The likelihood ratio and Bayesian signal processing.

Abstract

Over the past several years, we have been developing an architecture for classifying source depth associated with passive sonar signals. The classifiers utilize the statistics of a signal parameter which are estimated using knowledge of the environment and an acoustic propagation program. We have applied the likelihood ratio (LR) test to classify source depth using signal statistics from the SWellEx‐96 and 1996 Strait of Gibraltar sea tests. More recently Bissinger developed a Hellinger distance classifier, and Jemmott is developing a histogram (discrete Bayesian) filter for this purpose. In this talk, we examine the relationship between the LR test and a processor that makes use of Bayes rule. We consider some of the fundamentals. It is useful to understand the underlying assumptions of the LR, the likelihood function, and how they are related to a Bayesian processor which makes use of prior information and computes a posterior probability distribution function. Under what conditions do the two processors produce the same answer? When would the Bayesian processor be a better choice? We compare the processors and apply them to the SWellEx‐96 data. [Work supported by the Office of Naval Research Undersea Signal Processing.]