M-Decomposed Least Squares and Recursive Least Squares Identification Algorithms for Large-Scale Systems

Abstract

Two M-decomposed based identification algorithms are proposed for large-scale systems in this study. Since the least squares algorithms involve matrix inversion calculation, they can be inefficient for large-scale systems whose information matrices are ill-conditioned. To overcome this difficulty, the M-decomposed based least squares algorithm is developed, where the parameter vector is divided into M sub-vectors. Each sub-vector is estimated using the least squares algorithm, with the assumption that the other sub-vectors are known. The proposed algorithm has less computational efforts than those of the traditional least squares algorithm. To update the parameters with new arrived data, an M-decomposed based recursive least squares algorithm is also provided, this algorithm avoids matrix inversion calculation thus is more efficient. The simulation examples show the effectiveness of the proposed algorithms.