A noise reduction method for chaotic time series

Abstract

AbstractIntensive studies have recently been made on the noise reduction method for the chaotic time series. In those approaches, the trajectory of the attractor is reconstructed in the multidimensional space form the single‐variable time‐series data, and then the deviation of the trajectory is corrected. In the conventional method, the noise is assumed to be Gaussian distribution. Consequently, when the outliers are contained in the real data, they are difficult to delete.This paper intends to solve this problem and proposes a noise reduction method for the chaotic timeseries data, considering not only the noise with the Gaussian distribution, but also the outliers. A method is devised that eliminates the outliers efficiently using Biweight estimation and similar methods, and a program is constructed based on the idea. the experimental data are constructed by adding the pseudorandom variable with the Cauchy or Gaussian distribution to the chaotic timeseries data generated from the Hénon map and the Lorenz model. Using these data, the noise reduction experiment is conducted; the relative error, the phase plot and correlation dimensions are examined. It is verified as a result that the proposed method can reduce drastically the effect of the outliers compared to the conventional methods, and has nearly the same noise reduction performance as in the conventional methods for the noise with the Gaussian distribution.