Optimal generalized regularization approach to parameter identification by using band-limited input signal

Generalized regularization based on generalized singular value decomposition is presented in order to attain stabilized identification of an impulse response or transfer function by using bandlimited input signals. The optimal regularization parameters can be determined so as to minimize a new Bayesian information criterion, by which the smoothness order for the estimated impulse response can be given as well. In the case of the transfer function, a new idea is employed in estimating a system output to reduce the problem to the above linear regression problem. It is shown that the optimal regularization is closely related to the optimal choice of the initial conditions in the recursive least squares estimation and also to the optimal truncation of generalized singular values