Improvement Strategies for Monte Carlo Particle Filters

The particle filtering field has seen an upsurge in interest over recent years, and accompanying this upsurge several enhancements to the basic techniques have been suggested in the literature. In this paper we collect a group of these developments that seem to be particularly important for time series applications and give a broad discussion of the methods, showing the relationships between them. We firstly present a general importance sampling framework for the filtering/smoothing problem and show how the standard techniques can be obtained from this general approach. In particular, we show that the auxiliary particle filtering methods of (Pitt and Shephard: this volume) fall into the same general class of algorithms as the standard bootstrap filter of (Gordon et al. 1993). We then develop the ideas further and describe the role of MCMC resampling as proposed by (Gilks and Berzuini: this volume) and (MacEachern, Clyde and Liu 1999). Finally, we present a generalisation of our own in which MCMC resampling ideas are used to traverse a sequence of ‘bridging’ densities which lie between the prediction density and the filtering density. In this way it is hoped to reduce the variability of the importance weights by attempting a series of smaller, more manageable moves at each time step.