Regularized estimation of sums of exponentials in spaces generated by stable spline kernels

A new nonparametric paradigm to model identification has been recently introduced in the literature. Instead of adopting finite-dimensional models of the system transfer function, the system impulse response is searched for within an infinite dimensional space using regularization theory. The method exploits the so called stable spline kernels which are associated with hypothesis spaces embedding information on both regularity and stability of the impulse response. In this paper, the potentiality of this approach is studied with respect to the reconstruction of sums of exponentials. In particular, first, we characterize the learning rates of our estimator in reconstructing such class of functions also exploiting recent advances in statistical learning theory. Then, we use Monte Carlo studies to illustrate the definite advantages of this new nonparametric approach over classical parametric prediction error methods in terms of accuracy in impulse responses reconstruction.