Time-delay estimation for phase space reconstruction based on detecting nonlinear correlation of a system
XU Ya · Zhendong yu chongji · 2014
A new method to determine time-delay was proposed,it was called nonlinear multi-autocorrelation function method. With this method a high order multi-autocorrelation function R( τ) was used to calculate the nonlinear correlation of a system and estimate the optimal time delay by finding the first local minimum value of R( τ). The time complexity of R( τ) was low and its dependence on the length of data was not strong. The method was validated with four noisy chaotic time series. The time series were generated using four chaotic maps inputting Gaussian white noise with different levels. The numerical results showed that the proposed method is more appropriate with a good anti-noise ability.