Hammerstein system with a stochastic input of arbitrary/unknown autocorrelation – nonparametric estimator of the static nonlinear subsystem

Abstract

Abstract This study proposes the first estimator in the open literature (to the present authors' best knowledge) to nonparametrically estimate a Hammerstein system's nonlinear static subsystem when excited by an input that is temporally self‐correlated with an unknown spectrum, an unknown variance and an unknown mean (instead of the input as commonly presumed to be white and zero‐mean). This proposed nonparametric estimator is analytically proved here to be asymptotically unbiased and pointwise consistent. The proposed estimate's associated finite‐sample convergence rate is also derived analytically.

Keywords

• convergence
• estimation theory
• identification
• nonlinear systems
• nonparametric statistics
• stochastic processes