Parameter Identification of Hammerstein Models using Elimination Theory

A Hammerstein model is a system model in which the inputs go through a static nonlinearity followed by a linear time-invariant system. Often the static nonlinearity is modeled as a polynomial nonlinearity in the inputs or as a piecewise constant nonlinearity. Such models are nonlinear in the unknown parameters and therefore present a challenging identification problem. In this work, the authors show that elimination theory can be used to solve exactly for parameter values that minimize a least-square criterion. Thus, the approach guarantees the minimum can be found in a finite number of steps, unlike iterative methods that are currently used.