Frequency-domain least-squares support vector machines to deal with correlated errors when identifying linear time-varying systems

A Least-Squares Support Vector Machine (LS-SVM) estimator, formulated in the frequency domain is proposed to identify linear time-varying dynamic systems. The LS-SVM aims at learning the structure of the time variation in a data driven way. The frequency domain is chosen for its superior robustness w.r.t. correlated errors for the calibration of the hyper parameters of the model. The time-domain and the frequency-domain implementations are compared on a simulation example to show the effectiveness of the proposed approach. It is demonstrated that the time- domain formulation is mislead during the calibration due to the fact that the noise on the estimation and calibration data sets are correlated. This is not the case for the frequency-domain implementation.