改进局部投影算法的混沌降噪研究

The Study of Chaotic Noise Reduction Method with Improved Local Projection

针对混沌信号降噪算法中邻域和局部噪声子空间的选取问题,提出了一种改进的非线性混沌降噪方法,即将小波理论和非线性混沌降噪算法结合起来,利用小波分析方法对相空间中的点进行初始邻域半径的估计,自适应地在相空间中选取合适的邻域点;并针对每一个小邻域进行不同的非正交投影,从而更新数据点。仿真中分别对Henon映射产生的混沌序列和实际观测的大连降雨量混沌序列进行了研究,结果证明了该方法简单可靠,且能够较好地校正相空间中点的位置,逼近真实的混沌吸引子轨迹。

It is difficult to choose the neighborhood and noise subspace for the observed chaotic time series, therefore an improved nonlinear noise reduction method was proposed. Combining the wavelet analysis and chaotic noise reduction method, this method firstly uses wavelet analysis to estimate the initial neighbour radius and searches the neighbourhood adaptively in the phase space; What is more, non-onhogonal projective approach is used to different neighborhoods. Both the chaotic time series generated by Henon map and the measurement of Dalian rainfall time series were respectively applied for noise reduction using this method. The numerical experiments results show that the proposed method can better correct the position of data points in phase space and approximate the real chaotic attractor trajectories more closely.