Recursive computation for subspace identification methods

In this paper, we present a recursive computation for Subspace-based State Space System IDentification (4SID) methods. We develop another interpretation of the method by using Schur complement, and propose a recursive formula for the error covariance matrix in the 4SID procedure. In the ordinary MIMO Output-Error State space model identification (MOESP) algorithm, we show the estimate of the extended observability matrix is obtained by Schur complement of input-output data matrix. For the noisy case interpretation of the 4SID procedure is also presented. Finally, we illustrate a numerical example for the proposed algorithm.