Particle filters for combined state and parameter estimation

Filtering is a method of estimating, the conditional probability distribution of a signal based upon a noisy, partial, corrupted sequence of observations of the signal. Particle filters are a method of filtering in which the conditional distribution of the signal state is approximated by the empirical measure of a large collection of particles, each evolving in the same probabilistic manner as the signal itself. In filtering, it is often assumed that we have a fixed model for the signal process. In this paper, we allow unknown parameters to appear in the signal model, and present an algorithm to estimate simultaneously both the parameters and the conditional distribution for the signal state using particle filters. This method is applicable to general nonlinear discrete-time stochastic systems and can be used with various types of particle filters. It is believed to produce asymptotically optimal estimates of the state and the true parameter values, provided reasonable initial parameter estimates are given and further estimates are constrained to be in the vicinity of the true parameters. We demonstrate this method in the context of search and rescue problem using two different particle filters and compare the effectiveness of the two filters to each other.