Improvement on the Use of Matrix Inversion Lemma for Recursive PI-MOESP Identification with Fixed Input-output Data Size

抄録

We propose two singular value decomposition (SVD) based recursive PI-MOESP identification algorithms (PI-MOESP identification algorithms: the multiple-input multiple-output output-error state-space model (MOESP) identification algorithms using an instrumental variable consisting of past input (PI) data) with fixed input-output data size using the matrix inversion lemmas (MILs). It is clarified in the two proposed SVD-based recursive PI-MOESP identification algorithms (RPI- MOESPs) that computation time is reduced by using two MILs for addition of the latest input data and subtraction of the oldest input data separately (separated-type MILs) instead of a single MIL for the addition and the subtraction in an integrated manner (integrated-type MIL). Numerical experiments provide the following two results. The first result is that the computation time of the proposed SVD-based RPI-MOESP using the separated-type MILs is less than that of the proposed SVD-based RPI-MOESP using the integrated-type MIL despite achieving almost the same accuracy in the case of linear state-space model identification. The second result is that the two proposed SVD-based RPI-MOESPs can identify a time-varying system disturbed by colored measurement noise.