乘性和加性噪声中二维谐波频率估计

摘要

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.本文主要研究零均值乘性和加性噪声并存下的二维谐波信号频率估计问题,提出了一种基于数据矩阵的奇异值分解和子空间的旋转不变性的零均值乘性和加性噪声中的谐波频率的估计方法.乘性噪声为零均值情形下传统的估计方法往往难以直接应用或估计失效.本文利用谐波模型信号特征,通过对观测信号进行平方运算构造了一个数据矩阵.通过对数据矩阵的特征值进行理论分析,结合子空间旋转不变性,得到了零均值乘性和加性噪声中的谐波频率和数据矩阵之间的一种内在关系.这个性质可以用于零均值乘性和加性噪声并存下的二维谐波信号频率估计,并且所得的二维频率能自动配对.仿真实验验证了本文所提算法的有效性.%The harmonic retrieval in noise is a classical signal processing problem, and it has been applied in a wide range of signal processing areas. This paper addresses the problem of two-dimensional (2-D) harmonic frequency estimation in the presence of zero-mean multiplicative and additive noise, and proposes an algorithm to estimate the frequencies of two-dimensional harmonics in zero-mean multiplicative and additive noise based on the singular value decomposition of data matrix and the rotational invariance of subspace. It is difficult for the traditional methods to directly estimate frequency of two-dimensional harmonics or failure of estimation in zero-mean multiplicative and addition noise. The observed harmonic signals are first changed by squaring the sample data. Then, a data matrix is constructed using the characteristics of this changed model. The inherent relation between the frequencies of harmonics in zero-mean multiplicative and addition noise and the data matrix is derived, which can be used to estimate the frequencies of two-dimensional harmonics in zero-mean multiplicative and addition noise. Meanwhile, the estimated frequencies are automatically paired. The effectiveness of the proposed algorithm is verified by some numerical experiments.