一种混沌映射的相空间去噪方法

对于混沌映射来说，它们的频谱比混沌流的频谱更广阔，与噪声频谱的重叠率更高，所以混沌流的去噪方法对它们并不适用. 在半盲分析法的框架下，混沌系统的参数估计问题终将归结为最小二乘估计问题. 本文从最小二乘拟合的角度出发估计混沌映射的演化参数，进而通过相空间重构以及投影操作，实现对观测信号的噪声抑制. 实验结果表明，该算法的去噪效果优于扩展卡尔曼滤波器（extended Kalman filter，EKF）和无先导卡尔曼滤波器（unscneted Kalman filter，UKF），并且能够较大程度地将信号源的混沌特征量还原. 关键词： 混沌 噪声抑制 相空间重构 投影

A phase space denoising method for chaotic maps

The spectra of chaotic maps are much wider than those of chaotic flows, and their overlapped regions with Gaussian white noise are much larger, thus the denoising method for chaotic flows is unsuitable for chaotic maps. Within a semi-blind analysing framework, the parameter estimating problem for chaotic systems can be boiled down to a least square evaluating procedure. In this paper we start with estimating the evolution parameters of chaotic maps by using a least square fitting method. After that, phase space reconstruction and projection operation are employed to get noise suppression for the observed data. The simulation results indicate that the proposed algorithm surpasses the extended Kalman filter (EKF) and the unscented Kalman filter (UKF) in denoising, as well as maintaining the characteristic quantities of chaotic maps.
Keywords： chaos denoising phase space reconstruction projection