Noise-level estimation of noisy chaotic time series based on the invariant of the largest Lyapunov exponent

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.