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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。
As an important tool for multidimensional signal processing, quaternion algebra has been applied in many fields. The QMMSE algorithm is studied. First, the QRMMSE algorithm of quaternion real number form is deduced. The QMSMSE of quaternion complex number form is further deduced. Algorithm, and analyzes the difference between the two algorithms and the amount of computation. Finally, the QMMSE algorithm is applied to the beamforming of airborne simplified vector sensor array. Compared with the LVMMSE algorithm, the performance of QCMMSE algorithm is improved and the amount of computation is reduced. Computer simulation results verify the effectiveness of the proposed algorithm.