Expectation-Maximization Algorithm Based Identification of Hammerstein Nonlinear ARMAX Systems with Gaussian Mixture Noises

This paper presents a robust iterative identification scheme for a class of Hammerstein nonlinear ARMAX systems. The identification problem is formulated under the framework of maximum likelihood estimation and solved by the expectation-maximization (EM) algorithm. Instead of modeling the ambient noise with a Gaussian distribution, the heavy tailed Gaussian mixture distribution is utilized, which ensures the estimation algorithm is robust to the outliers. By means of the over-parameterization method and replacing the unmeasurable noise terms with the estimation residuals, the iterative algorithm is able to identify the system model and the parameters of noise distribution simultaneously. The simulation results indicate the effectiveness of the proposed algorithm.