基于子空间旋转不变性的加性有色噪声中谐波频率的估计

Estimating the frequencies of harmonics in additive colored noise based on the rotational invariance of subspace

噪声中的谐波恢复问题是信号处理领域的一个典型问题,在众多领域中有着广泛的应用。本文主要研究加性有色噪声中谐波频率的估计问题,提出了一种基于子空间旋转不变性的谐波频率的高分辨率估计方法。利用观测信号的自协方差函数构造了一个协方差矩阵,通过对协方差矩阵的特征值进行理论分析,结合子空间旋转不变性,得到了加性有色噪声中谐波的频率和协方差矩阵之间的一种内在联系。利用这个性质可以估计加性有色噪声中谐波的频率。本文方法对于有色噪声的模型无任何假设,而且对于噪声的分布也没有限制,对于高斯和非高斯有色噪声都适用。仿真实验验证了本文所提算法的有效性。

The harmonic retrieval in noise is the classic problem in the signal processing,and it has been applied to many signal processing areas.This paper studies the estimation of frequencies in additive colored noise,and proposes a method to estimate the frequencies of the harmonics based on the rotational invariance of subspace.A covariance matrix is constructed using the self-covariance of observed harmonic signals.The inherent relation between the frequencies of harmonics in additive colored noise and the covariance matrix is derived,and it can be used to estimate the frequencies of harmonics in additive colored noise.The proposed method does need to assume the model of the noise and can be implemented without the knowledge of the distribution of the noise.It can be applied to harmonic retrieval in Gaussian and non-Gaussian colored noise.The simulation results demonstrated the effectiveness of the proposed method.