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 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 ε . Numerical examples show that the proposed method is effective for system identification.


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    Title :

    Improved Solution of Equations by Regularizing Ill-Conditioned Coefficient Matrix for System Identification


    Contributors:

    Published in:

    AIAA Journal ; 51 , 9 ; 2076-2085


    Publication date :

    2013-07-01


    Size :

    10 pages




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English