Identification Models for Chaotic Systems from a Noisy Data: Implications for Performance and Nonlinear Filtering

This paper investigates the identification of global models from chaotic data corrupted by purely additive noise. It is verified that noise has a strong influence on the identification of chaotic systems. In particular, there seems to be a critical noise level beyond which the accurate estimation of polynomial models from chaotic data becomes very difficult. Similarities with the estimation of the largest Lyapunov exponent from noisy data suggest that part of the problem might be related to the limited ability of predicting the data records when these are chaotic. A nonlinear filtering scheme is suggested in order to reduce the noise in the data and thereby enable the estimation of good models. This prediction-based filtering incorporates a resetting mechanism which enables filtering chaotic data. Numerical examples which consider the double-scroll attractor anf the Duffing-Ueda oscillator are provided to illustrate the main points of the paper.