Impact of space-time covariance estimation errors on a parahermitian matrix EVD

Delaosa, Connor and Coutts, Fraser K. and Pestana, Jennifer and Weiss, Stephan (2018) Impact of space-time covariance estimation errors on a parahermitian matrix EVD. In: 10th IEEE Workshop on Sensor Array and Multichannel Signal Processing, 2018-07-08 - 2018-07-11.

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    Abstract

    This paper studies the impact of estimation errors in the sample space-time covariance matrix on its parahermitian matrix eigenvalue decomposition. We provide theoretical bounds for the perturbation of the ground-truth eigenvalues and of the subspaces of their corresponding eigenvectors. We show that for the eigenvalues, the perturbation depends on the norm of the estimation error in the space-time covariance matrix, while the perturbation of eigenvector subspaces can additionally be influenced by the spectral distance of the eigenvalues. We confirm these theoretical results by simulations.