Abstract
Resolving closely spaced phase fronts in both angle and frequency is a ubiquitous problem in the applied sciences. From radar to active sonar and remote sensing in astronomy, the fundamental limits on aperture and coherence time degrade the resolution performance of receivers. For localization of underwater acoustic scatterers, the problem is further complicated by a refractive medium requiring that the solution takes into account both the spatial dependence of angular refraction and the attendant differences in the propagation path Doppler. This thesis develops a computational Bayesian approach to address localization of an underwater scatterer by resolving closely spaced phase fronts in a horizontally stratified underwater environment. These arrivals are discerned from a single snapshot observation made with a vertical linear array of limited aperture. A Gibbs sampling scheme is employed that provides a numerical solution to the joint posterior probability density (PPD) of the angular and Doppler profiles. This scheme takes full advantage of the tractable conditional densities of the complex amplitudes and the ambient acoustic noise power that arise from the Normal-Inverse-Gamma family. However, conditional densities of the angles of arrival and Doppler frequencies are not tractable. Nevertheless, their constrained a priori domain admits the use of a 2-dimensional quantile sampling approach. To infer the location and state of motion of the submerged object, the PPD of the two dominant, scattered, refracted, and Doppler-shifted arrivals are mapped to the joint PPD of range, depth, and speed. This is accomplished using a computationally efficient propagation inversion approach based on eigenray interpolation. The posterior over range-depth-speed provides credible intervals essential to submersible localization and tracking applications. Simulations are presented to lend credence to the approach by exploring algorithm performance as a function of signal-to-noise ratio and aperture. A rich set of environments of varying complexity are considered, including a highly stratified environment that supports acoustic duct propagation using at-sea measured sound speed profiles.