Identification of discrete Hammerstein systems using kernel regression estimates

In this note a discrete-time Hammerstein system is identified. The weighting function of the dynamical subsystem is recovered by the correlation method. The main results concern estimation of the nonlinear memoryless subsystem. No conditions concerning functional form of the transform characteristic of the subsystem are made and an algorithm for estimation of the characteristic is presented.The algorithm is a nonparametric kernel estimate of regression functions calculated from dependent data. It is shown that the algorithm converges to the characteristic as the number of observations tend to infinity. For sufficiently smooth characteristics, the rate of convergence isO(n-2/5)in probability.