Bayesian Direction-of-Arrival Estimation Using Atomic Norm Minimization With Prior Knowledge

This article concerns the direction-of-arrival (DOA) estimation problem in the Bayesian framework by using the sparse methods that incorporate the prior knowledge within the array observation data. The obtained prior knowledge of DOAs is assumed to follow a prior distribution. Considering the unknown DOAs are random variables, we propose two sparse methods by effectively and efficiently exploiting the information from the observation data and prior knowledge. One is a grid-based sparse method using the second-order cone programming by discretizing the grids in the prescribed prior region where the targets occur with high probability. The other is a gridless sparse method using the atomic norm minimization by transforming the prior knowledge into a semidefinite constraint. The first is computationally efficient, but it suffers from grid mismatch problems in high SNR. The second further improves the estimation performance with high computational complexity. Simulation results demonstrate the superiority of the proposed methods when compared with the traditional DOA estimation methods together with the maximum a posteriori estimator and the Bayesian Cramér–Rao lower bounds.