基于相空间重构和奇异谱分析的混沌信号降噪

Noise Reduction of Chaotic Signals Based on Phase Space Reconstruction and Singular Spectrum Analysis

为了从被噪声严重污染的观测数据中重构混沌信号,文中提出了一种基于相空间重构和奇异谱分析的混沌信号自适应降噪方法.由于混沌信号具有类噪声特性,传统的奇异谱分析方法在处理混沌信号时难以辨识信号成分对应的奇异值数目.为此,文中通过在相空间比较混沌信号和噪声统计特性的差异来估计奇异值数,实现了自适应降噪.对计算机模拟生成的混沌信号和太阳黑子数的实际观测数据分别进行了降噪实验,结果表明:文中方法能准确地估计奇异值数目并有效地重构原混沌信号;与现有的混沌信号降噪方法相比,文中方法在噪声抑制性能上有优势,重构的相图质量也更好.

To reconstruct chaotic signals from noisy observation data,an adaptive noise reduction method based on phase space reconstruction and singular spectrum analysis（ SSA） is proposed. Due to the noise-like nature of chaos,it is difficult to identify the number of the singular values corresponding to the signal components when applying conventional SSA method to chaotic signals. To address this issue,the number of the singular values is estimated by comparing the statistical difference between the chaotic signals and the noise in the phase space. Accordingly,an adaptive noise reduction algorithm is designed. Noise reduction experiments corresponding to both chaotic signals generated by computer and the monthly mean sunspot number series are carried out. The results show that the proposed method can precisely estimate the number of the singular values of the signals,and effectively reconstruct the original chaotic signals. Compared with the conventional chaotic signal denoising methods,the proposed method has advantages in terms of both noise reduction performance and phase portrait restructuring quality.