Implementing particle filters with Metropolis-Hastings algorithms

A particle filter deals with state estimation problem or nonlinear models with non-Gaussian noise. In the framework of a particle filter, a resampling scheme is used to decrease the degeneracy phenomenon, however it also introduces the problem or sample impoverishment, which can be reduced by using the Markov Chain Monte Carlo (MCMC) method, such as the Metropolis-Hastings (M-H) algorithm. However, there are many possible choices within the family of M-H algorithms, and the performance of particle filters with MCMC moves is closely related to the choice of the M-H algorithm. This paper discusses the implementation of a particle filter with various M-H algorithms. A numerical example is presented, and the simulation results are given for discussion.