A divide and conquer strategy for multinomial particle filter resampling

TL;DR

This paper introduces a novel multinomial resampling method for particle filters, especially effective when sample size is less than or equal to the distribution size, demonstrating improved efficiency and performance.

Contribution

A new multinomial resampling procedure tailored for cases with small sample sizes relative to the distribution, enhancing computational efficiency and accuracy.

Findings

Our approach outperforms existing multinomial sampling methods in complexity and accuracy.

Numerical experiments confirm the superiority of the proposed resampling method.

The method is particularly suited for ensemble mixture model filters like the Gaussian mixture filter.

Abstract

This work provides a new multinomial resampling procedure for particle filter resampling, focused on the case where the number of samples required is less than or equal to the size of the underlying discrete distribution. This setting is common in ensemble mixture model filters such as the Gaussian mixture filter. We show superiority of our approach with respect two of the best known multinomial sampling procedures both through a computational complexity analysis and through a numerical experiment.