Application of Instrumental Variable Method to the Identification of Hammerstein-wiener Systems

Abstract. Application of least squares and instrumental variables to recovering parameters of nonlinear complex dynamic block-oriented systems is examined. For a system with the Hammerstein-Wiener structure the instrumental variable algorithm is designed and compared with the least squares algorithm for estimating system parameters. The advantages of the proposed instrumental variable estimator are discussed and in particular its weak consistency, even in the presence of correlated noise, is shown. The problem of generating optimal values of instrumental variables is analysed, rate of convergence of the proposed estimator is evaluated and simulation examples are included. The paper provides an extension of the results introduced in [1].