基于广义协方差矩阵的乘性和加性噪声中的谐波恢复

针对非零均值乘性噪声中的谐波恢复问题，本文提出一种基于广义协方差矩阵的乘性噪声中谐波个数和频率的估计方法。首先定义一类广义协方差并构造广义协方差矩阵，通过对广义协方差矩阵进行特征值理论分析，得到了非零均值乘性噪声中谐波分量个数与协方差矩阵特征值之间的内在联系，这个性质可以用来估计谐波分量个数。而且利用子空间旋转不变性技术，可以从协方差矩阵中估计出谐波的频率。本文所提方法对于乘性和加性噪声的颜色和分布均无任何假设，可以应用于任意分布和任意颜色的乘性和加性噪声中的谐波恢复。仿真实验表明，本文所提谐波恢复方法具有很高的频率分辨率。 

Harmonic retrieval in multiplicative and additive noise based on the generalized covariance matrix

For the harmonic retrieval in nonzero mean multiplicative noise,we propose a new method to estimate the number of harmonics and frequencies of the harmonics in multiplicative noise based on the generalized covariance matrix.We first define a generalized covariance,and then construct a covariance matrix using the defined generalized covariance.Analyzed the eigenvalues of the covariance matrix,we get the inherent relation between the number of harmonics and the eigenvalues of the covariance matrix.This relation can be used to estimate the number of harmonics in multiplicative noise.Moreover, the frequencies of harmonics can be estimated via subspace rotational invariance technique.The proposed method does not need to assume the color and distribution of the multiplicative and additive noise,and it can be applied to harmonic retrieval in multiplicative and additive noise with any color and any distribution.The simulation results demonstrated that the proposed method is high-resolution.