Improvement of the Particle Filter by Better Choice of the Predicted Sample Set

An improvement of the standard “particle filter” (PF) Monte Carlo Bayesian estimator is presented and compared with an existing improved reweighted filter in a target tracking example. The PF updates the probability density function (pdf) of the state, represented as the density of state samples (particles). Each particle is time-updated by applying to the state equation a sample from the forcing distribution. At the next observation, the likelihood of each particle is computed by substituting the prediction error into the observation-noise pdf. Any low-likelihood particle has a low probability of appearing in the resampled state set for the next update, so often the sample set collapses. The improved estimator represents the state pdf as weighted samples, and allows free choice of the values at which the posterior pdf is evaluated. This allows enough particles in regions of low probability density and avoids the need for most particles to be in high-density regions.