New results for Hammerstein system identification

A novel approach is presented for the analysis and design of identification algorithms for Hammerstein models, which consist of a static nonlinearity followed by an LTI system. The authors examine two identification problems. In the first problem, the system is excited with white noise and the LTI system is FIR, and they find a simple explicit solution for the optimal parameter estimate and show that for sufficiently large data lengths a standard iterative technique globally converges to this optimal value. In the second problem, the LTI system is given in state-space form and the authors show that standard state-space algorithms can be easily modified to identify Hammerstein models