Parametric identification of Wiener systems with invertible nonlinearities

The paper presents a new approach to identification of Wiener systems based on instrumental variables method. It is assumed that the linear dynamic system is represented by the discrete transfer function and the inverse characteristic of the nonlinear element is represented by any set of specified basis functions. It is shown that parameters of a modified series-parallel Wiener model estimated using the least squares method are inconsistent. To obtain consistent parameter estimates, the instrumental variables method is employed. The instrumental variables are generated by passing the system input through the linear dynamic model obtained with the least squares method. It is also shown that proposed identification method can be extended to Wiener systems with inverse nonlinear characteristics that does not contain the first order term. A simulation example is also included to show the effectiveness and practical feasibility and illustrate asymptotic convergence properties of the proposed approach.