Shallow water acoustic response and platform motion modeling via a hierarchical Gaussian mixture model

Abstract

A hierarchical Gaussian mixture model is proposed to characterize shallow water acoustic response functions that are time-varying and sparse. The mixture model is based on the assumption that acoustic paths can be partitioned into two sets. The first is a relatively coherent set of arrivals that on average exhibit Doppler spreading about a mean Doppler and the remaining set is of multiple surface scattered paths that exhibit a spectrally flat Doppler. The hierarchy establishes constraints on the parameters of each of these Gaussian models such that coherent components of the response are both sparse and in the ensemble obey the Doppler spread profile. This is accomplished with a Bernoulli model that indicates the ensonification state of each element in the bi-frequency representation of the acoustic response function. Estimators of the time-varying acoustic response for the full duration of a broadband transmission are developed and employed to compensate for the shared time-varying dilation process among the coherent arrivals. The approach ameliorates response coherence degradation and can be employed to enhance coherent multi-path combining and is a useful alternative to time recursive estimation. The model is tested with acoustic communication recordings taken in shallow water at low signal-to-noise ratios.

Evidence in support of Gaussian mixture models for sparse time varying ocean acoustic response functions

“…These posterior probabilities can then be used to construct a shrinkage rule for denoising the empirical coefficients. 1 Presented here is evidence in support of a modeling framework for sparse time varying acoustic response functions over finite observation periods and apertures. This letter presents results that lends credibility to a Gaussian mixture model over beam, channel bandwidth, and Doppler frequency.…”

“…Such models provide mean square error performance that outperforms simple least squares estimation and the resulting recursive schemes have proven effective for estimation of underwater acoustic channels. 1 One of the definitive features of a shallow water acoustic response that is leveraged for improved estimation is its relative sparsity. 1,2 Simply stated, the number of variables that describe the impulse response is smaller than the space in which the response function resides.…”

“…1 One of the definitive features of a shallow water acoustic response that is leveraged for improved estimation is its relative sparsity. 1,2 Simply stated, the number of variables that describe the impulse response is smaller than the space in which the response function resides. 3 The challenge is determining the particular variates that are descriptive for a particular channel realization and excluding those that are extraneous.…”

“…1 Let J specify the a priori unknown set of bases that are ensonified coherently for a particular realization of the channel. 1 The random set J can be specified with the use of Bernoulli indicator variables z 2 {0, 1} associated with a particular ocean realization…”

Norm Penalized Joint-Optimization NLMS Algorithms for Broadband Sparse Adaptive Channel Estimation

“…Additionally, the broadband multi-path channel or underwater communication channel might be a sparse channel, which has been studied in recent decades [13][14][15][16][17]. From the measurement of the wireless channel, the channel impulse response can be regarded as sparse channel.…”