Kernel-based SPS

One of the central issues in system identification consists not only in obtaining a good model of the process under study but also an informative confidence interval around it. This problem is often referred to as robust identification in the literature. Following the classical paradigm, one first obtains a model through prediction error minimization. Asymptotic theory is then invoked to extract quality tags from the normal approximation of the estimates’ distribution. This paper proposes an alternative route for robust linear system identification. Our procedure relies on the use of kernel-based regularization for both impulse response estimation and confidence intervals computation. The main novelty is that the kernel is not used to define a Gaussian density for the impulse response but just a prior satisfying some symmetry properties forming the basis of the recently developed sign-perturbed sums (SPS) framework. For system identification, SPS is then combined with the stable spline (SS) kernel to account for impulse response regularity and exponential stability. Numerical experiments show that SS+SPS can provide more accurate confidence intervals than those commonly achieved in the Gaussian regression framework (which, in turn, were already shown to outperform those based on the classical paradigm).