Impact of Space-Time Covariance Estimation Errors on a Parahermitian Matrix EVD
Connor Delaosa, Fraser K. Coutts, Jennifer Pestana, Stephan Weiss · 2018
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 distance between the eigenvalues. We confirm these theoretical results by simulations.