Fast Nonnegative Sparse Bayesian Deconvolution Method for Direction-of-Arrival Estimation

Sparse deconvolution beamforming exploits the convolutional relationship between the beam pattern and the source distribution embedded in conventional beamforming outputs, and introduces sparsity-promoting regularization to characterize the spatial distribution of acoustic sources. By deconvolving the beamforming results, the spatial blurring induced by the main lobe of the array’s beam pattern can be effectively suppressed, thereby significantly improving the direction-of-arrival (DOA) estimation accuracy for underwater targets. However, existing sparse deconvolution beamforming methods generally employ deterministic convex or nonconvex regularization to enforce source sparsity, lacking a data-adaptive mechanism for sparse representation. Moreover, the shift-invariant beam dictionary involved in the deconvolution model is typically high-dimensional, imposing substantial limitations on both localization accuracy and computational efficiency. To address these issues, this paper proposes a fast nonnegative sparse Bayesian deconvolution method for DOA estimation. The proposed method constructs a point-spread-function (PSF)-based deconvolution dictionary from the array’s beam pattern and employs Bayesian modeling—combined with nonnegativity constraints—to adaptively characterize the sparse spatial distribution of acoustic sources. Meanwhile, a dynamic active-set mechanism is introduced, wherein posterior inference is performed only for candidate directions exhibiting relatively high correlation with the observed data or significant energy. This strategy substantially reduces the computational burden associated with densely discretized angular dictionaries and improves overall inference efficiency. Moreover, an expectation-maximization (EM) algorithm is developed to derive iterative updates for the model hyperparameters, enable adaptive estimation of the noise power, and prune low-energy candidate directions. Consequently, adaptive DOA selection and sparse spatial-spectrum reconstruction are achieved within a unified Bayesian framework. Finally, extensive two-source simulations under various signal-to-noise ratio (SNR) conditions—as well as experimental data collected using a shallow-water towed array—are employed to validate the proposed method. The results demonstrate its effectiveness in sharpening spatial-spectrum peaks, resolving closely spaced targets, and enabling continuous DOA tracking.