Nonparametric identification of Hammerstein systems

A discrete-time nonlinear Hammerstein system is identified, and the correlation and frequency-domain methods for identification of its linear subsystem are presented. The main results concern the estimation of the nonlinear memoryless subsystem. No conditions concerning the functional form of the transform characteristic of the subsystem are made, and an algorithm for estimation of the characteristic is given. The algorithm is simply a nonparametric kernel estimate of the regression function calculated from dependent data. It is shown that the algorithm converges to the characteristic of the subsystem regardless of the probability distribution of the input variable. Pointwise as well as global consistencies are established. For Lipschitz characteristics the rate of the convergence in probability is O(n^-1/3 )