基于最大Lyapunov指数不变性的混沌时间序列噪声水平估计

摘要

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.%提出了一种基于最大Lyapunov指数不变性的计算混沌时间序列噪声水平的新方法.首先分析了噪声对相空间中两点距离的影响,然后基于最大Lyapunov指数在不同维数的嵌入相空间不变的性质,建立了估计噪声水平的方法.仿真计算结果表明,当噪声水平小于10%时,估计值与真实值符合良好.该方法对噪声分布类型不敏感,是一种有效的混沌时间序列噪声估计方法.