi-Bernoulli mixture filter for trajectory measurements
- 用轨迹集合建模传感器数据，通过PMBM密度传播目标状态
- 在双时间步窗口内实现闭式解，准确估计目标状态集
- 提出轻量替代方案，降低计算复杂度，适合实时系统
本文提出一种基于轨迹测量的泊松多伯努利混合（PMBM）滤波器，称为轨迹测量PMBM（TM-PMBM）滤波器。该滤波器在目标状态集合上维持一个PMBM后验密度，预测阶段生成过去两个时间步轨迹集合的PMBM密度，并利用轨迹测量集进行更新。更新后，将两步轨迹的联合后验边际化为当前时刻的目标状态集合的PMBM密度，从而提供闭式解，实现对每个时间窗口末尾目标状态集的估计。此外，通过在扩展空间中引入辅助变量并最小化Kullback-Leibler散度，推导出计算更轻量的泊松多伯努利（PMB）近似。仿真结果验证了所提滤波器的有效性与性能优势。
原文摘要 · Abstract (English)
This paper presents a Poisson multi-Bernoulli mixture (PMBM) filter for multi-target filtering based on sensor measurements that are sets of trajectories in the last two-time step window. The proposed filter, the trajectory measurement PMBM (TM-PMBM) filter, propagates a PMBM density on the set of target states. In prediction, the filter obtains the PMBM density on the set of trajectories over the last two time steps. This density is then updated with the set of trajectory measurements. After the update step, the PMBM posterior on the set of two-step trajectories is marginalised to obtain a PMBM density on the set of target states. The filter provides a closed-form solution for multi-target filtering based on sets of trajectory measurements, estimating the set of target states at the end of each time window. Additionally, the paper proposes computationally lighter alternatives to the TM-PMBM filter by deriving a Poisson multi-Bernoulli (PMB) density through Kullback-Leibler divergence minimisation in an augmented space with auxiliary variables. The performance of the proposed filters are evaluated in a simulation study.
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