Information-theoretic analysis of iterated Bayesian acoustic source localization in a static ocean waveguide

Fundamental constructs of information theory are applied to quantify the performance of iterated (sequential) Bayesian localization of a time-harmonic source in a range- and time-invariant acoustic waveguide using the segmented Fourier transforms of the received pressure time series. The nonlinear relation, defined by acoustic propagation, between the source location and the received narrowband spectral components is treated as a nonlinear communication channel. The performance analysis includes mismatch between the acoustic channel and the model channel on which the Bayesian inference is based. Source location uncertainty is quantified by the posterior probability density of source location, by the posterior entropy and associated uncertainty area, by the information gain (relative entropy) at each iteration, and by large-ensemble limits of these quantities. A computational example for a vertical receiver array in a shallow-water waveguide is presented with acoustic propagation represented by normal modes and ambient noise represented by a Kuperman-Ingenito model. Performance degradation due to noise-model mismatch is quantified in an example. Potential extensions to uncertain and stochastic environments are discussed.