Initial estimates for the dynamics of a Hammerstein system

This paper studies the generation of initial estimates for the dynamic part of a Hammerstein model. It will be shown that ARMAX or Box–Jenkins models result in better initial estimates than ARX or output-error (OE) models even in the absence of disturbing noise. This will be proven by noticing that a static nonlinear system can be replaced by a static gain plus a nonlinear noise source that acts in a completely similar way to disturbing noise for the study of the second-order properties of the estimators in the prediction error framework.