Least Squares and Instrumental Variables Identification of Polynomial Wiener Systems

The paper is addressed to a combined least squares (LS) and instrumental variables (IV) approach to identification of polynomial Wiener systems. It is assumed that the inverse nonlinear element can be described by a polynomial. It is shown that LS parameter estimates of polynomial Wiener system are inconsistent and to circumvent the consistency problem, the well-known IV method is used. To avoid the parameter redundancy, three different methods of calculation inverse nonlinear function parameters from the transformed model parameters are proposed. The simulation results are included that confirm the practical feasibility of the proposed approach. The highest parameter estimation accuracy has been obtained via solving an overdetermined system of equations, only insignificantly lower accuracy has been obtained using the mean value approach, and the lowest one calculating the inverse nonlinear function parameters from the sums of transformed Wiener model parameters.