Accelerated Particle Filtering using the Variational Bayes Approximation

In Bayesian filtering, the model may allow analytical marginalization over a subset, θ_1,t, of the parameters. The marginalized (Rao-Blackwellized) particle filter (MPF) exploits this, by requiring stochastic sampling only in the remaining parameters, θ_2,t, with the potential for major computational and convergence speed-ups. The marginalized filtering distribution in θ_1,t is expressed as a mixture of n analytical components, each conditioned on one of the n particle trajectories in θ_2,t; i.e. sufficient statistics must be stored and updated for each particle trajectory. In this paper, the variational Bayes (VB) approximation is used as a one-step approximation to extract necessary moments from the n particles in a principled manner, yielding a single-component marginalized filtering distribution. This formalizes and extends a recently reported certainty equivalence approach to accelerating MPFs. The comparative performance of the full and accelerated MPFs is explored via a scalar nonlinear filtering example.