Nonparametric models for Hammerstein-Wiener and Wiener-Hammerstein system identification

We propose a framework for modeling structured nonlinear systems using nonparametric Gaussian processes. In particular, we introduce a two-layer stochastic model of latent interconnected Gaussian processes suitable for modeling Hammerstein-Wiener and Wiener-Hammerstein cascades. The posterior distribution of the latent processes is intractable because of the nonlinear interactions in the model; hence, we propose a Markov Chain Monte Carlo method consisting of a Gibbs sampler where each step is implemented using elliptical-slice sampling. We present the results on two example nonlinear systems showing that they can effectively be modeled and identified using the proposed nonparametric modeling approach.