Sparse Bayesian Learning with Jeffreys’ Noninformative Prior for Off-Grid DOA Estimation

Abstract

Sparse Bayesian learning (SBL) algorithms are attractive methods for direction-of-arrival (DOA) estimation and have certain advantages over other sparse representation-based DOA estimation methods. In this paper, a new computationally efficient SBL algorithm for DOA estimation is developed which considers a noninformative prior for hyperparameters. This noninformative prior is obtained using the well-known Jeffreys’ rule which is based on the Fisher information and the hyperparameters are powers of the source signals. The Jeffreys’ prior that is obtained for the hyperparameters is different from the conventional Jeffreys’ prior used in the literature. Moreover, a method for refining the DOA estimates obtained by the SBL algorithm is derived to reduce the off-grid error. Analysis indicates that the computational complexity of the proposed SBL algorithm per iteration is less than that of other existing SBL algorithms. Simulation results exhibit the superior performance of the proposed SBL algorithm compared to state-of-the-art SBL algorithms in terms of DOA estimation accuracy and total computational complexity. Moreover, simulations reveal that, unlike certain other state-of-the-art SBL algorithms, the proposed algorithm is robust to changes in noise power.