Prediction error identification of linear systems: A nonparametric Gaussian regression approach

A novel Bayesian paradigm to identification of output error models has been recently proposed where, in place of postulating finitedimensional models of the system transfer function, the system impulse response is searched for within an infinite-dimensional space. In this paper, such nonparametric approach is applied to the design of optimal discrete-time predictors by interpreting the predictor coefficients as realizations of Gaussian processes. The proposed scheme describes the predictor impulse responses as the convolution of an infinitedimensional response with a low-dimensional parametric response that captures possible high frequency dynamics. Overparametrization is avoided because the model involves only few hyperparameters that are tuned via marginal likelihood maximization. Numerical experiments, with data generated by ARMAX and infinite-dimensional models, show the definite advantages of the new approach over standard parametric prediction error methods both in terms of predictive capability on new data and accuracy in reconstruction of system impulse responses.