Path storage in the particle filter

TL;DR

This paper addresses efficient path storage in particle filters, presenting a theoretical memory bound and an algorithm, supported by numerical experiments, to optimize memory use in sequential Monte Carlo methods.

Contribution

It introduces a novel algorithm for storing particle filter paths with a proven memory bound, improving efficiency over existing methods.

Findings

Memory cost bounded by T + C N log N

Algorithm demonstrated with numerical experiments

Efficient path storage in particle filters

Abstract

This article considers the problem of storing the paths generated by a particle filter and more generally by a sequential Monte Carlo algorithm. It provides a theoretical result bounding the expected memory cost by $T + C N \log N$ where $T$ is the time horizon, $N$ is the number of particles and $C$ is a constant, as well as an efficient algorithm to realise this. The theoretical result and the algorithm are illustrated with numerical experiments.