估计非线性时间序列嵌入延迟时间和延迟时间窗的C-C平均方法

C-C Average Method for Estimating the Delay Time and the Delay Time Window of Nonlinear Time Series Embedding

重构相空间是非线性分析的基础,利用关联积分导出的C-C方法是估计相空间重构参数延迟时间τd和延迟时间窗τw的有效方法。由于混沌系统的初值敏感性和实际序列长度有限并带噪,使得C-C方法估计出的τd和τw具有波动性。为了降低估值偏差,借鉴谱估计中平均法的思想,提出一种不同于已有文献利用整段序列估算τd和τw,而采用对序列分段估值后取平均的方法,并重点讨论了带噪序列的τd和τw估值及序列长度对估值的影响。数值仿真证明这种平均处理方法对τd和τw的估值具有较好的有效性和可靠性。

State space reconstruction is the basis of nonlinear analysis and the C-C method derived from the correla- tion integral is an efficient way to estimate the two parameters for state space reconstruction, the delay time Тd and delay time window Тw . For chaotic systems are sensitive to initial conditions, and measured data with finite number are noise-corrupted, the estimates of Тa and Тw with C-C method are fluctuant. In order to reduce estimate devia- tions, similar to the average method in spectral estimation, a time series was divided into several segments and each one was used to estimate corresponding values and the averages were taken as the estimates of Тa and Тw. This method differs from the ones in literature which used the data and the effects of series length on the estimates effective and reliable for estimates of ra and r,. entire series for estimate. The estimates with noise-corrupted were discussed. Numerical simulation showed that method is effective and reliable for estimates of Тa and Тw .