Recursive Identification of Multi-Input Multi-Output Errors-in-Variables Hammerstein Systems

The note considers the identification of multi-input multi-output errors-in-variables Hammerstein systems, in which both the input and output can be observed but with additive noises being ARMA processes with unknown coefficients. With the help of stochastic approximation combined with the deconvolution kernel function, the recursive algorithms are proposed for estimating coefficients of the linear subsystem and for the values of the nonlinear function. Under some reasonable conditions, all the estimates are proved to converge to the true values with probability one. These results include identification of the errors-in-variables linear systems as a special case. A simulation example is given justifying the theoretical analysis.