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

• Published in: IET signal processing Vol. 11; no. 8; pp. 975 - 985
• Main Authors: Chaudhary, Naveed Ishtiaq, Aslam, Muhammad Saeed, Raja, Muhammad Asif Zahoor
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 01.10.2017
• Subjects: adaptive signal processing; fractional order; Hammerstein nonlinear system identification; least mean squares methods; Nash–Sutcliffe efficiency; nonlinear filters; nonlinear Hammerstein Box‐Jenkins system; nonlinear recursive mechanism; Research Article; statistical analyses; VLMS approach; Volterra LMS algorithm; least mean squares methods; VLMS approach; adaptive signal processing; Nash–Sutcliffe efficiency; nonlinear recursive mechanism; Hammerstein nonlinear system identification; statistical analyses; Volterra LMS algorithm; nonlinear Hammerstein Box-Jenkins system; nonlinear filters; fractional order
• ISSN: 1751-9675; 1751-9683; 1751-9683
• DOI: 10.1049/iet-spr.2016.0578

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.