Simultaneous optimization method of regularization and singular value decomposition in least squares parameter identification

In order to attain stabilized convergence, the authors propose a generalized regularization scheme using multiple regularization parameters and an a priori estimate, and they obtain analytically the parameter values that minimize the mean-square error (MSE) or the estimated MSE using only accessible data signals. They show that method can give simultaneously the optimal regularization parameters and the optimal truncation of smaller eigenvalues in the singular value (or eigenvalue) decomposition (SVD or EVD). The proposed schemes for the optimized regularization and SVD are exemplified in impulse response identification using low-pass input and optimized extrapolation of the bandlimited signal.