A Novel LMS Algorithm with Double Fractional Order.

This paper presents a double fractional order LMS algorithm (DFOLMS) based on fractional order difference and fractional order gradient, in which a variable initial value strategy is introduced to ensure the convergence accuracy of the algorithm. Through a model approximation, the DFOLMS is transformed into two fractional order difference models to analyze its convergence and steady-state properties indirectly. It is shown that the DFOLMS has different convergence characteristics in different difference intervals; meanwhile, a larger difference order α and gradient order β would lead to a faster convergence speed but a larger steady-state noise. Finally, the effectiveness and superiority of the proposed DFOLMS are demonstrated by simulation examples. [ABSTRACT FROM AUTHOR]