Bayesian signal processing: A practical guide to particle filtering design and performance

Abstract

When uncertain acoustic processes can no longer be characterized by Gaussian or for that matter unimodal (single peak) distributions along with the fact that the underlying phenomenology is nonstationary (time-varying) and nonlinear, then more general Bayesian processors must be applied to solve the underlying signal enhancement/extraction problem. A particle filter provides a solution to this multimodal (multiple peaks) posterior distribution estimation problem in noisy acoustic environments. A particle filter is a sequential Markov chain Monte Carlo processor capable of providing reasonable performance for data evolving from a multimodal distribution by estimating a nonparametric representation of the posterior distribution from which a multitude of meaningful statistics can be retrieved. However, the question of evaluating its performance can be challenging even for the simplest of processes. For instance, it is well-known that Kalman filter optimality can be obtained only when the resulting error residuals (innovations) are zero-mean and white. It is not that simple for the particle filter. Once characterized, the performance of the particle filter must be analyzed for it to be of practical value. Here a set of design and analysis criteria is discussed and applied to demonstrate their ability to quantify particle filtering performance.