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 -distribution (MVT) with 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 -contaminated data. The robust SBL estimators perform well for all cases and nearly identical with classical SBL for Gaussian array data.

中文翻译：

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DOA 的稳健和稀疏 M 估计

针对遵循具有零均值和有限二阶矩的复椭圆对称 (CES) 分布的阵列数据，导出了稳健且稀疏的到达方向 (DOA) 估计器。推导允许选择损失函数，并详细讨论了四个损失函数：高斯损失，即循环对称复杂高斯分布的最大似然（ML）损失，复杂多元分布（MVT）的ML损失）具有自由度，以及 Huber 和 Tyler 损失函数。对于高斯损失，该方法简化为稀疏贝叶斯学习（SBL）。讨论了高斯、MVT 和 污染数据的导出估计量的均方根 DOA 误差。稳健的 SBL 估计器在所有情况下都表现良好，并且与高斯阵列数据的经典 SBL 几乎相同。