Abstract: This paper addresses the problem of two-dimensional（2-D） harmonic frequency estimation in additive noise, and a pairing-free estimation algorithm based on the rotational invariance of matrix is proposed to solve the disadvantages of low accuracy and high computational cost of current algorithm. By exploiting the rotational invariance property of the 2-D data matrix, a class of matrices with diagonal structures are established. By decomposing the sum of these matrices using singular value decomposition algorithm, two signal subspaces are obtained simultaneously. The 2-D frequency parameters can be estimated from the eigenvalues of the signal subspace-based structured matrices using singular value decomposition algorithm. Meanwhile, the estimated frequencies are automatically paired. The results of the numerical experiments show that the proposed algorithm is much better than the current algorithm in terms of accuracy and computational cost in case of short data length and low Signal-to-Noise Ratio（SNR）. For example, the accuracy of the proposed algorithm is nearly three times higher than the current algorithm when data size is [60×60] and SNR is 5 dB.

Key words: harmonics retrieval, frequency estimation, free-pairing, rotational invariance of matrix

摘要： 主要研究加性噪声中二维谐波频率的估计问题。针对现有算法估计精度不高和计算量较大的缺点，提出了一种基于矩阵旋转不变性的免配对谐波频率估计方法。利用矩阵旋转不变性，通过观测数据获得一组具有对角结构的矩阵组。将矩阵组相加并对此进行一次奇异值分解同时获得两个信号子空间。同时对角化信号子空间的构造矩阵，得到了二维频率的估计，并且所得的二维频率能自动配对。仿真实验结果表明，在数据维数和信噪比都比较低时，该算法明显优于现有算法。在数据矩阵维数[60×60]，信噪比[5 dB]时，该算法估计精度高于现有算法近3倍。

关键词: 谐波恢复, 频率估计, 免配对, 矩阵旋转不变性