Rao-Blackwellized point mass filter for reliable state estimation

We present a Rao-Blackwellized point mass filter (RB-PMF) as a deterministic counterpart of the Rao-Blackwellized marginal particle filter (RB-MPF). The main advantage of the proposed filter is its deterministic nature that results in the same estimate for repeated runs over the same data. Moreover, the point mass approximation offers more reliable representation of the tails of the posterior distribution. This results in more reliable tracking of low probability events, which is demonstrated on a simulated example of sine wave tracking. Due to Rao-Blackwellization, the proposed filter is capable to estimate problems of higher dimensions than the original point mass filter. This is demonstrated on estimation of a demanding five dimensional problem.