Nonlinear system identification using a Hammerstein model and a cumulant-based Steiglitz-McBride algorithm

In this paper, we address the problem of estimating the parameters of a Hammerstein model. Hammerstein models, which consist of a nonlinear memoryless gain followed by a linear time-invariant system, have been used to identify nonlinear systems. We assume that the gain is in polynomial form, and that the system is an ARMA filter. The input and output are available, and the output is assumed to be corrupted by additive Gaussian noise of unknown covariance. Transforming the problem into the cumulant domain, we suppress the effect of the noise and estimate the model parameters using a linear, iterative method. Simulations are presented to illustrate the performance of the proposed method