A computational Bayesian processor for inference regarding range, depth, and velocity of a mobile scatterer under limited aperture

Abstract

A computational Bayesian framework for inference regarding the range, depth and velocity of a submerged mobile localized body in an ocean waveguide is constructed. The approach incorporates the various mixed mode Doppler-frequency dispersion effects associated with the reverberant body’s vertical angle scattering. Such coupled eigen returns present angle-frequency modes of intermediate Doppler residing between that of the two coupled specular eigen path Doppler frequencies. It is exactly these modes which present a severe limitation to exploiting closely spaced arrivals in coherence and aperture limited environments. Conditional densities of arrival angle-Doppler are solved via a fast inverse quantile sampler. All other conditionals offer closed form representations in the Gaussian-inverse gamma family. The joint posterior probability density (PPD) of the arrivals are numerically solved and the implied PPD of the object's range, depth, and speed is inferred through acoustic ray interpolation. Case studies are presented with various refractive ocean waveguide environments as well as iso-velocity cases. The framework offers a means of incorporating spatio-temporal arrival structure for recursive tracking in an active sonar system. [Work is funded by the Office of Naval Research.]