Recursive identification of errors-in-variables Wiener–Hammerstein systems

This paper considers the recursive identification of errors-in-variables Wiener–Hammerstein system, which is composed of a static nonlinearity sandwiched by two linear dynamic subsystems. Both the system input and output are observed with additive noises being ARMA processes with unknown coefficients. By the stochastic approximation algorithms incorporated with the deconvolution kernel functions, the coefficients of the linear subsystems and the values of the nonlinear function are recursively estimated. All the estimates are proved to converge to the true values with probability one. A simulation example is given to verify the theoretical analysis.