Regularized impulse response estimation for systems with colored output noise

This paper addresses the use of the regularization feature on impulse response estimation for systems with colored output noise. Firstly, it is shown that the optimal regularization matrix for this scenario is quite different than the optimal for the white noise case and that there is a direct relationship between the Regularized Weighted Least-Squares with a Bayesian perspective of the identification problem for such case. Also, a new Empirical Bayes method, based on the Bayesian perspective, is introduced to estimate the regularization and noise covariance matrices from data. Finally, a numerical example demonstrates that this new methodology outperforms the traditional Regularized Least-Squares, producing better statistical properties and better results for a model fit measure.