Prior Checking and Moving Horizon Smoothing for Improved Particle Filtering

Abstract

Particle filtering, also known as sequential Monte Carlo (SMC) sampling, has been successfully applied to general state−space models for Bayesian inference. Being a simulation method, its performance relies to some extent on the generated samples or particles. For a poor initial guess a large fraction of particles is usually less representative of the underlying state’s distribution and could even cause SMC to diverge. In this paper, an intuitive statistic, predictive density is proposed to monitor the particles’ performance. When below a statistically controlled threshold value, our approach triggers smoothing for obtaining a better estimate of the initial state in the case of a poor prior. We find that combining a moving horizon smoother with SMC is very effective for recovering from a poor prior and develop an integrated practical approach that combines these two powerful tools.