The Study Of Nonlinear Noise Reduction For Chaotic Time Series

It is inevitable that the measurements of the time series for all the nonlinear dynamical systems are contaminated by noise. Noise destroys the internal chaotic dynamics and influenced the prediction of univariate or multivariate chaotic time series. Therefore, it is necessary for us to study the noise reduction methods for the chaotic time series.This paper is focused on the research of the nonlinear noise reduction method, and different chaotic time series such as the sunspots numbers and rainfall of Dalian are considered. An adaptive neighborhood selection method for locally projective noise reduction is presented. Considering different neighborhood ought to possess different local characteristic and each neighbor should correspond to different optimal radius, we utilize an adaptive algorithm to choice the size of each neighbor, by which neighborhood can be optimized one by one and each neighbor can be enabled to have different radius. Second, another factor which influence locally projective noise reduction is considered, the accuracy ratio of the selected neighbors for the local projection noise reduction is analysed. An improved neighborhood selection method combing with the singular spectrum analysis technique is proposed. The singular spectrum analysis is performed for the noise corrupted phase space, and principal component is chosen to reconstruct a less noisy phase space. By searching in the reconstructed phase space, the accuracy of the selected neighbors is elevated effectively. In the end, a global noise reduction method based on gradient descent for chaotic time series is studied. A combination between the gradient descent noise reduction method and the polynomial fitting algorithm based on least square parameter estimation is realized and the blind of the model for the real-world time series can be overcome. Simulations are conducted with the real world time series such as the monthly sunspots data and the monthly rainfall data in Dalian in China, and the laboratorial time series generated by the Lorenz equations and the Henon map. The results proved that the improved neighborhood selection methods and the GD-LS global noise reduction presented in this paper have a better noise reduction effect.