Independent Resampling Sequential Monte Carlo Algorithms

TL;DR

This paper introduces an independent resampling scheme for Sequential Monte Carlo algorithms, improving particle diversity and estimation accuracy, especially in challenging high-dimensional or informative measurement scenarios.

Contribution

It proposes a novel independent resampling method that replaces traditional bootstrap resampling, providing theoretical analysis and a new particle filtering algorithm with enhanced performance.

Findings

Independent resampling yields more diverse particles.

The new algorithm demonstrates improved estimation accuracy.

Simulation results validate the method's effectiveness.

Abstract

Sequential Monte Carlo algorithms, or Particle Filters, are Bayesian filtering algorithms which propagate in time a discrete and random approximation of the a posteriori distribution of interest. Such algorithms are based on Importance Sampling with a bootstrap resampling step which aims at struggling against weights degeneracy. However, in some situations (informative measurements, high dimensional model), the resampling step can prove inefficient. In this paper, we revisit the fundamental resampling mechanism which leads us back to Rubin's static resampling mechanism. We propose an alternative rejuvenation scheme in which the resampled particles share the same marginal distribution as in the classical setup, but are now independent. This set of independent particles provides a new alternative to compute a moment of the target distribution and the resulting estimate is analyzed through a CLT. We next adapt our results to the dynamic case and propose a particle filtering algorithm based on independent resampling. This algorithm can be seen as a particular auxiliary particle filter algorithm with a relevant choice of the first-stage weights and instrumental distributions. Finally we validate our results via simulations which carefully take into account the computational budget.