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

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.