A simulated maximum likelihood method for estimation of stochastic Wiener systems

This paper introduces a simulation-based method for maximum likelihood estimation of stochastic Wiener systems. It is well known that the likelihood function of the observed outputs for the general class of stochastic Wiener systems is analytically intractable. However, when the distributions of the process disturbance and the measurement noise are available, the likelihood can be approximated by running a Monte-Carlo simulation on the model. We suggest the use of Laplace importance sampling techniques for the likelihood approximation. The algorithm is tested on a simple first order linear example which is excited only by the process disturbance. Furthermore, we demonstrate the algorithm on an FIR system with a cubic nonlinearity. The performance of the algorithm is compared to the maximum likelihood method and other recent techniques.