Consider a spatial blind source separation model in which the observed multivariate spatial data are assumed to be a linear mixture of latent stationary spatially uncorrelated random fields. The objective is to recover an unknown mixing procedure as well as the latent random fields. Recently, spatial blind source separation methods that are based on the simultaneous diagonalization of two or more scatter matrices were proposed. In cases involving uncontaminated data, such methods can solve the blind source separation problem, however, in the presence of outlying observations, these methods perform poorly. We propose a robust blind source separation method that employs robust global and local covariance matrices based on generalized spatial signs in simultaneous diagonalization. Simulation studies are employed to illustrate the robustness and efficiency of the proposed methods in various scenarios.

考虑空间盲源分离模型，其中观察到的多元空间数据被假设为潜在平稳空间不相关随机场的线性混合。目的是恢复未知的混合过程以及潜在的随机场。最近，提出了基于两个或多个散射矩阵同时对角化的空间盲源分离方法。在涉及未污染数据的情况下，此类方法可以解决盲源分离问题，但是，在存在外围观测值的情况下，这些方法表现不佳。我们提出了一种鲁棒的盲源分离方法，该方法采用基于同时对角化中的广义空间符号的鲁棒全局和局部协方差矩阵。采用仿真研究来说明所提出的方法在各种情况下的鲁棒性和效率。