Order-Determination of Transfer Function Model From Noisy Input-Output Signals

Abstract

A regularization scheme is investigated to determine the 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) estimate, it is shown that the system order can be determined by comparing each eigenvalue and a corresponding optimal regularization parameter, which minimizes the mean-square error (MSE) of the regularized estimate. An asymptotic MSE is given, and an analytical expression of the optimal regularization parameters is also clarified. Furthermore, a data adaptive iterative algorithm is presented to estimate the system model order and noise variances simultaneously.