Qualitatively Robust Bayesian Learning for DOA from Array Data using M-Estimation of the Scatter Matrix

The qualitative robustness of direction of arrival estimation using Sparse Bayesian Learning (SBL) is assessed by evaluating the corresponding empirical influence function (EIF). The EIF indicates that SBL is sensitive to deviations from the underlying joint Gaussian assumption on signal and noise. To improve its qualitative robustness, we modify SBL by plugging-in the sample covariance matrix of the phase-only array data instead of the conventional sample covariance. A qualitatively more robust DOA estimate is derived as maximum likelihood estimate based on the complex multivariate t-distribution as the model-distribution for array data. Finally, we discuss and compare the qualitative robustness of the derived DOA estimators by evaluating the corresponding EIFs.