Kernel-based model order selection for linear system identification

The mainstream approach to identification of linear discrete-time models is given by parametric Prediction Error Methods (PEM). As a rule, the model complexity is unknown and model order selection (MOS) is a key ingredient of the estimation process. A different approach to linear system identification has been recently proposed where impulse responses are described in a Bayesian framework as zero-mean Gaussian processes. Their covariances are given by the so-called SS (stable spline), TC or DC kernels that encode information on regularity and BIBO stability. In this paper, we show that these new kernel-based techniques lead also to a new effective MOS method for PEM. Furthermore, this paves the way to the design of a new impulse response estimator that combines the regularized approaches and the classical parametric PEM. Numerical experiments show that the performance of this technique is very similar to that of PEM equipped with an oracle that selects the best model order.