Learning and filtering via simulation: smoothly jittered particle filters

A key ingredient of many particle filters is the use of the sampling importance resampling algorithm (SIR), which transforms a sample of weighted draws from a prior distribution into equally weighted draws from a posterior distribution. We give a novel analysis of the SIR algorithm and analyse the jittered generalisation of SIR, showing that existing implementations of jittering lead to marked inferior behaviour over the basic SIR algorithm. We show how jittering can be designed to improve the performance of the SIR algorithm. We illustrate its performance in practice in the context of three filtering problems.