Key Laboratory of Coal Gasification and Energy Chemical Engineering of Ministry of Education, East China University of Science and Technology, P.O. Box 272, Shanghai 200237, China.
Chaos. 2012 Sep;22(3):033102. doi: 10.1063/1.4731800.
A novel method for estimating simultaneously the largest Lyapunov exponent (LLE) and noise level (NL) from a noisy chaotic time series is presented in this paper. We research the influence of noise on the average distance of different pairs of points in an embedding phase space and provide a rescaled formula for calculating the LLE when the time series is contaminated with noise. Our algorithm is proposed based on this formula and the invariant of the LLE in different dimensional embedding phase spaces. With numerical simulation, we find that the proposed method provides a reasonable estimate of the LLE and NL when the NL is less than 10% of the signal content. The comparison with Kantz algorithm shows that our method gives more accurate results of the LLE for the noisy time series. Furthermore, our method is not sensitive to the distribution of the noise.
本文提出了一种从噪声混沌时间序列中同时估计最大 Lyapunov 指数（LLE）和噪声水平（NL）的新方法。我们研究了噪声对嵌入相空间中不同点对平均距离的影响，并提供了一种在时间序列受到噪声污染时计算 LLE 的重标度公式。我们的算法是基于这个公式和 LLE 在不同维嵌入相空间中的不变性提出的。通过数值模拟，我们发现当 NL 小于信号含量的 10%时，所提出的方法可以合理地估计 LLE 和 NL。与 Kantz 算法的比较表明，我们的方法对于噪声时间序列的 LLE 给出了更准确的结果。此外，我们的方法对噪声的分布不敏感。
