  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
discretization bias and finite variance. Our approach is based upon a novel
double application of the randomization methods of Rhee & Glynn (2015) along
with the multilevel particle filter (MLPF) approach of Jasra et al (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.
