A kernel-based identification approach for a class of nonlinear systems with quantized output data

Abstract

In this paper, we consider the problem of identification for a class of nonlinear systems with Hammerstein structure, which is a combination of some basis functions for the static nonlinearity and finite impulse response models for the linear block under quantized output data. Following the empirical Bayes method, we model the impulse response of the system using a Gaussian process whose covariance matrix depends on some suitable kernels. Then, we compute the minimum mean-square error estimation of the impulse response via a special case of Markov Chain Monte Carlo sampling approach, namely, Gibbs sampler. The estimation of the impulse response depends on the kernel hyperparameters, the noise variance and the coefficients of the static nonlinearity. These unknowns are estimated by the marginal likelihood maximization, which is solved via the expectation-conditional maximization algorithm combining the Gibbs sampler. The expectation-conditional maximization method is a variation of the standard expectation-maximization method for solving maximum-likelihood problems. Numerical simulations show the effectiveness of the proposed scheme.