基于局部投影方法的混沌信号去噪

提出一种以Takens嵌入定理和影子定理为理论依据的对混沌信号较有效的去噪方法，该方法先根据Takens嵌入定理将待处理的含噪时间序列嵌入到合适的相空间M'中，由于混有噪声，相空间中的点将偏离真实动力学系统嵌入的流形M，去噪的目的就是估计M的位置，并将偏离M的点移近它。从而更新原时间序列。实验比较了局部投影去噪方法和小波函数方法的去噪效果，结果表明本文的方法对混沌信号的去噪很有效，且比单纯利用小波函数去噪的效果更好。

Noise reduction for chaotic signal based on local-projection method

A new local projection method is presented based on Takens time delay embedding theorem and shadowing theorem for noise reduction which are applicable to time series produced by chaotic systems. The noise reduction idea is that in the presence of noise these points typically deviate the embedded image of the manifold for the dynamics due to the fact that noise has generally very high dimension. The basic idea of the method is to estimate where the real manifold M is and move the errant points closer to it to form a candidate replacement trajectory. The method does not require prior knowledge for an underlying dynamics. By performing the experiments, the results of the local projection method for noise reduction is compared with wavelet functions for noise reduction. It shows that local projection method is an effective denoising one and is better than wavelet functions for noise reduction.