Independent particle filters

Abstract

Sequential Monte Carlo methods, especially the particle filter (PF) and its various modifications, have been used effectively in dealing with stochastic dynamic systems. The standard PF samples the current state through the underlying state dynamics, then uses the current observation to evaluate the sample's importance weight. However, there is a set of problems in which the current observation provides significant information about the current state but the state dynamics are weak, and thus sampling using the current observation often produces more efficient samples than sampling using the state dynamics. In this article we propose a new variant of the PF, the independent particle filter (IFF), to deal with these problems. The IPF generates exchangeable samples of the current state from a sampling distribution that is conditionally independent of the previous states, a special case of which uses only the current observation. Each sample can then be matched with multiple samples of the previous states in evaluating the importance weight. We present some theoretical results showing that this strategy improves efficiency of estimation as well as reduces resampling frequency. We also discuss some extensions of the IPF, and use several synthetic examples to demonstrate the effectiveness of the method. © 2005 American Statistical Association.