Application of particle filters to single-target tracking problems

In a Bayesian framework, all single target tracking problems reduce to recursive computation of the posterior density of the target state. Particle filters approximate the optimal Bayesian recursion by propagating a set of random samples with associated weights. In the last decade, there have been numerous contributions to the theory and applications of particle filters. Much study has focussed on design issues such as appropriate selection of the importance density, the use of resampling techniques which mitigate sample degeneracy and the choice of a suitable random variable space upon which to implement the particle filter in order to minimise numerical complexity. Although the effect of these design choices is, in general, well known, their relevance to target tracking problems has not been fully established. These design issues are considered for single target tracking applications involving target manoeuvres and clutter. Two choices of importance density are studied and methods for enhancing particle diversity through the avoidance of particle duplication in the resampling step are considered for each importance density. The possibility of reducing the dimension of the space over which the particle filter is implemented is considered. Based on simulation results, a few key observations are drawn about which aspects of particle filter design most influence their performance in target tracking applications. The numerical simulations also provide insights into the relationship between the state dimension and the number of particles needed to improve upon the performance of the standard tracking filters.