Particle Filtering with Progressive Gaussian Approximations to the Optimal Importance Density

A new algorithm, the progressive proposal particle filter, is introduced. The performance of a standard particle filter is highly dependent on the choice of importance density used to propagate the particles through time. The conditional posterior state density is the optimal choice, but this can rarely be calculated analytically or sampled from exactly. Practical particle filters rely on forming approximations to the optimal importance density, frequently using Gaussian distributions, but these are not always effective in highly nonlinear models. The progressive proposal method introduces the effect of each observation gradually and incrementally modifies the particle states so as to achieve an improved approximation to the optimal importance distribution.