Adapting the Number of Particles in Sequential Monte Carlo Methods through an Online Scheme for Convergence Assessment

TL;DR

This paper introduces an online method to assess convergence and adapt the number of particles in particle filters, improving approximation quality in real-time for state-space models.

Contribution

It presents a novel online convergence assessment technique and a simple scheme for dynamically adjusting the number of particles during filtering.

Findings

The method accurately assesses convergence in real-time.

The adaptive scheme improves filter performance on the Lorenz system.

The approach is theoretically rigorous and practically effective.

Abstract

Particle filters are broadly used to approximate posterior distributions of hidden states in state-space models by means of sets of weighted particles. While the convergence of the filter is guaranteed when the number of particles tends to infinity, the quality of the approximation is usually unknown but strongly dependent on the number of particles. In this paper, we propose a novel method for assessing the convergence of particle filters online manner, as well as a simple scheme for the online adaptation of the number of particles based on the convergence assessment. The method is based on a sequential comparison between the actual observations and their predictive probability distributions approximated by the filter. We provide a rigorous theoretical analysis of the proposed methodology and, as an example of its practical use, we present simulations of a simple algorithm for the dynamic and online adaption of the number of particles during the operation of a particle filter on a stochastic version of the Lorenz system.