A fractional taylor series-Based least mean square algorithm, and its application to power signal estimation

Furqan Iqbal, Muhammad Tufail, Shakeel Ahmed, Muhammad Tahir Akhtar

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


The definition of fractional derivative by Caputo and Riemann inspired the researchers to develop new adaptive algorithms having better convergence properties in comparison with integer-gradient based adaptive algorithms. As reported in many studies, the existing fractional gradient-based adaptive algorithms lack justification for using fractional derivative in addition to integer-gradient, may become inconsistent in the event of negative weights, and may yield more or less same performance as compared to the conventional integer-derivative-based algorithms by appropriate selection of step-size parameter. Accordingly, this paper presents a novel fractional adaptive algorithm based on Fractional Taylor Series. Unlike (most of) the existing fractional-derivative-based algorithms, the proposed algorithm only involves fractional-derivative and ensures convergence of mean square error (MSE) provided the step-size is chosen appropriately. Simulation results are presented in order to depict a scenario where exploitation of fractional-derivative in the weight-update equation yields better convergence as compared to LMS algorithm in the context of power signal parameters estimation.

Original languageEnglish
Article number108405
JournalSignal Processing
Publication statusPublished - Apr 2022


  • Adaptive signal processing
  • Caputo derivative
  • Fractional gradient
  • Fractional taylor series
  • Least mean square
  • Power signal estimation

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Electrical and Electronic Engineering


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