Abstract
Identification of an impulse response by using strongly correlated input signals is a typical ill-posed least squares estimation problem. To attain stability of identification, we consider a weighted squares error criterion in which we can take into account various types of derivative smoothness of the estimated response in time and frequency domains. In order to discuss optimal regularization and truncation in a unified way, we take the generalized singular value decomposition (GSVD) in which we utilize multiple regularization parameters efficiently. On the Bayesian statistical approach we will give a new information theoretic criterion for determining the optimal regularization parameters. By applying the proposed scheme for regularization we can identify oscillatory peaks outside the frequency range of the input power spectrum, even if the PE condition is not satisfied or even when the number of input-ouput data is less than the length of an impulse response to be identified.
