DOA M-Estimation Using Sparse Bayesian Learning

Recent investigations indicate that Sparse Bayesian Learning (SBL) is lacking in robustness. We derive a robust and sparse Direction of Arrival (DOA) estimation framework based on the assumption that the array data has a centered (zero-mean) complex elliptically symmetric (ES) distribution with finite second-order moments. In the derivation, the loss function can be quite general. We consider three specific choices: the ML-loss for the circularly symmetric complex Gaussian distribution, the ML-loss for the complex multivariate t-distribution (MVT) with nu degrees of freedom, and the loss for Huber's M-estimator. For Gaussian loss, the method reduces to the classic SBL method. The root mean square DOA performance of the derived estimators is discussed for Gaussian, MVT, and epsilon-contaminated noise. The robust SBL estimators perform well for all cases and nearly identical with classical SBL for Gaussian noise.