Unbiased filtering of a class of partially observed diffusions

Abstract In this article we consider a Monte-Carlo-based method to filter partially observed diffusions observed at regular and discrete times. Given access only to Euler discretizations of the diffusion process, we present a new procedure which can return online estimates of the filtering distribution with no time-discretization bias and finite variance. Our approach is based upon a novel double application of the randomization methods of Rhee and Glynn ( Operat. Res. 63 , 2015) along with the multilevel particle filter (MLPF) approach of Jasra et al. ( SIAM J. Numer. Anal. 55 , 2017). A numerical comparison of our new approach with the MLPF, on a single processor, shows that similar errors are possible for a mild increase in computational cost. However, the new method scales strongly to arbitrarily many processors.