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一种混沌映射的相空间去噪方法

吕善翔 冯久超

引用本文:
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一种混沌映射的相空间去噪方法

吕善翔, 冯久超

A phase space denoising method for chaotic maps

Lü Shan-Xiang, Feng Jiu-Chao
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  • 对于混沌映射来说,它们的频谱比混沌流的频谱更广阔,与噪声频谱的重叠率更高,所以混沌流的去噪方法对它们并不适用. 在半盲分析法的框架下,混沌系统的参数估计问题终将归结为最小二乘估计问题. 本文从最小二乘拟合的角度出发估计混沌映射的演化参数,进而通过相空间重构以及投影操作,实现对观测信号的噪声抑制. 实验结果表明,该算法的去噪效果优于扩展卡尔曼滤波器(extended Kalman filter,EKF)和无先导卡尔曼滤波器(unscneted Kalman filter,UKF),并且能够较大程度地将信号源的混沌特征量还原.
    The spectra of chaotic maps are much wider than those of chaotic flows, and their overlapped regions with Gaussian white noise are much larger, thus the denoising method for chaotic flows is unsuitable for chaotic maps. Within a semi-blind analysing framework, the parameter estimating problem for chaotic systems can be boiled down to a least square evaluating procedure. In this paper we start with estimating the evolution parameters of chaotic maps by using a least square fitting method. After that, phase space reconstruction and projection operation are employed to get noise suppression for the observed data. The simulation results indicate that the proposed algorithm surpasses the extended Kalman filter (EKF) and the unscented Kalman filter (UKF) in denoising, as well as maintaining the characteristic quantities of chaotic maps.
    • 基金项目: 国家自然科学基金(批准号:60872123)、国家-广东省自然科学基金联合基金(批准号:U0835001)、广东省高层次人才项目基金(批准号:N9101070)和中央高校基本业务费(批准号:2012ZM0025)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 60872123), the Joint Fund of the National Natural Science Foundation and the Natural Science Foundation of Guangdong Province, China (Grant No. U0835001), the Fund for Higher-level Talent in Guangdong Province (Grant No. N9101070), and the Fundamental Research Fund for the Central Universities of China (Grant No. 2012ZM0025).
    [1]

    Han M, Xu M L 2013 Acta Phys. Sin. 62 120510 (in Chinese) [韩敏, 许美玲 2013 物理学报 62 120510]

    [2]

    Niu H, Zhang G S 2013 Acta Phys. Sin. 62 130502 (in Chinese) [牛弘, 张国山 2013 物理学报 62 130502]

    [3]

    Feng J C 2012 Chaotic Signals and Information Processing (Beijing: Tsinghua Univ. Press)pp 32–35 (in Chinese) [冯久超 2012 混沌信号与信息处理 (清华大学出版社)第32–35页]

    [4]

    Li R H, Chen W S 2013 Chin. Phys. B 22 040503

    [5]

    Hossein G, Amir H, Azita A 2013 Chin. Phys. B 22 010503

    [6]

    Constantine W L B, Reinhall P G 2001 Int. J. Bifurcation Chaos 11 483

    [7]

    Han M, Liu Y H, Xi J H, Guo W 2007 IEEE Signal Process. Lett. 14 62

    [8]

    Gao J B, Sultan H, Hu J, Tung W W 2010 IEEE Signal Process. Lett. 17 237

    [9]

    Tung W W, Gao J B, Hu J, Yang L 2011 Phys. Rev. E 83 046210

    [10]

    Wang W B, Zhang X D, Wang X L 2013 Acta Phys. Sin. 62 050201 (in Chinese) [王文波, 张晓东, 汪祥莉 2013 物理学报 62 050201]

    [11]

    Cawley R, Hsu G H 1992 Phys. Rev. A 46 3057

    [12]

    Wang F P, Wang Z J, Guo J B 2002 Acta Phys. Sin. 51 474 (in Chinese) [汪芙平, 王赞基, 郭静波 2002 物理学报 51 474]

    [13]

    Feng J C 2005 Chinese Phys. Lett. 22 1851

    [14]

    Feng J C, Tse C K 2001 Phys. Rev. E 63 026202

    [15]

    Wu Y, Hu D, Wu M, Hu X 2005 IEEE Signal Process. Lett. 12 357

    [16]

    Arasaratnam I, Haykin S, Hurd T R 2010 IEEE Tran. Signal Process. 58 4977

    [17]

    Wang S Y, Long Z J, Wang J, Guo J 2011 2011 4th International Congress on Image and Signal Processing Shanghai Oct.15–17, 2011 p2303

    [18]

    Gerald C F, Wheatley P O 2004 Applied Numerical Analysis, seventh edition (New York: Pearson Addition Wesley) pp 266–270

    [19]

    Johnson M T, Povinelli R J 2005 Physica D 201 306

    [20]

    Takens F 1981 Lecture Notes in Mathematics (Berlin: Springer) pp 366–381

    [21]

