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Journal of Applied Mathematics
Volume 2013, Article ID 983051, 9 pages
Research Article

Incomplete Phase Space Reconstruction Method Based on Subspace Adaptive Evolution Approximation

1School of Electrical and Information Engineering, Chongqing University of Science and Technology, Chongqing 401331, China
2School of Electronic Engineering, Xi'an Shiyou University, Xi’an 710065, China

Received 19 July 2013; Accepted 19 September 2013

Academic Editor: Baocang Ding

Copyright © 2013 Tai-fu Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The chaotic time series can be expanded to the multidimensional space by phase space reconstruction, in order to reconstruct the dynamic characteristics of the original system. It is difficult to obtain complete phase space for chaotic time series, as a result of the inconsistency of phase space reconstruction. This paper presents an idea of subspace approximation. The chaotic time series prediction based on the phase space reconstruction can be considered as the subspace approximation problem in different neighborhood at different time. The common static neural network approximation is suitable for a trained neighborhood, but it cannot ensure its generalization performance in other untrained neighborhood. The subspace approximation of neural network based on the nonlinear extended Kalman filtering (EKF) is a dynamic evolution approximation from one neighborhood to another. Therefore, in view of incomplete phase space, due to the chaos phase space reconstruction, we put forward subspace adaptive evolution approximation method based on nonlinear Kalman filtering. This method is verified by multiple sets of wind speed prediction experiments in Wulong city, and the results demonstrate that it possesses higher chaotic prediction accuracy.