全局耦合映象格子的信号初值估计

Estimate the Initial Conditions of Globally Coupled Map Lattices

耦合映象格子系统用于信号处理研究时,从中恢复出系统的初始条件是一个非常重要的问题。本文针对现有方法存在的不足,对映象系数进行了合理地修正,提出一种基于时变映象系数恢复信号初值的新方法。实验结果表明,在系统不存在噪声污染的情况下,本文方法能够较好地恢复系统初值的统计特性。同时,还研究了一组脑电信号。结果表明,采用时变映象系数恢复的信号值与原信号之间的偏差、均方误差都较传统方法小,而且具有与原信号之间较强的相关性,能够更好地刻画实际信号的物理过程,从而对实际系统的初始条件做出更优地估计。

The initial conditions of coupled map lattices （CML） are very important for chaotic signal processing with CML. A novel algorithm with time-varying parameter was proposed based on the traditional symbolic dynamic-based method. The globally coupled logistic map is applied to test the properties of the proposed method. Several numerical simulations showed that it can recover the statistical property of initial conditions when there were noiseless. From the results obtained from EEG data, it is obvious to see that this method has minor biases, lower mean square errors （MSE） and a higher correlation with the given data. So it is more appropriate to describe the physical property of practical systems and given a better estimation.