A proof of uniform convergence over time for a distributed particle filter

TL;DR

This paper proves that a specific distributed particle filter converges uniformly over time under certain conditions, ensuring bounded errors with fixed computational resources, and validates these findings through simulations.

Contribution

It provides a rigorous proof of uniform convergence for a distributed particle filter based on a non-proportional weight-allocation scheme, addressing a gap in theoretical understanding.

Findings

Distributed PF maintains bounded errors over time.

Simulations confirm negligible performance loss compared to centralized filters.

Key assumptions of the theoretical analysis are empirically validated.

Abstract

Distributed signal processing algorithms have become a hot topic during the past years. One class of algorithms that have received special attention are particles filters (PFs). However, most distributed PFs involve various heuristic or simplifying approximations and, as a consequence, classical convergence theorems for standard PFs do not hold for their distributed counterparts. In this paper, we analyze a distributed PF based on the non-proportional weight-allocation scheme of Bolic {\em et al} (2005) and prove rigorously that, under certain stability assumptions, its asymptotic convergence is guaranteed uniformly over time, in such a way that approximation errors can be kept bounded with a fixed computational budget. To illustrate the theoretical findings, we carry out computer simulations for a target tracking problem. The numerical results show that the distributed PF has a negligible performance loss (compared to a centralized filter) for this problem and enable us to empirically validate the key assumptions of the analysis.