A non-Euclidean approach to source localization in an ocean waveguide

Abstract

In recent years, there has been significant interest in the natural extension of signal processing techniques based on Euclidean distances to non-Euclidean metrics. Covariance or cross-spectral density matrices (CSDMs), often the basis for localization and detection processors, can be interpreted as “points” in a Riemannian manifold on which a distance metric can be defined. This mathematical structure has proven quite useful in a number of processing schemes involving detection, source localization and classification of data. In this presentation, I consider a fully geometric, non-Euclidean approach to source localization in a simulated shallow water ocean waveguide where the sound speed field is stochastic due to the presence of internal gravity waves. A number of different CSDM estimators are constructed by formulas describing the mean or median of a set of sample dyads obtained from Green function realizations of the propagating field from a source point to a vertical array of acoustic sensors. These CSDM estimates are not derived by statistics, but through the geometric structure of the CSDM. The resulting estimates are incorporated into matched-field localization processors whose measure of similarity or distance between CSDMs is determined on the manifold. Work supported by funds from the Office of Naval Research.