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In sparse signal recovery methods for direction of arrival (DOA) estimation, a set of uniform angular grid points is usually predefined. Dense grid points will improve the resolution and precision, but increase computational workload distinctly. To improve the efficiency and performance when using coarse initial grid points, an adaptive grid refinement (AGR) sparse Bayesian learning (SBL) method is proposed. The key idea of the proposed method is to adaptively insert new grid points based on the spatial spectrum learned from SBL iterations, as a result, grid points become denser and denser around the potential DOAs. The number of total grid points in the AGR process is much smaller than that of traditional uniform grid points, which enhances the computation efficiency. After the improved on-grid estimation of the AGR process, a post-processing DOA search procedure is implemented to reduce the off-grid DOA error. Furthermore, the proposed method is extended into the wideband case. Simulation results demonstrate that the proposed method has higher computation efficiency and precision than the classical off-grid SBL methods in scenarios of low SNR and limited snapshots. The effectiveness of the proposed method is also validated using the data of the SWellEx-96 ocean acoustic experiment.

Three-dimensional (3-D) source localization based on 1-D angles of arrival (AOA) measurements from multiple linear arrays have attracted much attention due to the low cost of linear arrays and the easy access to 1-D AOAs. However, most existing methods are restricted to specific array deployments, and the convex optimization methods applicable to the linear array with arbitrary deployments have drawbacks such as high computational complexity and nonportability to small industrial equipment. In this article, we propose two 1-D AOA-based source localization methods. The first method uses the iterative reweighted least square (IRLS) to obtain a coarse solution and a deviation refinement (DR) procedure to refine the estimation. Each step in IRLS-DR has a closed-form solution; thus, it is computationally efficient. Moreover, it applies to arbitrary interarray deployments, and theoretical analysis shows that its performance can approach the Cramér–Rao lower bound (CRLB) at small noise levels. The second method addresses the maximum likelihood estimation (MLE). A modified Levenberg–Marquardt (MLM) method is proposed, which focuses on designing a new selection strategy of the regularization parameter to realize a high convergence probability and localization accuracy. Experiments based on computer simulations and SWellEx96-S59 ocean acoustic measurements are carried out to verify the performance and advantages of the proposed methods.