Hierarchical iterative identification of output nonlinear Box-Jenkins Wiener model with ARMA noise

This paper focuses on development of a three-stage iterative identification algorithm for parameter estimation of a Wiener model with autoregressive moving average (ARMA) noise entering between linear and nonlinear part. The proposed three-stage algorithm is developed based on generalized extended gradient iterative (GEGI) algorithm to increase the convergence rate at a low number of iterations. To increase the convergence rate, a second algorithm is derived based on generalized extended least squares algorithm (GELSI). The proposed 3-stage generalized extended least square iterative (3S-GELSI) algorithm will also decrease the computational burden compared to the single-stage algorithm. Finally, to show that the discussed methods can identify the considered system effectively, simulation results of three examples are provided. The results demonstrate that the 3-stage GEGI (3S-GEGI) algorithm outperforms its basic single-stage counterpart in terms of convergence rate. Moreover, the proposed 3S-GELSI algorithm exhibits even greater superiority in terms of convergence rate compared to other existing methods. Additionally, it will be demonstrated that the computational burden decreases in the 3S-GELSI algorithm, as indicated by the reduced number of total flops.