A robust and sparse Direction of Arrival (DOA) estimator is derived for array data that follows a Complex Elliptically Symmetric (CES) distribution with zero-mean and finite second-order moments. The derivation allows to choose the loss function and 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 data. The robust SBL estimators perform well for all cases and nearly identical with classical SBL for Gaussian noise.

翻译：针对服从均值为零且二阶矩有限的复椭圆对称（CES）分布的阵列数据，推导出一种稳健且稀疏的波达方向（DOA）估计器。该推导允许选择损失函数，并详细讨论了四种损失函数：对应圆对称复高斯分布的极大似然（ML）损失——高斯损失、自由度为ν的复多元t分布（MVT）的ML损失，以及Huber损失函数和Tyler损失函数。对于高斯损失，该方法退化为稀疏贝叶斯学习（SBL）。分别在高斯噪声、MVT噪声及ε-污染噪声下，讨论了所推导估计器的均方根DOA误差。所提出的稳健SBL估计器在所有情形下均表现良好，且在噪声为高斯分布时，其性能与经典SBL几乎一致。