On identification of harnmerstein systems using excitation with a finite number of levels

Abstract

Identification of nonlinear systems of Hammerstein type is considered in a scenario where the input signal is constrained to attain only a finite number of amplitude levels. This leads to the possibility to obtain asymptotically unbiased point-wise estimates of the nonlinear function without the need for a priori assumptions about the shape of the function. A three step identification procedure is presented which starts with a sub-space based method to estimate the poles of the linear system. Two alternative techniques are then outlined for the estimation of the zeros of the linear system and the non-linearity. The simpler procedure can be used if the initial condition of the system is known while an iterative procedure is employed when the initial condition is unknown. In a third step the preliminary estimate given by the first two steps are refined by the prediction error method