Nonlinearity estimation in Hammerstein systems based on ordered observations

The nonlinear subsystem of a Hammerstein system is identified, i.e., its characteristic is recovered from input output ohservations of the whole system. The input and disturbance are white stochastic processes. The identified characteristic satisfies a piecewise Lipschitz condition only. Algorithms presented in the paper are calculated from ordered input-output observations, i.e., from pairs of observations arranged in a sequence in which input measurements increase in value. The mean integrated square error converges to zero as the number of observations tends to infinity. Convergence rates are insensitive to the shape of the probability density of the input signal. Results of numerical simulation are also shown.