A sorted weighting lookahead sampling scheme for accurate and fast particle filtering

Abstract

The particle filter is known to be a powerful tool for estimating hidden Markov processes in nonlinear and nonGaussian state space models. The filter involves generating new particles from old ones, from regions of high importance in the state space using a proposal distribution and then weighing them using the incoming observation. However a poor choice of the proposal distribution may migrate the new particles into regions that do not contribute to the posterior and hence lead to one particle accumulating all the weight (termed particle degeneracy). This degeneracy is overcome using the resampling step that eliminates those particles with low weights and replaces them by those with large weights. However this resampling step is a computationally demanding operation. In the literature, the methods that speed up the particle filter, like the Gaussian particle filter, trade tracking accuracy with speed while methods that sample particles from high importance regions, like the auxiliary particle filters and lookahead particle filters, trade speed with accuracy. In this paper we propose a simple lookahead sampling scheme. Here the particles that fall into high importance regions are predetermined (seen ahead) and then propagated in copies to make up for those that should be discarded. This strategy avoids the resampling step and consequently leads to high speed and accuracy. Using two nonlinear models, we show the tracking efficiency of the proposed method.