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access icon free Modified Volterra LMS algorithm to fractional order for identification of Hammerstein non-linear system

© The Institution of Engineering and Technology
Received 21/10/2016, Accepted 28/06/2017, Revised 18/06/2017, Published 06/07/2017

In this study, a new non-linear recursive mechanism for Volterra least mean square (VLMS) algorithm is proposed in the domain of non-linear adaptive signal processing and control. The proposed adaptive scheme is developed by applying concepts and theories of fractional calculus in weight adaptation structure of standard VLMS approach. The design scheme based on fractional VLMS (F-VLMS) algorithm is applied to parameter estimation problem of non-linear Hammerstein Box-Jenkins system for different noise and step size variations. The adaptive variables of F-VLMS are compared from actual parameters of the system as well as with the results of conventional VLMS for each case to verify its correctness. Comprehensive statistical analyses are conducted based on sufficient large number of independent runs and performance indices in terms of mean square error, variance account for and Nash–Sutcliffe efficiency establish the worth and effectiveness of the scheme.

Inspec keywords: adaptive signal processing; nonlinear filters; least mean squares methods

Other keywords: nonlinear recursive mechanism; statistical analyses; Hammerstein nonlinear system identification; VLMS approach; fractional order; Volterra LMS algorithm; nonlinear Hammerstein Box-Jenkins system; Nash–Sutcliffe efficiency

Subjects: Filtering methods in signal processing; Interpolation and function approximation (numerical analysis); Signal processing theory; Interpolation and function approximation (numerical analysis)

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