A General Test for the Linear Structure of Covariance Matrices of Gaussian Populations
A General Test for the Linear Structure of Covariance Matrices of Gaussian Populations
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DOI：
10.1109/icassp40776.2020.9053718
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发表时间：
2020-05
期刊：
影响因子：
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通讯作者：
Yuhang Xiao;D. Ramírez;P. Schreier
中科院分区：
文献类型：
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作者：
Yuhang Xiao;D. Ramírez;P. Schreier
本文讨论了检验一个协方差矩阵是否可以由一组已知矩阵的未知线性组合或由一组不同但已知的矩阵的另一未知线性组合来表示的问题。这一问题在雷达、声纳和频谱感知等实际应用中具有广泛的应用价值。我们在高斯假设下研究了这一问题，并给出了广义似然比检验。由于GLRT所需的协方差矩阵的极大似然(ML)估计不存在通用的闭式解，因此我们求助于一种强大的逆迭代算法。最后，给出了一个算例和数值结果来说明该方法。
This paper addresses the problem of testing whether a covariance matrix can be expressed by an unknown linear combination of a set of known matrices or by another unknown linear combination of a set of different, but known, matrices. This problem is of interest in a wide range of real-world applications, such as radar, sonar, and spectrum sensing. We study the problem under the Gaussian assumption and derive the generalized likelihood ratio test (GLRT). Since there is no general closed-form solution for the maximum likelihood (ML) estimates of the covariance matrices, which are required for the GLRT, we resort to a powerful inverse iteration algorithm. Finally, an example, along with numerical results, is given to illustrate the methodology.