关键词: 谐波恢复, 频率估计, 免配对, 矩阵旋转不变性

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