Ma Hongguang1,Li Xihai2,Wang Guohua2,Han Chongzhao1,Xu Jianfeng2,Zhu Xiaofei2
(1.School of Electronics and Information Engineering,Xi'an Jiaotong University,Xi'an 710049,China;2.Research Institute of High Technology,Xi'an 710025,China)
Abstract:A new algorithm is proposed for computing the embedding dimension and delay time in phase space reconstruction.It makes use of the zero of nonbias multiple autocorrelation function of the chaotic time series to determine the time delay, which efficiently depresses the computing error caused by tracing the slope varying of average displacement (AD) arbitrarily in AD algorithm. Thereafter, by means of the iterative algorithm of multiple autocorrelation and Γ-test, the near-optimum parameters of embedding dimension and delay time are estimated.This algorithm provides with a sound theoretic basis, and its computing complexity is relatively lower and not strongly depended on the data length.The simulated experimental results indicate that the relative error of the correlation dimension of standard chaotic time series is decreased from 4.4% by the conventional algorithm to 1.06% by using this algorithm.The accuracy of invariants in phase space reconstruction is greatly improved.
Keywords:phase space reconstruction;embedding dimension;delay time;multiple autocorrelation