Outlier-Robust Estimation of Uncertain-Input Systems With Applications to Nonparametric FIR and Hammerstein Models

In this letter, we present an extension of the class of uncertain-input models to handle cases of measurements with outliers. The general uncertain-input model framework allows us to treat system identification problems in which a linear system, represented by its impulse response, is subject to an input about which we have partial information. Both the impulse response and the input are modeled as Gaussian processes and the kernels are used to encode the information available. The whole model is then estimated using an approximate empirical Bayes approach. We extend the uncertain-input model framework to non-Gaussian measurement models by considering the noise precisions as realizations of a Gamma prior. We validate the approach on a dataset of linear systems and on a dataset of Hammerstein systems where the measurements are corrupted by outliers.