A fast-weighted Bayesian bootstrap filter for nonlinear model state estimation

In discrete-time system analysis, nonlinear recursive state estimation is often addressed by a Bayesian approach using a resampling technique called the weighted bootstrap. Bayesian bootstrap filtering is a very powerful technique since it is not restricted by model assumptions of linearity and/or Gaussian noise. The standard implementation of the bootstrap filter, however, is not time efficient for large sample sizes, which often precludes its utilization. We propose an approach that dramatically decreases the computation time of the standard bootstrap filter and at the same time preserves its excellent performance. The time decrease is realized by resampling the prior into the posterior distribution at time instant k by using sampling blocks of varying size, rather than a sample at a time as in the standard approach. The size of each block resampled into the posterior in the algorithm proposed here depends on the product of the normalized weight determined by the likelihood function for each prior sample and the sample size N under consideration.