Bayesian approach to model‐based signal processing: An overview.

Abstract

Although available for a long time with the advent of high‐speed/high‐throughput computing, the development of Bayesian processing techniques has evolved recently in acoustical signal processing. Bayesian signal processing is concerned with the estimation of the underlying probability distribution of a random signal in order to perform statistical inferences such as the conditional mean estimation. Knowledge of this distribution provides all of the essential information available required for problem solution. The usual limitations of nonlinear approximations and non‐gaussian processes prevalent in classical algorithms (e.g., Kalman filters) are no longer a restriction to perform Bayesian inference. This approach enables the next generation of processors called particle filters that are sequential Monte Carlo methods providing an estimate of the underlying discrete probability distribution. In this overview, Bayesian signal processing is presented from a probabilistic perspective starting with Bayes rule and evolving to the development of a bootstrap particle filter perhaps one of the most common and simplest constructs available. The relationship of Bayesian processing to the concept of maximum entropy is discussed. Maximum entropy and its applicability in Bayesian processing is also mentioned briefly.