Direction of arrival (DOA) estimation is one of the most important techniques applied in many practical engineering applications. Multiple signal classification (MUSIC) has gained increasing attention due to its high resolution in space. Many methods have been studied to handle the noise of Alpha-stable distribution within the framework of non-Gaussian signal processing. Inspired by a state-of-the-art concept, bounded nonlinear covariance (BNC), a more generalized concept, named generalized covariance (GC), is proposed. A series of existing concepts based on the fractional lower-order moment (FLOM), the correntropy, and the BNC are unified in the name of GC. Then, the convergence of GC under Alpha-stable distributed random variables is addressed. Furthermore, four different types of nonlinear functions are introduced for GC and BNC to handle impulsive noise, including sigmoid functions, score functions, FLOM mapping, Gaussian-like functions. These curves with different parameters are also exhibited in detail to illustrate their capabilities to suppress outliers. Also, GC-MUSIC is proposed, and its performances are compared with other 6 MUSIC-like algorithms in the presence of heavy-tailed impulsive noise. Besides, Cramer-Rao bound (CRB) of root mean squared error is also deduced and exhibited. Through Monte-Carlo simulations, the superiority of GC-MUSIC and BNC-MUSIC under Alpha-stable distributed noise is demonstrated.

到达方向（DOA）估计是许多实际工程应用中应用的最重要技术之一。多信号分类（MUSIC）由于其在空间上的高分辨率而倍受关注。在非高斯信号处理的框架内，已经研究了许多方法来处理Alpha稳定分布的噪声。受最新概念的启发，有界非线性协方差（BNC）提出了一个更广义的概念，称为广义协方差（GC）。基于分数低阶矩（FLOM），肾上腺皮质激素和BNC的一系列现有概念以GC的名称统一。然后，研究了在α稳定分布随机变量下GC的收敛性。此外，针对GC和BNC引入了四种不同类型的非线性函数来处理脉冲噪声，包括S型函数，得分函数，FLOM映射，高斯函数。还详细展示了这些具有不同参数的曲线，以说明它们抑制异常值的能力。此外，提出了GC-MUSIC，并在存在重尾脉冲噪声的情况下将其性能与其他6种类似MUSIC的算法进行了比较。此外，还推导并展示了均方根误差的Cramer-Rao界（CRB）。通过蒙特卡洛仿真，证明了在Alpha稳定分布噪声下GC-MUSIC和BNC-MUSIC的优越性。还详细展示了这些具有不同参数的曲线，以说明它们抑制异常值的能力。此外，提出了GC-MUSIC，并在存在重尾脉冲噪声的情况下将其性能与其他6种类似MUSIC的算法进行了比较。此外，还推导并展示了均方根误差的Cramer-Rao界（CRB）。通过蒙特卡洛模拟，证明了在Alpha稳定分布噪声下GC-MUSIC和BNC-MUSIC的优越性。还详细展示了这些具有不同参数的曲线，以说明它们抑制异常值的能力。此外，提出了GC-MUSIC，并在存在重尾脉冲噪声的情况下将其性能与其他6种类似MUSIC的算法进行了比较。此外，还推导并展示了均方根误差的Cramer-Rao界（CRB）。通过蒙特卡洛仿真，证明了在Alpha稳定分布噪声下GC-MUSIC和BNC-MUSIC的优越性。