一种新的正弦波频率估计方法研究

A NEW APPROACH TO SINUSOIDAL FREQUENCY ESTIMATION

对相关阵的最大特征值所对应的特征矢量按一定规则排列的非对称矩阵,其奇异值/奇异矢量分解(SVD)的右奇异矢量同样存在两个子空间,并因此提出了一种新的谱估计方法,即基于相关阵信号子空间的正交矢量(Orthogonal Vector spectral estimation based on correlation matrix Signal-Subspace),简称OVSS法。OVSS法源于相关阵信号子空间,对噪声和数据长度敏感性较小,同时它又是正交矢量法,且源于高阶模型,具有高阶MUSIC法的分辨率,而且是低阶矩阵SVD,没有伪峰。大量模拟试验显示OVSS法是一种具有高分辨率、高统计稳定性、计算量相对增加较小的高质量谱估计方法。

In this paper, it is verified that the eigen-vector corresponding to the maximum eigenvalue of the correlation matrix is arranged as an unsymmetrical matrix by definite rule (named eigen-matrix) and there are also signal-subspace and orthogonal subspace in the sigular value decomposition of the eigen-matrix. The orthogonal vector spectral estimation method based on the orthogonal subspace of eigen-matrix, deriving from signal subspace of correlation matrix, possesses high statistical stability, and it is an orthogonal method as well, so it is of high resolution. The eigen-matrix arranged by first eigen-vector processes lower dimensionality, so no pseudo peak appears. The new method is abbreviated as OVSS (Orthogonal Vector spectral estimation method based on correlation matrix Signal-Subspace). Lots of Monto-Carlo simulations have verified that the new spectral estimation method-OVSS is of high resolution, high statistical stability and less increments of calculation burden.