This paper shows that the Poisson multi-Bernoulli mixture (PMBM) density is a multi-target conjugate prior for general target-generated measurement distributions and arbitrary clutter distributions. That is, for this multi-target measurement model and the standard multi-target dynamic model with Poisson birth model, the predicted and filtering densities are PMBMs. We derive the corresponding PMBM filtering recursion. Based on this result, we implement a PMBM filter for point-target measurement models and negative binomial clutter density in which data association hypotheses with high weights are chosen via Gibbs sampling. We also implement an extended target PMBM filter with clutter that is the union of Poisson-distributed clutter and a finite number of independent clutter sources. Simulation results show the benefits of the proposed filters to deal with non-standard clutter.

翻译：本文证明了在通用目标生成测量分布与任意杂波分布条件下，泊松多伯努利混合密度具有多目标共轭先验性质。即针对该多目标测量模型及含泊松新生模型的标准多目标动态模型，预测密度与滤波密度均为PMBM形式。我们推导了相应的PMBM滤波递归公式。基于此成果，我们实现了针对点目标测量模型及负二项杂波密度的PMBM滤波器，其中采用吉布斯采样选取高权重数据关联假设。另外还实现了杂波由泊松分布杂波与有限独立杂波源联合构成的扩展目标PMBM滤波器。仿真结果表明，所提滤波器在处理非标准杂波场景时具有显著优势。