Identification of fractional-order ARX Wiener systems in the presence of noise in the input signals

The paper describes the parametric identification of fractional-order Wiener ARX (Autoregressive with exogenous input) systems in the presence of noise in the input signals. The criterion for evaluating the parameters of these systems is proposed which is a generalization of the method of least squares. It is proved that the interference class martingale-difference derived parameter estimates will have the property of strong consistency. It is shown that in the case of constant noise variance to obtain consistent estimates it is sufficient to know the ratio of their variances.