Cost-reference particle filtering for dynamic systems with nonlinear and conditionally linear states

Cost-reference particle filtering (CRPF) is a methodology for recursive estimation of unobserved states of dynamic systems using a stream of particles and their associated costs. It is similar to the standard particle filtering (SPF) methodology in that it is comprised of similar steps, that is, (1) propagation of particles, (2) cost (weight) computation, and (3) resampling. The main difference between CRPF and SPF is that the former uses very mild statistical assumptions and the latter is based on strong probabilistic assumptions. In problems where some of the states are linear given the rest of the states, one can employ an SPF scheme with improved filtering performance. In the literature on SPF, this methodology is known as Rao-Blackwellized particle filtering. In this paper, we show how we can exploit a similar idea in the context of CRPF.