针对稀疏分解(sparse decomposition)类算法在恢复矢量阵列信号时收敛速度慢的问题, 本文将稀疏分解理论推广到四元数空间,提出了一种声矢量阵列波达方向估计的四元数正交匹配追踪算法。首先, 建立声矢量阵列的四元数模型, 然后将方向矢量矩阵在四元数空间展开作为冗余字典, 最后利用正交匹配追踪算法恢复原始信号得到目标方位信息。实验结果表明：在四元数空间建立的冗余字典强化了声矢量传感器各输出分量间正交性, 与长矢量模型即在复数域的冗余字典相比恢复性能更好。具体表现为：冗余字典原子长度降为长矢量方法的1/3, 并有效去除长矢量方法在DOA估计角度真值附近1°范围内的偏差。仿真结果验证了算法的有效性。

This work extended sparse decomposition (SD) into quaternion space in order to find a better sparse representation for acoustic vector array (AVA). A novel sparse decomposition algorithm based on the well-known orthogonal matching pursuit (OMP) for quaternionic signals was proposed and it was used to solve the question of direction of arrival (DOA) estimation of AVA in small snapshot number, coherent signal source and low signal noise ratio (SNR) case. Compare with the complex field SD algorithm, The results illustrate that the atomic length of the over-complete dictionary is reduced to one-third of that from the long vector model, while errors in DOA estimation are effectively eliminated using the long vector method when the true angles of DOA estimation lie within 1°. Simulation results verify the validity of this algorithm.