On the Convergence, Bias and Degeneracy Properties of Iterative Multiple Disturbance Particle Filtering

The interest of this paper is the design of Bayesian particle filters for nonlinear state estimation (target tracking) applications. Particle filters employ a point mass representation of the probability densities using a set of weighted particles, in order to propagate the statistical characteristics useful for online target state estimation. The filter requires that the particles are sampled from high probability regions in the posterior density to ensure convergence, unbiassedness and low degeneracy. However achieving this is not analytically straightforward and switched by either resampling or lookahead sampling approaches like the auxiliary particle filter. Resampling is sequential and computation expensive, while the auxiliary particle filter can suffer from divide-by-zero errors during its second stage sampling. A recent class of filters, the iterative multiple disturbance filters, have been proposed to overcome these problems. The key idea in one variant was to repeatedly sample multiple target heading disturbances for each particle until the weights satisfy an unbiasedness criterion. This approach is highly parallelisable and was previously tested in a limited scenario. In this paper, we present theoretical proofs for its convergence, bias and effective sample size properties, and evaluate its performance in two challenging scenarios and thereby establish its relevance in particle filtering for highly nonlinear state estimation problems.