| A modified fractional least mean square algorithm for chaotic and nonstationary time series prediction |
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| 作者姓名： | Bilal Shoaib Ijaz Mansoor Qureshi Ihsanulhaq Shafqatullah |
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| 基金项目： | 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.
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| 关 键 词： | 非线性时间序列预测 最小均方算法 混沌时间序列 分数步长 修改 FLMS算法 非平稳 LMS自适应滤波器 |
A modified fractional least mean square algorithm for chaotic and nonstationary time series prediction |
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| Bilal Shoaib,Ijaz Mansoor Qureshi,Ihsanulhaq,Shafqatullah.A modified fractional least mean square algorithm for chaotic and nonstationary time series prediction[J].Chinese Physics B,2014(3):159-164. |
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| Authors: | Bilal Shoaib Ijaz Mansoor Qureshi Ihsanulhaq Shafqatullah |
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| 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. |
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| Keywords: | fractional least mean square kernel methods Reimann-Lioville derivative Mackey glass timeseries |
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