Exact Approximation of Rao-Blackwellised Particle Filters*

Particle methods are a category of Monte Carlo algorithms that have become popular for performing inference in non-linear non-Gaussian state-space models. The class of “Rao-Blackwellised” particle filters exploits the analytic marginalisation that is possible for some state-space models to reduce the variance of the Monte Carlo estimates. Despite being applicable to only a restricted class of state-space models, such as conditionally linear Gaussian models, these algorithms have found numerous applications. In scenarios where no such analytical integration is possible, it has recently been proposed in Chen et al. [2011] to use “local” particle filters to carry out this integration numerically. We propose here an alternative approach also relying on “local” particle filters which is more broadly applicable and has attractive theoretical properties. Proof-of-concept simulation results are presented.