Fusion of Information in Multiple Particle Filtering in the Presence of Unknown Static Parameters

TL;DR

This paper introduces a fusion strategy for multiple particle filtering that enables sharing of unknown static parameters, improving estimation accuracy and efficiency in high-dimensional systems with separable states and observations.

Contribution

It proposes a principled fusion approach for sharing static parameters in MPF, addressing a gap in existing methods for high-dimensional systems.

Findings

Fusion strategy improves estimation accuracy.

Fewer time steps needed for reliable estimates.

Outperforms existing algorithms in simulations.

Abstract

An important and often overlooked aspect of particle filtering methods is the estimation of unknown static parameters. A simple approach for addressing this problem is to augment the unknown static parameters as auxiliary states that are jointly estimated with the time-varying parameters of interest. This can be impractical, especially when the system of interest is high-dimensional. Multiple particle filtering (MPF) methods were introduced to try to overcome the curse of dimensionality by using a divide and conquer approach, where the vector of unknowns is partitioned into a set of subvectors, each estimated by a separate particle filter. Each particle filter weighs its own particles by using predictions and estimates communicated from the other filters. Currently, there is no principled way to implement MPF methods where the particle filters share unknown parameters or states. In this work, we propose a fusion strategy to allow for the sharing of unknown static parameters in the MPF setting. Specifically, we study the systems which are separable in states and observations. It is proved that optimal Bayesian fusion can be obtained for state-space models with non-interacting states and observations. Simulations are performed to show that MPF with fusion strategy can provide more accurate estimates within fewer time steps comparing to existing algorithms.