基于Hamilton四元数矩阵奇异值分解的二维谐波频率参量估计

Parameters Estimation of Two-Dimensional Harmonics Based on Singular Value Decomposition of Quaternion Matrix

对于二维谐波信号的四元数模型,首先论述其与二维谐波的实数模型和复数模型之间的对应与转换关系,之后提出运用四元数矩阵奇异值分解估计二维谐波中频率参量的算法.这种算法首先可以利用四元数矩阵的奇异值判断出原始的二维谐波信号个数,然后再分别利用四元数矩阵的左、右奇异向量中的噪声向量构造的噪声子空间估计出两维的谐波频率参量.算法本身需要的数据量少,数据矩阵构造简单,并且可以同时估计出两维谐波频率参量.从仿真实验中可以看出,本文提出的算法计算量相对其它针对二维谐波四元数模型的算法要小.仿真实验验证了本文算法的正确性.

For quaternion model of two-dimensional harmonics, the inner relationship between real model, complex model and quaternion model was discussed at first. We presented the singular values decomposition method of quaternion matrix to estimate frequency pairs of two-dimensional harmonics. This method can estimate the number of signals with singular values. Then, left and right singular vectors can be used to estimate frequency pairs. This method needs less data and its data matrix is very simple. It can also estimate frequencies at the same time. From simulations, our method can decrease computation burden effectively than those of other methods.