Abstract
Particle filters (PF) and auxiliary particle filters (APF) are widely used sequential Monte Carlo (SMC) techniques for estimating the a posteriori filtering probability density function (pdf) in a Hidden Markov Chain (HMC). These algorithms have been theoretically analysed from an asymptotical statistics perspective. In this paper we provide a non asymptotical, finite number of samples comparative analysis of two particular SMC algorithms : the Sampling Importance Resampling (SIR) PF with optimal conditional importance distribution (CID), and the fully adapted APF (FA). Starting from a common set of N particles, we compute closed form expressions of the mean and variance of the empirical Monte Carlo (MC) estimators of a moment of the a posteriori filtering pdf. Both algorithms have the same mean, but in the case where resampling is used, the variance of the SIR algorithm always exceeds that of the FA algorithm.
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