四四元数域低秩逼近及其在矢量阵列波达方向和估计中的应用

提出了新的多元数概念——四四元数,以及四四元数框架下特征分解和奇异值分解等信号处理领域常用的矩阵运算新规则.在此基础上提出了四四元数矩阵的一种低秩逼近算法,并将其用于矢量传感器阵列信号建模及波达方向(DOA)估计中.结果表明,四四元数特征分解及奇异值分解能获得比现有方法更好的低秩逼近性能,基于四四元数模型的矢量传感器阵列信号DOA估计算法,在资源占用、子空间逼近以及对模型误差的鲁棒性等方面均明显优于传统算法.

Quad-Quaternion Low Rank Approximation with Applications to Vector-Sensor Array Direction of Arrival Estimation

Introduces a new multidimensional algebra named the quad-quaternion.Several matrix operations which are commonly used in array signal processing,including eigenvalue decomposition(EVD) and singular value decomposition(SVD),are extended to quad-quaternions.A low rank approximation algorithm for quad-quaternion matrices is proposed and further applied to vector-sensor array signal modeling and direction of arrival estimation.The quad-quaternion based direction of arrival(DOA) estimation algorithms are demonstrated to be superior to the classical methods with respect to memory requirement,accuracy of subspace estimation,and robustness to model error due to more accurate low rank approximation obtained via quad-quaternion based EVD or SVD.