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In the least squares (LS) type of parameter estimation, we are often encountered with ill-posed cases where an input covariance matrix becomes nearly singular due to use of band-limited input signals. In order to attain stabilized convergence of the estimation, the present paper proposes a generalized regularization scheme using multiple regularization parameters and an a priori estimate, and gives analytical discussions on their optimal values which minimize the mean square error (MSE) or the estimated MSE using only accessible signal data. It will also clarify the relationship with the optimal number of truncated smaller eigenvalues in the eigenvalue decomposition. These results discover successfully an explicit form of the optimal initial condition for the recursive least squares algorithm so that the MSE can be minimized at each instant. Finally an on-line regularization scheme is presented.

Optimized Regularization in Least Squares Type of System Identification and Optimal Initial Conditions of Recursive Least Squares Algorithm