Information-theoretic analysis of Bayesian localization of a narrowband source in an uncertain environment

Previous work has explored the application of fundamental information-theoretic constructs, including posterior entropy of source location and per-iteration information gain (relative entropy) and their large-ensemble limits, to quantify the performance of iterated (sequential) Bayesian localization of an acoustic source. These information-theoretic quantities are closely tied to Bayesian inference and provide global measures of the uncertainty of source location that is represented by the Bayesian posterior probability density. The present work extends this analysis to the localization of a narrowband acoustic source in an acoustic environment having uncertain sound speed and attenuation represented by a joint pdf of the two quantities. The fundamental principle relating the environmental and acoustic field uncertainties is the change-of-variables theorem of probability theory. The degradation of localization performance due to the environmental uncertainty is quantified by the increase in posterior entr...