Optimally regularized local basis function approach to identification of time-varying systems

Accurate identification of stochastic systems with fast-varying parameters is a challenging task which cannot be accomplished using model-free estimation methods, such as weighted least squares, which assume only that system coefficients can be regarded as locally constant. The current state of the art solutions are based on the assumption that system parameters can be locally approximated by a linear combination of appropriately chosen basis functions. The paper shows that when the internal correlation structure of estimated parameters is known, the tracking performance of the local basis function estimation algorithms can be further improved by means of regularization. The optimal form of the regularization matrix is derived analytically and it is shown that the best settings of the regularized algorithm can be determined in the computationally efficient way using cross-validation.