An off-grid direction-of-arrival estimator based on sparse Bayesian learning with three-stage hierarchical Laplace priors

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 hyper parameters 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 stateof-the-art methods.