Improved Particle Approximations to the Joint Smoothing Distribution Using Markov Chain Monte Carlo

Particle filtering and smoothing algorithms approximate posterior state distributions with a set of samples drawn from those distributions. Conventionally, samples from the joint smoothing distribution are generated by sequentially resampling from the particle filter results. If the number of filtering particles is high, this process is limited by computational complexity. In addition, the support of the smoothing distribution is restricted to the values which appear in the filtering approximation. In this paper, a Metropolis-Hastings sampling procedure is used to improve the efficiency of the particle smoother, achieving comparable error performance but with a lower execution time. In addition, an algorithm for approximating the joint smoothing distribution without limited support is presented, which achieves simultaneous improvements in both execution time and error. These algorithms also provide a greater degree of flexibility over existing methods, allowing a trade-off between execution time and error, controlled by the length of the Markov chains.