一种快速稳定的非双曲线型非线性时间序列去噪算法  

A Highly-fast-but-stable Noise Reduction Algorithm for Series of Non-hyperbolic Nonlinear Systems

作　　者：张政伟[1,2] 樊养余[1] 王凤琴[1] 

机构地区：[1]西北工业大学电子信息学院,陕西西安710072 [2]中国电子科技集团第28研究所,江苏南京210003

出　　处：《航空学报》2009年第1期136-142,共7页Acta Aeronautica et Astronautica Sinica

基　　金：国家自然科学基金(60872159);航空科学基金(04F53035);陕西省自然科学基金(2003F40)

摘　　要：非双曲线型非线性系统同宿切面点和同宿横截点的存在,使得其时间序列的去噪或轨迹重影变得十分困难。在充分挖掘非线性系统本身特性的基础上,结合Gradient Descent算法的稳定性和Newton-Raphson算法的快速收敛性,提出了一种快速稳定的非双曲线型非线性时间序列去噪新算法,在机器精度内实现了非双曲线型非线性时间序列的去噪。该方法首先计算受扰序列的局部稳定流形和不稳定流形方向,进而确定同宿切面点存在的位置,很大程度上降低了同宿切面对算法性能的影响。不同于现有文献忽视同宿横截点对算法性能影响的做法,研究得出了同宿横截点间的最小距离和干扰噪声均方差二者间的关系,首次定量地估计了同宿横截点可能对算法造成的影响,这无疑对其他算法也将是一个有益的启示。The presence of homoclinic tangencies and homoclinic intersection makes it difficult if not impossible,to denoise or shadow the trajectory of a non-hyperbolic nonlinear system.By exploiting the properties of chaotic systems,a new highly-fast-but-stable algorithm is developed which improves both on the speed of convergence of the Gradient Descent algorithm and the inadequacy of stability of the Newton-Raphson algorithm.With this algorithm machine precision could be obtained for the noisy time series of non-hyperbolic nonlinear systems.Different from former methods,this method first computes the local stable and unstable manifolds of the noisy trajectory,and then determines the locations of the homoclinic tangencies.Thus the effects of the homoclinic tangencies on the algorithm can be reduced to a great extent.Different from those methods which take it for granted that the failure of denoising algorithms is related the homoclinic tangencies only,experiments in this article demonstrate a quantitative correlation between the minimal distance of homoclinic intersections and the standard variance of noise.Thus the probability is great that the algorithm converges to the true trajectory and this strategy could suggest a heuristic approach to similar methods.

关 键 词：非双曲线型非线性系统 序列去噪 Newton-Raphson算法 梯度下降 同宿切面 同宿横截点 参数估计 

分 类 号：N94[自然科学总论—系统科学]