Comparison of Resampling Schemes for Particle Filtering

TL;DR

This paper compares different resampling methods in particle filtering, showing residual and stratified methods outperform multinomial resampling, while analyzing their large-sample behavior and establishing a CLT for residual resampling.

Contribution

It provides a comparative analysis of resampling schemes in particle filtering, highlighting the advantages of residual and stratified methods and deriving a CLT for residual resampling.

Findings

Residual and stratified resampling outperform multinomial resampling.

Systematic resampling does not always improve over multinomial.

A central limit theorem is established for residual resampling.

Abstract

This contribution is devoted to the comparison of various resampling approaches that have been proposed in the literature on particle filtering. It is first shown using simple arguments that the so-called residual and stratified methods do yield an improvement over the basic multinomial resampling approach. A simple counter-example showing that this property does not hold true for systematic resampling is given. Finally, some results on the large-sample behavior of the simple bootstrap filter algorithm are given. In particular, a central limit theorem is established for the case where resampling is performed using the residual approach.