Statistics and Computing

, Volume 10, Issue 3, pp 197–208

On sequential Monte Carlo sampling methods for Bayesian filtering

  • Arnaud Doucet
  • Simon Godsill
  • Christophe Andrieu
Article

DOI: 10.1023/A:1008935410038

Cite this article as:
Doucet, A., Godsill, S. & Andrieu, C. Statistics and Computing (2000) 10: 197. doi:10.1023/A:1008935410038

Abstract

In this article, we present an overview of methods for sequential simulation from posterior distributions. These methods are of particular interest in Bayesian filtering for discrete time dynamic models that are typically nonlinear and non-Gaussian. A general importance sampling framework is developed that unifies many of the methods which have been proposed over the last few decades in several different scientific disciplines. Novel extensions to the existing methods are also proposed. We show in particular how to incorporate local linearisation methods similar to those which have previously been employed in the deterministic filtering literature; these lead to very effective importance distributions. Furthermore we describe a method which uses Rao-Blackwellisation in order to take advantage of the analytic structure present in some important classes of state-space models. In a final section we develop algorithms for prediction, smoothing and evaluation of the likelihood in dynamic models.

Bayesian filteringnonlinear non-Gaussian state space modelssequential Monte Carlo methodsparticle filteringimportance samplingRao-Blackwellised estimates

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Arnaud Doucet
    • 1
  • Simon Godsill
    • 2
  • Christophe Andrieu
    • 3
  1. 1.Signal Processing Group, Department of EngineeringUniversity of CambridgeCambridgeUK
  2. 2.Signal Processing Group, Department of EngineeringUniversity of CambridgeCambridgeUK
  3. 3.Signal Processing Group, Department of EngineeringUniversity of CambridgeCambridgeUK