鲁棒的四元数空间平滑算法

本文针对相干信号波达方向(DOA)估计问题，利用简化电磁矢量传感器阵列提出了一种基于四元数模型的空间平滑(Q-SS)算法。首先，根据四元数的正交特性能够很好地描述矢量传感器阵元内部信号分量之间的垂直关系这一特点，将每个阵元的两分量接收数据合成为一个四元数，建立了简化电磁矢量传感器阵列的四元数接收模型，该模型比传统的长矢量模型更适合于矢量传感器阵列的信号处理。在此基础上，利用本文提出的Q-SS算法对相干信号进行预处理，实现了解相干，并对解相干性能进行了分析，然后通过四元数域的ESPRIT算法估计出相干信号的DOA。理论分析表明Q-SS算法比传统的长矢量空间平滑(V-SS)方法有更高的DOA估计精度，具有对矢量传感器内部电场噪声分量解相关的能力，这是V-SS算法所不具备的优势。最后，通过计算机仿真实验比较和分析了所提算法的有效性。 

A Robust Quaternion Spatial Smoothing Algorithm

To estimate the direction of arrival (DOA) of coherent signals, a novel quaternion spatial smoothing (Q-SS) algorithm is proposed using simplified electromagnetic vector sensor array. Since the orthogonality of quaternion is quite suitable for describing the orthogonal relation of a vector sensor, the two-component complex-valued signal of each vector array element constitutes the quaternion-valued signal, and the quaternion model of simplified electromagnetic vector sensor array is first set. This kind of model is more appropriate for vector sensor array signal processing than the traditional long vector model. Then the newly proposed Q-SS algorithm is used to preprocess the incident coherent signals on the basis of the quaternion model. The preprocessing performance is also analyzed, and a quaternion ESPRIT method is applied to estimate the DOA in the sequel. Theoretical analysis show that the proposed algorithm results in a high estimation accuracy in contrast to the traditional spatial smoothing based on long vector model (V-SS). What is more, the Q-SS algorithm is able to decorrelate the coherent noise among the orthogonal components of a vector sensor without any additional procession, while V-SS method does not have the advantage of it. Finally, the performance of the proposed algorithm is evaluated through computer simulation examples, and its efficacy is verified.