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 ε to its diagonal elements. 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 obtain an accurate solution. This paper gives a method that estimates the rank by setting an appropriate value of ε. A numerical example shows that the proposed method is effective for system identification.
展开▼
