W. Greblicki, NONLINEARITY ESTIMATION IN HAMMERSTEIN SYSTEMS BASED ON ORDERED OBSERVATIONS, IEEE transactions on signal processing, 44(5), 1996, pp. 1224-1233
The nonlinear subsystem of a Hammerstein system is identified, i.e., i
ts characteristic is recovered from input-output observations of the w
hole system. The input and disturbance are white stochastic processes,
The identified characteristic satisfies a piecewise Lipschitz conditi
on 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 observation
s tends to infinity. Convergence rates are insensitive to the shape of
the probability density of the input signal. Results of numerical sim
ulation are also shown.