一类非线性信号去噪的奇异值分解有效迭代方法

对于一类非线性信号的去噪问题，该文提出一种基于奇异值分解(Singular Value Decomposition, SVD)的有效迭代方法。对现有奇异值差分谱方法在两类不同非线性信号上的去噪效果进行了对比，指出在信号不具有明显特征频率、非周期性变化时这一方法并不适用，并分析了现象产生的原因；然后针对该类信号的特点重新定义了Hankel矩阵结构，给出有效奇异值的确定方式，并通过SVD多次迭代过程实现对该类信号的有效去噪。对实际飞行数据去噪的实验结果表明，该方法对提出的一类信号对象不仅去噪效果良好，而且可提高运算效率。

Effective Iteration Method of a Class of Nonlinear Signal Denoising Based on Singular Value Decomposition

To solve a class of nonlinear signal denoising, an effective iteration method based on the Singular Value Decomposition (SVD) is proposed. When the signals have no obvious characteristic frequency and non-periodic change, the current difference spectrum method is not applicable by comparing the results on the two class of nonlinear signal, and then the corresponding reason is analyzed. According to the signal feature, the structure of the Hankel matrix is defined again and the valid singular values are determined. The effective denoising is realized by the repeated iteration which is based on the SVD. The results of the flight data demonstrate that the proposed method can effectively reduce the noise and improve the computing efficiency as well.