中国物理B ›› 2014, Vol. 23 ›› Issue (3): 30502-030502.doi: 10.1088/1674-1056/23/3/030502

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A modified fractional least mean square algorithm for chaotic and nonstationary time series prediction

Bilal Shoaiba, Ijaz Mansoor Qureshib, Ihsanulhaqa, Shafqatullahc   

  1. a Department of Electronic Engineering, Faculty of Engineering and Technology, International Islamic University, Islamabad, Pakistan;
    b Department of Electrical Engineering, AIR University, Islamabad, Pakistan;
    c School of Engineering and Applied Sciences, ISRA University, Islamabad, Pakistan
  • 收稿日期:2013-07-14 修回日期:2013-09-06 出版日期:2014-03-15 发布日期:2014-03-15
  • 基金资助:
    Project supported by the Higher Education Commission of Pakistan.

A modified fractional least mean square algorithm for chaotic and nonstationary time series prediction

Bilal Shoaiba, Ijaz Mansoor Qureshib, Ihsanulhaqa, Shafqatullahc   

  1. a Department of Electronic Engineering, Faculty of Engineering and Technology, International Islamic University, Islamabad, Pakistan;
    b Department of Electrical Engineering, AIR University, Islamabad, Pakistan;
    c School of Engineering and Applied Sciences, ISRA University, Islamabad, Pakistan
  • Received:2013-07-14 Revised:2013-09-06 Online:2014-03-15 Published:2014-03-15
  • Contact: Bilal Shoaib E-mail:bilal.phdee42@iiu.edu.pk
  • Supported by:
    Project supported by the Higher Education Commission of Pakistan.

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摘要： A method of modifying the architecture of fractional least mean square (FLMS) algorithm is presented to work with nonlinear time series prediction. Here we incorporate an adjustable gain parameter in the weight adaptation equation of the original FLMS algorithm and absorb the gamma function in the fractional step size parameter. This approach provides an interesting achievement in the performance of the filter in terms of handling the nonlinear problems with less computational burden by avoiding the evaluation of complex gamma function. We call this new algorithm as the modified fractional least mean square (MFLMS) algorithm. The predictive performance for the nonlinear Mackey glass chaotic time series is observed and evaluated using the classical LMS, FLMS, kernel LMS, and proposed MFLMS adaptive filters. The simulation results for the time series with and without noise confirm the superiority and improvement in the prediction capability of the proposed MFLMS predictor over its counterparts.

关键词: fractional least mean square, kernel methods, Reimann–, Lioville derivative, Mackey glass time series

Abstract: A method of modifying the architecture of fractional least mean square (FLMS) algorithm is presented to work with nonlinear time series prediction. Here we incorporate an adjustable gain parameter in the weight adaptation equation of the original FLMS algorithm and absorb the gamma function in the fractional step size parameter. This approach provides an interesting achievement in the performance of the filter in terms of handling the nonlinear problems with less computational burden by avoiding the evaluation of complex gamma function. We call this new algorithm as the modified fractional least mean square (MFLMS) algorithm. The predictive performance for the nonlinear Mackey glass chaotic time series is observed and evaluated using the classical LMS, FLMS, kernel LMS, and proposed MFLMS adaptive filters. The simulation results for the time series with and without noise confirm the superiority and improvement in the prediction capability of the proposed MFLMS predictor over its counterparts.

Key words: fractional least mean square, kernel methods, Reimann–Lioville derivative, Mackey glass time series

中图分类号:  (Fractals)

  • 05.45.Df
05.30.Pr (Fractional statistics systems) 05.45.Tp (Time series analysis) 92.60.Wc (Weather analysis and prediction)