二维正弦信号频率估计的ESPRIT方法研究

为了在噪声背景下估计二维正弦信号的频率,并获得较高的估计精度,给出了二维相关阵的大特征值所对应的主特征向量,位于由信号向量张成的信号子空间的结论,并因此提出了一种新的基于最大特征值所对应的第1特征向量的二维谐波频率估计ESPRIT(Estimation of Signal Parameters Via Rotational Invariance Techniques)方法.该方法用此第1特征向量构造一个特殊矩阵代替MEMP(Matrix Enhancement and Matrix Pencil)方法中的数据矩阵,进一步用二维ESPRIT方法来估计谐波频率.该方法依赖于信号子空间,对噪声和数据长度敏感性小,同时它不需进行谱峰搜索,可以得到较高的估计精度.同时给出了较为简便的频率配对算法.仿真实验证明了算法的正确性.

Two-Dimensional ESPRIT Method for Sinusoidal Signal Frequency Estimation

In order to estimate the frequencies of two-dimensional (2-D) harmonic signal in noise and to gain high resolution, we verified that first eigenvector corresponding to the maximum eigenvalue of the autocorrelation matrix belongs to the span of signal vector. A 2-D ESPRIT(Estimation of Signal Parameters Via Rotational Invariance Techniques) approach based on the first eigenvector is presented to extract out the 2-D sinusoidal signal frequencies. we form a matrix using the first eigenvector instead of the original data matrix in MEMP(Matrix Enhancement and Matrix Pencil) method. Because of using the first eigenvector, our method possesses high statistical stability and high resolution. A new pairing method was also presented.