Bayesian signal processing in acoustics: detection, estimation and tracking
Leon H. Sibul · The Journal of the Acoustical Society of America · 2001
A tutorial introductory lecture on Bayesian signal processing for detection, estimation, and tracking is presented. After a brief historical overview, Bayes rule and risk are defined and used for development of detectors that minimize Bayes risk. Detectors that minimize Bayes risk are called Bayes detectors. Bayes risk in statistical signal processing is the expected cost of making a wrong decision. The decision process of deciding between to mutually exclusive and exhaustive alternatives (i.e., an echo and noise are present versus noise only is present) is a binary hypothesis test or detector. We show how Bayes detectors are related to the maximum likelihood test and Neyman–Pearson and minimax criteria. Multiple hypotheses tests are also reviewed. Estimate of random parameters that minimize the risk are called Bayes estimates and the resulting risk, the Bayes risk. Minimum mean square error (MMSE), MAP (mode of the posteriori density) and other estimates can be derived using appropriate cost functions. Sequential application of Bayes rule can be used to derive Wiener and Kalman filters. Some of the basic difficulties and issues of Bayesian signal processing will be discussed. [Supported by ONR, Code 333, Les Jacobi, Program Officer.]