Robust and Sparse M-Estimation of DOA

A robust and sparse Direction of Arrival (DOA) estimator is derived based on general loss functions. It is an M-estimator because it is derived as an extremum estimator for which the objective function is a sample average. In its derivation it is assumed that the array data follows a Complex Elliptically Symmetric (CES) distribution with zero-mean and finite second-order moments. Four loss functions are discussed in detail: the Gauss loss which is the Maximum-Likelihood (ML) loss for the circularly symmetric complex Gaussian distribution, the ML-loss for the complex multivariate t-distribution (MVT) with {\nu} degrees of freedom, as well as Huber and Tyler loss functions. For Gauss loss, the method reduces to Sparse Bayesian Learning (SBL). The root mean square DOA error of the derived estimators is discussed for Gaussian, MVT, and $\epsilon$-contaminated array data. The robust SBL estimators perform well for all cases and nearly identical with classical SBL for Gaussian noise.