Covariance Analysis of the Estimated Markov Parameters in a Subspace Identification Method

It is important to provide a covariance of the estimates to ensure the quality of the identification results. This paper proposes a covariance of the estimated Markov parameters in a method previously proposed by the authors. The proposed covariance uses the gap between singular subspaces to estimate the perturbation of the extended observability matrix. The gap based analysis gives a simple expression in the sense that the estimated error in the singular subspace is strictly linear with respect to the perturbation of the original matrix and the left and right singular vectors. Numerical simulation shows the validity of the proposed covariance of the estimated Markov parameters. Copyright (C) 2024 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licneses/by-nc-nd/4.0/)