SVD-based Recursive Subspace System Identification with Fixed Input-output Data Size Using Matrix Inversion Lemma

Abstract

We propose a singular value decomposition-based recursive subspace state-space system identification algorithm (R4SID) with fixed input-output data size using the matrix inversion lemma (MIL). The proposed R4SID improves the computational efficiency of recursions because it updates an inverse matrix by the MIL and computes the multiplication of vectors instead of matrices. We clarify the following two effectiveness of the proposed R4SID through numerical experiments. The first effectiveness is that the proposed R4SID can identify a time-varying system disturbed by white Gaussian measurement noise. The second effectiveness is that the accuracy of the proposed R4SID is less sensitive to the choice of data length in the case of the white Gaussian measurement noise whose level is sufficiently smaller than that of input signal.