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A Novel LMS Algorithm with Double Fractional Order

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Abstract

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 \(\alpha \) and gradient order \(\beta \) 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.

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Acknowledgements

This work is supported by National Natural Science Foundation (NNSF) of China (Grant No. 61973329) and the Beijing Natural Science Foundation (Grant No. Z180005).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Beijing Technology and Business University, Beijing, 100048, People’s Republic of China

    Haozhe Zhang & Lipo Mo

  2. Research Center for Consumption Big Data and Intelligent Decision-Making, Beijing Technology and Business University, Beijing, 100048, People’s Republic of China

    Lipo Mo

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  1. Haozhe Zhang
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Zhang, H., Mo, L. A Novel LMS Algorithm with Double Fractional Order. Circuits Syst Signal Process 42, 1236–1260 (2023). https://doi.org/10.1007/s00034-022-02192-3

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