用于声矢量阵列波达方向估计的四元数最小范数法

Quaternion min-norm algorithm for DOA estimation with acoustic vector sensor array

由于四元数MUSIC(Multiple Signal Classification)算法计算量较大,本文结合声矢量传感器的四元数导向矢量模型,提出了一种声矢量阵列波达方向估计的四元数最小范数法。首先,将声矢量阵列输出协方差矩阵奇异值分解所得到的(M-N)×M维(M为阵元数、N为信源数)噪声子空间依最小范数(Minimum-Norm,MN)准则构建为一个新的四元数域1×M维噪声矢量。接着,提出了简化的谱峰搜索公式,理论分析了四元数最小范数法在搜索计算量上的优势。对提出的算法与Q-MUSIC算法进行了对比。结果显示:该算法至少能节省50%的谱峰搜索量。同时,提出的算法构建的低维噪声矢量与导向矢量间的正交性优于高维噪声子空间与导向矢量间的正交性,在0dB时,其范德蒙范数和谱峰分别为Q-MUSIC算法的1/3和3倍。另外,该算法在减小谱峰搜索量的同时,可以较好地分辨信源波达方向,且其统计特性与四元数MUSIC算法相当。提出的算法不局限于L线阵,也适用于双平行线阵及面阵。

To reduce the calculation amount of quaternion Multiple Signal Classification（MUSIC）algorithm,a Minimum Norm（MN）quaternion method based on the quaternion form of an acoustic sensor vector was proposed for estimating Direction of Arrival（DOA）.First,based on the MN principle,the（M-N）×Mdimension（Mis the number of array sensors,Nis the number of signal sources）orthogonal noise subspace vectors were converted to a 1×M dimension quaternion noise vector.Then,a simplified formula for peak search was proposed.The searching computation amount of Quaternion MN（Q-MN）was analyzed theoretically.Compared with the Q-MUSIC algorithm,the Q-MN algorithm can save at least 50% of the peak search volume.Experimental results show that the orthogonality of the steering vector with the low-dimensional noise vector derived by proposed methodis superior to that with high dimensional noise subspace.When the Signal to Noise Ratio（SNR）is 0dB,the Vandermonde norm and the spatial spectrum peak value of Q-MN algorithm are 1/3 times and 3 times as much as those of Q-MUSIC.The Q-MN algorithm can successfully identify the DOA of signal sources,and its resolution is equivalent to that of Q-MUSIC algorithm.Moreover,it can be applied to not only L-shaped arrays,but also plane arrays and parallel linear arrays.