Rao-Blackwellised Particle Filtering for Dynamic Bayesian Networks

TL;DR

This paper introduces Rao-Blackwellised particle filters (RBPFs) that leverage the structure of dynamic Bayesian networks to improve inference accuracy and efficiency over standard particle filters, demonstrated through applications in regression and robotics.

Contribution

The paper presents a novel approach combining particle filtering with exact marginalization via Rao-Blackwellisation to enhance performance in dynamic Bayesian networks.

Findings

RBPFs outperform standard PFs in accuracy.

RBPFs are effective in non-stationary online regression.

RBPFs improve robot localization and mapping.

Abstract

Particle filters (PFs) are powerful sampling-based inference/learning algorithms for dynamic Bayesian networks (DBNs). They allow us to treat, in a principled way, any type of probability distribution, nonlinearity and non-stationarity. They have appeared in several fields under such names as "condensation", "sequential Monte Carlo" and "survival of the fittest". In this paper, we show how we can exploit the structure of the DBN to increase the efficiency of particle filtering, using a technique known as Rao-Blackwellisation. Essentially, this samples some of the variables, and marginalizes out the rest exactly, using the Kalman filter, HMM filter, junction tree algorithm, or any other finite dimensional optimal filter. We show that Rao-Blackwellised particle filters (RBPFs) lead to more accurate estimates than standard PFs. We demonstrate RBPFs on two problems, namely non-stationary online regression with radial basis function networks and robot localization and map building. We also discuss other potential application areas and provide references to some finite dimensional optimal filters.