    Wu K L, Yang M S 2002 Pattern Recognition 35 2267

    [22]

    Phatak S C, Rao S S 1995 Phys. Rev. E 51 3670

    [23]

    Gallas J A C 1993 Phys. Rev. Lett. 70 2714

    [24]

    Rosenstein M T, Collins J J, De L, Carlo J 1993 Physica D: Nonlinear Phenomena 65 117

  • [1]

    Han M, Xu M L 2013 Acta Phys. Sin. 62 120510 (in Chinese) [韩敏, 许美玲 2013 物理学报 62 120510]

    [2]

    Niu H, Zhang G S 2013 Acta Phys. Sin. 62 130502 (in Chinese) [牛弘, 张国山 2013 物理学报 62 130502]

    [3]

    Feng J C 2012 Chaotic Signals and Information Processing (Beijing: Tsinghua Univ. Press)pp 32–35 (in Chinese) [冯久超 2012 混沌信号与信息处理 (清华大学出版社)第32–35页]

    [4]

    Li R H, Chen W S 2013 Chin. Phys. B 22 040503

    [5]

    Hossein G, Amir H, Azita A 2013 Chin. Phys. B 22 010503

    [6]

    Constantine W L B, Reinhall P G 2001 Int. J. Bifurcation Chaos 11 483

    [7]

    Han M, Liu Y H, Xi J H, Guo W 2007 IEEE Signal Process. Lett. 14 62

    [8]

    Gao J B, Sultan H, Hu J, Tung W W 2010 IEEE Signal Process. Lett. 17 237

    [9]

    Tung W W, Gao J B, Hu J, Yang L 2011 Phys. Rev. E 83 046210

    [10]

    Wang W B, Zhang X D, Wang X L 2013 Acta Phys. Sin. 62 050201 (in Chinese) [王文波, 张晓东, 汪祥莉 2013 物理学报 62 050201]

    [11]

    Cawley R, Hsu G H 1992 Phys. Rev. A 46 3057

    [12]

    Wang F P, Wang Z J, Guo J B 2002 Acta Phys. Sin. 51 474 (in Chinese) [汪芙平, 王赞基, 郭静波 2002 物理学报 51 474]

    [13]

    Feng J C 2005 Chinese Phys. Lett. 22 1851

    [14]

    Feng J C, Tse C K 2001 Phys. Rev. E 63 026202

    [15]

    Wu Y, Hu D, Wu M, Hu X 2005 IEEE Signal Process. Lett. 12 357

    [16]

    Arasaratnam I, Haykin S, Hurd T R 2010 IEEE Tran. Signal Process. 58 4977

    [17]

    Wang S Y, Long Z J, Wang J, Guo J 2011 2011 4th International Congress on Image and Signal Processing Shanghai Oct.15–17, 2011 p2303

    [18]

    Gerald C F, Wheatley P O 2004 Applied Numerical Analysis, seventh edition (New York: Pearson Addition Wesley) pp 266–270

    [19]

    Johnson M T, Povinelli R J 2005 Physica D 201 306

    [20]

    Takens F 1981 Lecture Notes in Mathematics (Berlin: Springer) pp 366–381

    [21]

    Wu K L, Yang M S 2002 Pattern Recognition 35 2267

    [22]

    Phatak S C, Rao S S 1995 Phys. Rev. E 51 3670

    [23]

    Gallas J A C 1993 Phys. Rev. Lett. 70 2714

    [24]

    Rosenstein M T, Collins J J, De L, Carlo J 1993 Physica D: Nonlinear Phenomena 65 117

计量
  • 文章访问数:  1907
  • PDF下载量:  576
  • 被引次数: 0
出版历程
  • 收稿日期:  2013-08-08
  • 修回日期:  2013-08-27
  • 刊出日期:  2013-12-05

一种混沌映射的相空间去噪方法

  • 1. 华南理工大学, 电子与信息学院, 广州 510641
    基金项目: 

    国家自然科学基金(批准号:60872123)、国家-广东省自然科学基金联合基金(批准号:U0835001)、广东省高层次人才项目基金(批准号:N9101070)和中央高校基本业务费(批准号:2012ZM0025)资助的课题.

摘要: 对于混沌映射来说,它们的频谱比混沌流的频谱更广阔,与噪声频谱的重叠率更高,所以混沌流的去噪方法对它们并不适用. 在半盲分析法的框架下,混沌系统的参数估计问题终将归结为最小二乘估计问题. 本文从最小二乘拟合的角度出发估计混沌映射的演化参数,进而通过相空间重构以及投影操作,实现对观测信号的噪声抑制. 实验结果表明,该算法的去噪效果优于扩展卡尔曼滤波器(extended Kalman filter,EKF)和无先导卡尔曼滤波器(unscneted Kalman filter,UKF),并且能够较大程度地将信号源的混沌特征量还原.

English Abstract

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