Non-Euclidean estimation of acoustic cross-spectral density matrices: Evaluation by matched-field localization in an ocean waveguide

A set of non-Euclidean cross-spectral density matrix (CSDM) estimators based on the Frechet mean and median is applied to spatially localize an acoustic source in a stochastic shallow water environment driven by internal gravity waves. The resulting geometric-based matrix estimates are incorporated into matched-field processors defined through steering matrices using intrinsic distance measures between pairs of CSDMs on a Riemannian manifold for each replica source location. Their performance is evaluated using the probability of correct localization to determine any improvement in source localization over the conventional (maximum likelihood) statistical approach for CSDM estimation.