Identification of Wiener, Hammerstein, and NARX systems as Markov Chains with improved estimates for their nonlinearities

The Wiener, Hammerstein, and nonlinear ARX systems are identified not only for their linear subsystems (if they exist) but also for the nonlinearities with their first derivatives. It is assumed that the input signals and noises are mutually independent and both are sequences of independent and identically distributed (iid) random variables. The estimates based on the stochastic approximation algorithms with expanding truncations (SAAWET) are proved to be strongly consistent with the help of the Markov properties possessed by these systems. The estimates of the first derivatives improve the accuracy of interpolating the nonlinearity curves as validated by simulation examples.