中文摘要：

作为多维信号处理的一个重要工具,四元数代数已在各个领域有所应用。对四元数最小均方误差（QMMSE）算法进行了研究,首先推导了四元数实数形式的最小均方误差（QRMMSE）算法,进一步推导了四元数复数形式的最小均方误差（QCMMSE）算法,并且分析了两种算法的区别和计算量。最后将QMMSE算法应用到机载简化矢量传感器阵列的波束形成中,与复数长矢量最小均方误差（LVMMSE）算法相比较,QCMMSE算法的性能有所提高,计算量有所减少。计算机仿真结果验证了所提算法的有效性。

英文摘要：

As an important tool in multi-dimension signal processing,quaternion algebra is applied to many domains.A quaternion minimum-mean-square-error（QMMSE） algorithm is proposed in this paper.First,a QMMSE algorithm based on the real-expansion of a quaternion（QRMMSE） is derived.Then,another form of the QMMSE algorithm based on the complex-expansion of the quaternion（QCMMSE） is derived.The difference of the two algorithms and the computational complexity are analyzed.Finally,the QMMSE algorithm is applied to the beamforming of an airborne trimmed vector-sensor array.Comparing with a complex long-vector MMSE（LVMMSE） algorithm,the QCMMSE algorithm has a better performance and lower computational load.Simulation results are given to validate the performance of the proposed algorithms.