A hierarchical mixture model for sparse broadband scattering functions between moving platforms

Abstract

A hierarchical mixture model is considered for sparse broadband acoustic Green's functions [J. Acoust. Soc. Am. 130, 2346, Canadian Acoust. 40(3)]. Such a mixture model can be employed to match arbitrary second order statistics of a channel over time-bandwidth and angle. The model matches these statistics while simultaneously admitting the degree of sparsity necessary to capture propagation between moving platforms through the ocean waveguide. The uppermost stage of the hierarchy is specified by a mean bulk relative platform speed. Conditioned on this is a structured field of beta distributions associated with the probabilities of ensonified paths over beam-Doppler and frequency. The mixture model of the response is built from Bernoulli indicator variables whose probabilities are drawn from the field of betas. Posterior mean and variance are reviewed and used in an underwater acoustic receiver structure to replace Kalman like estimators of response as well as phase looked loop structures for symbol timing. The performance in terms of mean squared error is 10 dB lower than conventional Wiener filtering schemes when the channel response is significantly sparse. Reduction of this margin occurs as either sparsity or SNR is degraded. This degradation in performance is quantified under a range of sparsity constraints associated with the beta variates. [Work supported by the Naval Innovative Science and Engineering Program and the Office of Naval Research.]