Wavelet based de-noising for chaotic signal prediction using the trajectory parallel measure

In this paper, a new wavelet based de-noising for noisy chaotic signal prediction using the trajectory parallel measure is proposed. As the chaotic signal is similar to noise, the traditional de-noising criterion based on the noise variance is not effective for noisy chaotic signal filtering and prediction. In order to achieve the accurate prediction, the wavelet based prediction with de-noising for attractor using the trajectory parallel measure is applied to noisy chaotic signals. In the de-noising process, the observed signal is judged whether it is chaotic or close to noise using the measure. To verify the effectiveness of the proposed method, it is demonstrated that noisy chaotic signals are predicted with smaller prediction error compared with the conventional chaotic signal prediction in the simulations.