Design of fractional adaptive strategy for input nonlinear Box-Jenkins systems

In this study, the strength of fractional signal processing is exploited in designing fractional adaptive algorithms for parameter estimation of input nonlinear Box-Jenkins (INBJ) systems. The idea is to develop fractional least mean square (F-LMS) and auxiliary model F-LMS (AM-FLMS) algorithms with three values of fractional order to adopt the variables of INBJ system for different scenarios based on noise and step size variations. The comparative study of the proposed results is made with true values of the system, as well as, with the results of Volterra and Kernel LMS adaptive algorithms in order to establish the correctness of the design scheme. The accuracy and convergence of the proposed scheme is analyzed on large data set generated through statistical analysis based on sufficient number of independent runs of the algorithm and result in term of performance measures established the worth of the scheme. (C) 2015 Elsevier B.V. All rights reserved.