Robust Bayesian Acoustic DOA Estimation With Passive Synthetic Aperture Arrays

Traditional synthetic aperture direction-of-arrival (DOA) estimation methods are sensitive to the spatial and temporal incoherence introduced by the towed array shape deformation and phase unstability. This motivates us to propose a Bayesian acoustic DOA estimator, which is less sensitive to fluctuations in source phase and perturbations in array manifold in this article. The proposed technique extends the physical aperture in beamspace by leveraging the Fourier coefficients of the collected data computed at a given frequency for a successive time interval. A parameterized stochastic model for nonideal signal conditions is developed, and an interpretation of how the signal decorrelation is accomplished within a Bayesian framework is presented. Based on the probabilistic model, an iterative algorithm is developed by maximizing the marginal likelihood. Since this learning procedure is computationally intractable, we derive a variational expectation–maximization algorithm, which approximates the posterior probability distributions for the computation of the expectations over the latent variables. In addition, a 1-D search in the reconstruction result is designed to refine the coarse DOA estimates. Multisource simulations are used to illustrate the robustness of our learning algorithm to various data perturbations.