基于数据矩阵奇异值分解的免配对二维谐波信号参数估计算法

A parameter estimation algorithm of 2D harmonic signal based on SVD of data matrix without pairing

本文提出了一种基于数据矩阵奇异值分解、免配对的二维谐波信号参数估计算法。该方法将二维谐波信号的参数估计问题转换为两个多样本的一维谐波信号参数估计问题,通过对数据矩阵的一次奇异值分解同时获得两个方向上的信号子空间,并利用这两个信号子空间的对应关系同时对角化两个方向上的构造矩阵Fx和Fy,从而在估计两个方向一维极点的同时完成了极点配对。该方法不需要将数据矩阵重新排列为Hankel块形式进行奇异值分解,也不需要额外的配对步骤,极大地降低了运算量,在数据矩阵维数较高时优势明显。仿真实验及实测数据处理结果证明了该方法的正确性和有效性。

In this paper,we put forward a parameter estimation algorithm of two-dimensional harmonic signal.It＇s based on the singular value decomposition（SVD） of data matrix,and the pairing step is performed at the same time.In the algorithm,the parameter estimation problem of two-dimensional harmonic signal is decomposed to the problem of two one-dimensional harmonic signal estimation in multi-sample condition.We can perform SVD of data matrix once to obtain the signal subspace in two directions at the same time,and use the corresponding relationship between these two signal subspaces to diagonalize Fx and Fy in the two directions at the same time.Thus we can complete the pairing step of poles in the two directions,when estimating the parameters of the two one-dimensional harmonic signal.This algorithm does not need to rearrange the data matrix in the form of Hankel block for SVD,and does not need extra pairing step.Those characteristics reduce the computational complexity greatly.And obvious superiority is exhibited when the dimension of data matrix is high enough.The results using simulation and measured data prove the correctness and effectiveness of the algorithm.