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A novel method of estimating the noise level from a noisy chaotic time series based on the invariant of the largest Lyapunov exponent is presented in this paper. The influence of noise on the distance between two points in an embedding phase space is considered, and then based on the invariant of the largest Lyapunov exponent in a different dimensional embedding phase space, the algorithm is proposed to estimate the noise level. Simulation results show that the estimated values of noise level agree well with the true values when the noise level is less than 10%. And this method is not sensitive to the distribution of noise. Therefore, the method is useful for estimating the noise level of noisy chaotic time series.
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Keywords:
- chaos /
- time series /
- the largest Lyapunov exponent /
- noise
[1] Tulu S, Yilmaz O 2010 Chaos 20 043103
[2] Skufca J D, Yorke J A, Eckhardt B 2006 Phys. Rev. Lett. 96 174101
[3] Krasny R, Nitsche M 2002 J. Fluid Mech. 454 47
[4] Brackley C A, Ebenhoh O, Grebogi C, Kurths J, Moura A D, Romanno M C, Thiel M 2010 Chaos 20 045101
[5] Ghosh-Dastidar S, Adeli H, Dadmehr N 2007 IEEE Trans. Biomed. Eng. 54 1545
[6] Chen W C 2008 Chaos, Solitons and Fractals 36 1305
[7] Schreiber T 1999 Phys. Rep. 308 1
[8] Wang H C, Chen G R, L¨u J H 2004 Phys. Lett. A 333 246
[9] Liu H F, Zhao Y Y, Dai Z H, Gong X, Yu Z H 2001 Acta Phys. Sin. 50 2311 (in Chinese)[刘海峰, 赵艳艳, 代正华, 龚欣, 于遵宏 2001 50 2311]
[10] Zhou Y D, Ma H, L¨u W Y, Wang H Q 2007 Acta Phys. Sin. 56 6809 (in Chinese)[周永道, 马洪, 吕王勇, 王会琦 2007 56 6809]
[11] Zhang J F, Hu S S 2008 Acta Phys. Sin. 57 2708 (in Chinese)[张军峰, 胡寿松 2008 57 2708]
[12] Liu H F, Dai Z H, Li W F, Gong X, Yu Z H 2005 Phys. Lett. A 341 119
[13] Gong Z Q, Feng G L, Dong W J, Li J P 2006 Acta Phys. Sin. 55 3180 (in Chinese)[龚志强, 封国林, 董文杰, 李建平 2006 55 3180]
[14] Wu Y D, Xie H B 2007 Acta Phys. Sin. 56 6294 (in Chinese)[吴延东, 谢洪波 2007 56 6294]
[15] Schreiber T 1993 Phys. Rev. E 48 13
[16] Yu D, Small M, Harrison R G, Diks C 2000 Phys. Rev. E 61 3750
[17] Jayawardena A W, Xu P, Li W K 2008 Chaos 18 023115
[18] Urbanowicz K, Holyst J A 2003 Phys. Rev. E 67 046218
[19] Urbanowicz K, Holyst J A 2006 Int. J. Bifurcat. Chaos 16 1865
[20] Strumik M,Macek WM, Redaelli S 2005 Phys. Rev. E 72 036219
[21] Moriya N 2010 Nucl. Instrum. Methods Phys. Res. A 618 306
[22] Takens F 1981 Dynamical System and Turbulence, Lecture Notes in Mathematics (Berlin: Springer-Verlag) p366
[23] Rosenstein M T, Collins J J, De Luca C J 1993 Physica D 65 117
[24] Kantz H 1994 Phys. Lett. A 185 77
[25] Guegan D, Leroux J 2009 Chaos Solitons and Fractals 41 2401
[26] Hénon M 1976 Commun. Math. Phys. 50 69
[27] Baier G, Klein M 1990 Phys. Lett. A 151 281
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[1] Tulu S, Yilmaz O 2010 Chaos 20 043103
[2] Skufca J D, Yorke J A, Eckhardt B 2006 Phys. Rev. Lett. 96 174101
[3] Krasny R, Nitsche M 2002 J. Fluid Mech. 454 47
[4] Brackley C A, Ebenhoh O, Grebogi C, Kurths J, Moura A D, Romanno M C, Thiel M 2010 Chaos 20 045101
[5] Ghosh-Dastidar S, Adeli H, Dadmehr N 2007 IEEE Trans. Biomed. Eng. 54 1545
[6] Chen W C 2008 Chaos, Solitons and Fractals 36 1305
[7] Schreiber T 1999 Phys. Rep. 308 1
[8] Wang H C, Chen G R, L¨u J H 2004 Phys. Lett. A 333 246
[9] Liu H F, Zhao Y Y, Dai Z H, Gong X, Yu Z H 2001 Acta Phys. Sin. 50 2311 (in Chinese)[刘海峰, 赵艳艳, 代正华, 龚欣, 于遵宏 2001 50 2311]
[10] Zhou Y D, Ma H, L¨u W Y, Wang H Q 2007 Acta Phys. Sin. 56 6809 (in Chinese)[周永道, 马洪, 吕王勇, 王会琦 2007 56 6809]
[11] Zhang J F, Hu S S 2008 Acta Phys. Sin. 57 2708 (in Chinese)[张军峰, 胡寿松 2008 57 2708]
[12] Liu H F, Dai Z H, Li W F, Gong X, Yu Z H 2005 Phys. Lett. A 341 119
[13] Gong Z Q, Feng G L, Dong W J, Li J P 2006 Acta Phys. Sin. 55 3180 (in Chinese)[龚志强, 封国林, 董文杰, 李建平 2006 55 3180]
[14] Wu Y D, Xie H B 2007 Acta Phys. Sin. 56 6294 (in Chinese)[吴延东, 谢洪波 2007 56 6294]
[15] Schreiber T 1993 Phys. Rev. E 48 13
[16] Yu D, Small M, Harrison R G, Diks C 2000 Phys. Rev. E 61 3750
[17] Jayawardena A W, Xu P, Li W K 2008 Chaos 18 023115
[18] Urbanowicz K, Holyst J A 2003 Phys. Rev. E 67 046218
[19] Urbanowicz K, Holyst J A 2006 Int. J. Bifurcat. Chaos 16 1865
[20] Strumik M,Macek WM, Redaelli S 2005 Phys. Rev. E 72 036219
[21] Moriya N 2010 Nucl. Instrum. Methods Phys. Res. A 618 306
[22] Takens F 1981 Dynamical System and Turbulence, Lecture Notes in Mathematics (Berlin: Springer-Verlag) p366
[23] Rosenstein M T, Collins J J, De Luca C J 1993 Physica D 65 117
[24] Kantz H 1994 Phys. Lett. A 185 77
[25] Guegan D, Leroux J 2009 Chaos Solitons and Fractals 41 2401
[26] Hénon M 1976 Commun. Math. Phys. 50 69
[27] Baier G, Klein M 1990 Phys. Lett. A 151 281
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