A Method for Estimating the Lyapunov Exponents of Chaotic Time Series Corrupted by Random Noise Using Extended Kalman Filter

Abstract

Identification of chaos in experimental data is essential for characterizing the system and for analyzing the predictability of the data under analysis. The Lyapunov exponents provide a quantitative measure of the sensitivity to initial conditions and are the most useful dynamical diagnostic for chaotic signals. However, it is difficult to accurately estimate the Lyapunov exponents of chaotic signals which are corrupted by a random noise. In this work, a method for estimation of Lyapunov exponents from noisy time series using Extended Kalman Filter (EKF) is proposed. The proposed methodology was validated using time series obtained from known chaotic maps. The proposed method seems to be advantageous since it can be used for online estimation of Lyapunov exponents. In this paper, the objective of the work, the proposed methodology and validation results are discussed in detail.