Parameter estimation error bounds for Hammerstein nonlinear finite impulsive response models

Abstract

This paper presents a parameter estimation algorithm for a class of Hammerstein nonlinear systems – input nonlinear FIR (finite impulse response) models, and studies in detail the convergence properties of the proposed identification algorithm in the stochastic framework, and derives the upper and lower bounds of the parameter estimation errors (PEE) from the available input–output data. The analysis indicates that the mean square PEE upper and lower bounds of the algorithm approach zero as the data length increases. A simulation example is given.