Iterative estimation methods for Hammerstein controlled autoregressive moving average systems based on the key-term separation principle

This paper considers iterative identification problems for a Hammerstein nonlinear system which consists of a memoryless nonlinear block followed by a linear dynamical block. The difficulty of identification is that the Hammerstein nonlinear system contains the products of the parameters of the nonlinear part and the linear part, which leads to the unidentifiability of the parameters. In order to obtain unique parameter estimates, we express the output of the system as a linear combination of all the system parameters by means of the key-term separation principle and derive a gradient based iterative identification algorithm by replacing the unknown variables in the information vectors with their estimates. The simulation results indicate that the proposed algorithm can work well.