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The auxiliary particle filter (APF) introduced by Pitt and Shephard Pitt, M.K., Shephard, N., 1999. Filtering via simulation: Auxiliary particle filters. J. Am. Statist. Ass. 94, 590–599 is a very popular alternative to Sequential Importance Sampling and Resampling (SISR) algorithms to perform inference in state-space models. We propose a novel interpretation of the APF as an SISR algorithm. This interpretation allows us to present simple guidelines to ensure good performance of the APF and the first convergence results for this algorithm. Additionally, we show that, contrary to popular belief, the asymptotic variance of APF-based estimators is not always smaller than those of the corresponding SISR estimators — even in the ‘perfect adaptation’ scenario.
Johansen et al. (Fri,) studied this question.