Kernel-based model order selection for identification and prediction of linear dynamic systems

When adopting parametric Prediction Error Methods (PEM) for linear system identification, model complexity is typically unknown and needs to be inferred from data. This calls for a model order selection step which may have a major effect on the quality of the final estimate. A different Bayesian approach to linear system identification has been recently proposed which avoids model order determination. System or predictor impulse responses are interpreted as zero-mean Gaussian processes. Their covariances (kernels) embed information on regularity and BIBO stability and depend on few parameters which can be estimated from data. This paper exploits this new class of kernel-based estimators to obtain a new effective model order selection method for PEM. In particular, numerical experiments regarding ARMAX models identification show that the performance of the proposed estimator, in terms of prediction capability on future data, is close to that of PEM equipped with an oracle. The latter selects the best model order having knowledge of the true system.