A Fast MCMC Particle Filter

Relying on the idea of importance sampling for substantiating the Bayesian filtering recursion, particle filters may become prohibitively inefficient even for moderate state dimensions and likewise whenever the signal to noise ratio is relatively high, as is the case with nearly deterministic state dynamics or random parameters. Markov chain Monte Carlo particle filters completely avoid importance sampling and by that circumvent many of the deficiencies associated with conventional particle filters. These methods may nevertheless suffer from slow convergence rate once inadequate or computationally intractable proposal distributions are used for generating new candidate samples in the underlying Markov chain. In this work, we devise a new Markov chain Monte Carlo particle filter whose sampling mechanism employs jumping Gaussian distributions. This technique enhances the underlying sampling efficiency and leads to significant reduction in the computational cost. The newly derived filter is shown to outperform the conventional (regularised) particle filter both in terms of accuracy and computational overhead, particularly when applied to estimation in systems with low intensity noise or of relatively high state dimensions.