Efficient Implementations of Extended Object PMBM Filters with Blocked Gibbs Sampling

2026-04-26

AI Summary

This work addresses the high computational complexity of data association in Poisson multi-Bernoulli mixture (PMBM) filters for extended object multi-target tracking by proposing an efficient approximate inference method based on an augmented state space. The approach introduces auxiliary variables to construct a joint posterior distribution and exploits its factorized structure to design a block Gibbs sampler. A collapsed Gibbs sampling variant is further developed by marginalizing Bernoulli existence variables to accelerate the initialization of new targets. Integrated with a Gamma Gaussian inverse-Wishart measurement model, the proposed method significantly reduces computational overhead during PMBM updates. Experimental results demonstrate that it achieves tracking accuracy comparable to particle belief propagation while substantially decreasing runtime.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Topic discovery and tracking
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

Abstract

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.

Problem

• extended object tracking
• data association
• PMBM filtering
• multiple target tracking
• Bayesian inference

Innovation

• blocked Gibbs sampling
• extended object tracking
• PMBM filter
• collapsed Gibbs sampling
• data association