Novel generalization of Volterra LMS algorithm to fractional order with application to system identification

In the present study, a novel generalization of Volterra least mean square (V-LMS) algorithm to fractional order is presented by exploiting the renowned strength of fractional adaptive signal processing. The fractional derivative term is introduced in weight adaptation mechanism of standard V-LMS to derive the recursive relations for modified V-LMS (MV-LMS) algorithm. The design scheme of MV-LMS algorithm is applied to parameter identification of Box–Jenkins system by taking different values of fractional orders, step-size variations and small to high signal-to-noise ratios. The proposed adaptive variables of MV-LMS are compared from true parameters of Box–Jenkins systems as well as with the results of the V-LMS for each case. The correctness and reliability of the given scheme MV-LMS are also validated from the results of statistical performance measures calculated on large dataset based on multiple independent runs.