低信噪比混沌信号的维数计算

A New and More Effective Approach for Improving G-P Algorithm

维数的分析与计算在混沌信号处理中有着重要作用。而基于 Hausdorff维数理论的 G- P算法在计算混沌吸引子的关联维数时存在抗噪声干扰能力差、运算时间长等缺点。通过对重构空间引入奇异谱分析 ,将状态矢量变换到一组正交坐标系 ,进而计算其关联维数 ,克服了原算法的不足 ,同时具有可靠性高 。

Past attempts at improving G P(Grassberger Procaccia) algorithm, which was traditionally used in dimension calculation of chaotic signals, are still somewhat unsatisfactory in improving SNR (Signal to Noise Ratio). We propose a new approach to achieve comparatively marked improvement on previous approaches. Our new approach utilizes SSA (Singular System Analysis) method, which was firstly proposed by Broomhead and King . Section 2 discusses how to use SSA to improve G P algorithm. Eq.(10) in section 2 is quite important. Vector y(t) in Eq.(10) is the principal element of the reconstructed space. The variance of y(t) is relatively large and corresponds to relatively large SNR. Section 3 discusses in much detail a numerical example. Figs. 1, 2, and 3 in section 3 give simulation results that do confirm preliminarily that relatively marked improvement in SNR is obtained; thus our approach is more robust against noise. Besides our approach is more stable and its computing is easily done.