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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.
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Keywords:
- chaos /
- denoising /
- phase space reconstruction /
- projection
[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
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[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
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