Improved Solution of Equations by Regularizing Ill-Conditioned Coefficient Matrix for System Identification
Masayoshi Misawa, Takashi Sekiya, Masaki Oba · AIAA Journal · 2013
A numerical method is proposed for solving a set of simultaneous equations with an ill-conditioned coefficient matrix to apply system identification. To find an approximate solution, the coefficient matrix is regularized by adding a small positive value to its diagonal terms. A regularized matrix is provided in different expressions that depend on the coefficient matrix. This paper regularizes a rectangular coefficient matrix and then a square coefficient matrix. Improvement of solution accuracy is possible by removing the very small singular values. Therefore, rank estimation of the coefficient matrix is a key to obtaining an accurate solution. This paper gives a method that estimates the rank by setting an appropriate value of . Numerical examples show that the proposed method is effective for system identification.