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For direction-of-arrival (DOA) estimation problems in a sparse domain, sparse Bayesian learning (SBL) is highly favored by researchers owing to its excellent estimation performance. However, traditional SBL-based methods always assign Gaussian priors to parameters to be solved, leading to moderate sparse signal recovery (SSR) effects. The reason is Gaussian priors play a similar role to l 2 regularization in sparsity constraint. Therefore, numerous methods are developed by adopting hierarchical priors that are used to perform better than Gaussian priors. However, these methods are in straitened circumstances when multiple measurement vector (MMV) data are adopted. On this basis, a block-sparse SBL method (named BSBL) is developed to handle DOA estimation problems in MMV models. The novelty of BSBL is the combination of hierarchical priors and block-sparse model originating from MMV data. Therefore, on the one hand, BSBL transfers the MMV model to a block-sparse model by vectorization so that Bayesian learning is directly performed, regardless of the prior independent assumption of different measurement vectors and the inconvenience caused by the solution of matrix form. On the other hand, BSBL inherited the advantage of hierarchical priors for better SSR ability. Despite the benefit, BSBL still has the disadvantage of relatively large computation complexity caused by high dimensional matrix operations. In view of this, two operations are implemented for low complexity. One is reducing the matrix dimension of BSBL by approximation, generating a method named BSBL-APPR, and the other is embedding the generalized approximate message passing (GAMB) technique into BSBL so as to decompose matrix operations into vector or scale operations, named BSBL-GAMP. Moreover, BSBL is able to suppress temporal correlation and handle wideband sources easily. Extensive simulation results are presented to prove the superiority of BSBL over other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

• A DOA estimation method based on variational Bayesian inference is proposed. • The minimum hole array is adopted to maximize the array aperture based sparse representation. • A sparsity-inducing Bayesian framework with three-stage hierarchical Laplace priors is developed. • The unknown noise is eliminated by a selection matrix. • A refinement operation based on Newton's method is developed to compensate the off-grid errors. For direction-of-arrival (DOA) estimation problems, sparse Bayesian learning (SBL) has achieved excellent estimation performance, especially in sparse arrays. However, numerous SBL-based methods with hyperparameters assigned to Gaussian priors cannot enhance sparsity well, and mainly focus on the nested array (NA) or the co-prime array (CPA) that cause relatively large degree of freedom (DOF) losses. Based on this, we propose a novel method with a Bayesian framework containing three-stage hierarchical Laplace priors that significantly promote sparsity. Moreover, the proposed method is based on the minimum hole array (MHA) that retains a larger array aperture than NA or CPA after redundancy removal, which is required and achieved simultaneously by a denoising operation. In addition, to correct the intractable off-grid model errors caused by grid mismatch, a new refinement operation is developed. And, the refinement empirically outperforms others based on Taylor expansion. Extensive simulations are presented to confirm the superiority of the proposed method beyond state-of-the-art methods. [ABSTRACT FROM AUTHOR]