A Wavelet Based De-noising Method for Noisy Chaotic Signals and Application to Prediction

Abstract

In this paper, a new wavelet based de-noising method for noisy chaotic signal using the trajectory parallel measure method is proposed. As the chaotic signal is similar to noise, the traditional de-noising criterion based on the noise variance is not successful when applying to noisy chaotic signal filtering and prediction. In order to reduce the observation noise, the threshold can be determined based on whether the signal is chaotic or close to noise using the trajectory parallel measure. Further, the method is applied to the prediction problem of chaotic signal.
In order to verify the effectiveness of the proposed method, it is demonstrated that the observation noise component is effectively reduced compared with the traditional method in the numerical experiments. The usefulness for chaotic signal prediction is also examined in the simulations.