Recursive Identification of Hammerstein Models

The nonlinear Hammerstein model, which consists of a static nonlinear block followed by a linear dynamic block, is considered. A recursive prediction error algorithm is derived. The linear block is modelled as a single-input single-output transfer function, and the nonlinearity as a linear combination of basis functions. The case when the nonlinear block is modelled as a piecewise linear function is studied in detail. A direct computation of the gradient allows the number of estimated parameters to be minimized, a fact that is crucial when small data sets are used. Numerical examples validate the algorithm, and shows that the scheme successfully identifies a biomedical model from 200 measurements.