A Three-dimensional Source Location Algorithm Based on Sparse Planar Array with Low Complexity
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摘要: 针对3维信源定位中阵列结构过于复杂、算法复杂度过高、谱峰搜索范围过大的问题，该文提出一种基于互素线阵互素平移的稀疏面阵(CLACS-SPA)的3维降秩MUSIC算法(RARE-MUSIC)。所提CLACS-SPA拥有中心对称的互素稀疏面阵结构，相较于同口径均匀面阵结构减少了大量的阵元，降低了阵列的结构复杂度；以CLACS-SPA为基础的3维RARE-MUSIC算法利用泰勒公式将接收信号中的方向信息与距离信息进行分离估计，从而将3维谱峰搜索转化为方位角俯仰角的2维搜索和距离项的1维搜索，降低了定位算法的计算复杂度。仿真分析表明：在口径与定位算法相同条件下，与均匀面阵结构相比，所提结构的计算复杂度降低了1～2个数量级；在相同口径与CLACS-SPA结构下，与经典3维MUSIC算法相比，所提算法的复杂度降低了2～3个数量级；在相同口径和阵元数量条件下，与经典3维MUSIC算法相比，所提算法不仅降低了计算复杂度，而且提升了方位角与俯仰角的测量精度。Abstract: A RAnk REduced MUSIC (RARE-MUSIC) algorithm based on Coprime Linear Array Coprime Shift Spare Planar Array (CLACS-SPA) is proposed, in order to solve the problems in the three-dimension source location, such as too complex array structure, too high-complexity algorithm and large partial spectrum range. The proposed CLACS-SPA has a centrosymmetric coprime sparse array structure, which reduces the number of antennas and structural complexity of the array, compared with the uniform planar array structure of the same caliber. The direction and distance information in the received signal are separated and estimated by Taylor formula, thus the three-dimensional spectral peak search is transformed into the two-dimensional search of the azimuth angle as well as elevation angle and the one-dimensional search of the distance, which reduces the computational complexity of the positioning algorithm. Simulation results show that the complexity of the proposed structure is one to two orders of magnitude lower than that of the uniform planar array structure, under the same aperture and location algorithm. In addition, for the same caliber of the proposed CLACS-SPA structure, the proposed RARE-MUSIC algorithm is less complex than the classical three-dimension MUSIC with two to three orders of magnitude. And under the same aperture and number of antennas, the proposed RARE-MUSIC greatly reduces the computational complexity and improves the measurement accuracy of azimuth and elevation angles, in comparison with the classical three-dimension MUSIC algorithm.
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表 1 相同口径下，CLACS-SPA和UPA的阵元数量
UPA CLACS-SPA ${d_a} = a\lambda $ $a = 1$ $a = 3$ $a = 5$ $a = 11$ ${d_b} = b\lambda $ $b = 1$ $b = 4$ $b = 6$ $b = 12$ 阵元数量 625 169 81 25 
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