A divide and conquer strategy for multinomial particle filter resampling

2026-04-01

AI Summary

This work addresses the inefficiency of multinomial resampling in particle filtering when the number of samples does not exceed the support size of the discrete distribution. To overcome this limitation, the authors propose an efficient multinomial resampling algorithm based on a divide-and-conquer strategy. By recursively partitioning the probability mass, the method substantially reduces computational complexity and is particularly well-suited for ensemble mixture models such as Gaussian mixture filters. Theoretical analysis and numerical experiments demonstrate that the proposed algorithm significantly outperforms two classical resampling approaches in both computational efficiency and sampling accuracy, offering an improved resampling solution for large-scale particle filtering applications.

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.

Problem

• particle filter
• resampling
• multinomial sampling
• computational complexity

Innovation

• divide and conquer
• multinomial resampling
• particle filter
• computational complexity
• ensemble mixture model