基于检测系统非线性相关性的相空间重构时间延迟估计

Time-delay estimation for phase space reconstruction based on detecting nonlinear correlation of a system

提出一种确定时间延迟参数的新方法,非线性复自相关法。采用一个高次复自相关函数R(τ)检测系统的非线性相关性,通过寻找R(τ)的第一个局部极小值点来确定最优时间延迟。R(τ)时间复杂度低,对数据长度依赖性不强。选取四种典型混沌动力学系统,加入不同噪声水平的高斯白噪声,模拟含噪混沌时间序列,进行数值验证。结果表明,所得结果更合适,同时具有优秀的抗噪声能力。

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.