This paper considers multiple extended object tracking based on Poisson multi-Bernoulli mixture (PMBM) filtering, which gives the closed-form Bayesian solution for standard multiple extended object models with Poisson birth. To efficiently address the challenging extended object data association problem in PMBM filtering, we develop implementations of the extended object PMBM filter using blocked Gibbs sampling. By formulating the PMBM density on an augmented state space with auxiliary variables and leveraging the Poisson object measurement model, we first derive a joint posterior over potential objects, previous global hypotheses, and current measurement association variables, together with its corresponding factorization. This factorized representation leads to blocked Gibbs samplers that efficiently generate high-weight global hypotheses and thereby provide an efficient implementation of the PMBM update step. We further introduce a collapsed Gibbs sampling variant, in which the Bernoulli object existence variables are marginalized out, yielding higher sampling efficiency, especially for the initiation of newly detected objects. The proposed methods, implemented under the gamma Gaussian inverse-Wishart model, are compared with an extended object Poisson multi-Bernoulli filter based on particle belief propagation. Simulation results demonstrate that the proposed approaches achieve comparable tracking performance while requiring substantially less runtime.

翻译：本文研究基于泊松多伯努利混合（PMBM）滤波的多个扩展物体跟踪问题，该滤波为具有泊松新生机制的标准多扩展物体模型提供了闭式贝叶斯解。为有效解决PMBM滤波中极具挑战性的扩展物体数据关联问题，我们开发了基于分块吉布斯采样的扩展物体PMBM滤波器实现方法。通过定义带有辅助变量的增广状态空间上的PMBM密度，并利用泊松物体测量模型，我们首先推导出潜在物体、先前全局假设与当前测量关联变量的联合后验分布及其对应的因子分解形式。该因子化表示可构造分块吉布斯采样器，高效生成高权重全局假设，从而为PMBM更新步骤提供高效实现方案。我们进一步引入折叠吉布斯采样变体，通过边缘化伯努利物体存在变量，显著提升采样效率，尤其适用于新检测物体的初始化。在伽马高斯逆威沙特模型框架下实现所提方法，并与基于粒子置信传播的扩展物体泊松多伯努利滤波器进行对比。仿真结果表明，所提方法在实现相当跟踪性能的同时，大幅降低了运行时间开销。