Improving the Performance of the Two-Stage Sampling Particle Filter: A Statistical Perspective

In this paper we study asymptotic properties of weighted samples produced by the two-stage sampling (TSS) particle filter, which is a generalization of the auxiliary particle filter proposed by [1]. Besides establishing a central limit theorem (CLT) for the particle estimator of the smoothing measure, we also present bounds on the Lp error and bias of the same for a finite particle sample size. The main contribution of this article, being based on [2], is the identification of first-stage importance weights for which the increase of asymptotic variance of the CLT at a single iteration of the algorithm is minimal. Finally, we let a simple numerical example illustrate our findings.