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

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.

A preliminary version of this work was presented at the IEEE SAM 2014 workshop. This work has been accepted for publication in Elsevier Signal Processing

References in corpus (3)

• On the role of interaction in sequential Monte Carlo algorithms
• Uniform observability of hidden Markov models and filter stability for unstable signals
• Uniform Time Average Consistency of Monte Carlo Particle Filters

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• A Survey of Monte Carlo Methods for Parameter Estimation
• Group Importance Sampling for Particle Filtering and MCMC
• Compressed Monte Carlo with application in particle filtering
• Parallelising Particle Filters with Butterfly Interactions
• Fluctuations, stability and instability of a distributed particle filter with local exchange