Abstract
A regularization approach is investigated to determine an order of a transfer function model in the presence of input and output noises. By introducing multiple regularization parameters to the corrected least squares (CLS) estimation, we clarify that the system order can be determined by comparing each optimal regularization parameter, which minimizes the mean squares error (MSE) of the estimate, with a corresponding eigenvalue of the covariance matrix of the input-output data. An asymptotic MSE is given, and an analytical expression of the optimal regularization parameters is clarified. An iterative algorithm is proposed by using the only accessible input-output data, in which the system model order and the noise variances can be calculated simultaneously.
