On the Convergence of Belief Propagation for Multipath Data Association in Target Tracking

2026-07-09

AI Summary

This study addresses the lack of convergence guarantees for belief propagation (BP) algorithms in multi-path data association (MPDA), where a single target generates multiple measurements via distinct paths, resulting in a tripartite association among targets, paths, and measurements. For the first time, this work establishes a rigorous convergence theory for BP in this setting. By leveraging graphical model inference and fixed-point analysis, it proves that the message update rules converge to a unique fixed point. Simulation results demonstrate that the proposed approach outperforms both single-scan and two-scan multiple hypothesis trackers in balancing accuracy and computational efficiency, thereby filling a critical gap in the theoretical understanding of BP algorithms under tripartite associations.

Abstract

Belief propagation (BP) is widely used for data association (DA) in target tracking. Existing convergence analyses of BP for DA address only the two-way correspondence between targets and measurements, where each target generates at most one measurement per scan. Multipath DA (MPDA) allows a single target to produce multiple measurements via distinct propagation paths, creating a three-way correspondence among targets, paths, and measurements, for which a complete convergence proof has not yet been provided. We provide such a proof for the BP updates in MPDA, establishing convergence to a unique fixed point. Simulations illustrate the convergence behavior of BP in MPDA and demonstrate a favorable accuracy--efficiency trade-off relative to both single-scan and two-scan variants of the multiple-detection multiple-hypothesis tracker.

Problem

• belief propagation
• data association
• multipath
• target tracking
• convergence

Innovation

• belief propagation
• multipath data association
• convergence proof
• target tracking
• three-way correspondence