INTERPRETATION AND SOLUTION OF ILL-CONDITIONED EQUATIONS ARISING IN PARAMETER-ESTIMATION AND SYSTEM-IDENTIFICATION

A new method, named Epsilon Decomposition (E-D), for the efficient solution of ill-conditioned linear algebraic equations is presented. It represents a significant improvement over Singular Value Decomposition (SVD), which requires the user to obtain all the eigenvalues and eigenvectors of all ill-conditioned matrix. The efficiency associated with E-D, for problems arising in system identification, resides in the fact that the user need only obtain the zero, near-zero and the lowest non-zero eigenvalues of the coefficient matrix of the system of equations. Physical and mathematical interpretations of the procedures are offered as well as insights regarding the highly sensitive nature of ill-conditioned equations. Suggestions are also provided for stabilizing results obtained for such systems.