Process-noise models for particle filtering under bounded forcing with unknown distribution
Paul Weston, John P. Norton · 2001
In a conventional Monte Carlo Bayesian state estimator, the posterior state distribution is given by the particles, predicted in the previous time update then weighted with their likelihoods, found by substituting the observation prediction errors into the observation noise probability density function (PDF). The time update applies to each particle a sample from the specified PDF of the unknown forcing (process noise). An inappropriate model of the forcing may well result in a high proportion of particles reaching predicted states having very low likelihoods. This paper examines alternatives to specifying forcing by a fixed PDF. In particular, the process noise is assumed to have known bounds but uncertain and perhaps strongly non-stationary distribution. The motivating example is target tracking, in which the target's manoeuvres are limited by physical constraints. The results of particle filter experiments with various forcing models are compared, noting the number of particles needed for adequate tracking and the tracking accuracy for a worst-case trajectory.