Three-dimensional beamforming for small aperture planar acoustic vector sensor array
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摘要:
提出了一种基于声场多极子展开的小尺寸声矢量平面阵三维波束形成方法。该方法利用了声场的垂直振速信息, 并结合球谐波函数与多极子模态之间的联系, 可用二维的阵列结构合成指向任意方向的三维波束图, 简化了三维波束形成所需的阵列结构。以3 × 3均匀矩形阵为例的仿真结果表明, 在相邻阵元间距小于0.2倍信号波长时, 所提方法引入的差分近似误差可被忽略, 所得阵列波束图接近理论波束图。相比于声压球面阵三维波束形成方法, 所提方法在低频段能在获得相同阵增益的同时有着更好的稳健性, 为实现小尺寸阵列的三维波束形成提供了一种可靠的方法。
Abstract:A method of three-dimensional beamforming, based on the multipole expansions of the sound field, is proposed in this paper and applied to the small aperture acoustic vector planar array. The desired three-dimensional beam pattern can be synthesized with a two-dimensional array structure by combining the vertical particle velocity component of the sound field and the relationship between the spherical harmonics and the multipole modes. Therefore, the required array structure can be simplified for a three-dimensional beamforming. For illustration, a 3 × 3 rectangular vector sensor array was considered. Simulation results indicate that the error introduced by the approximations for multipole modes extraction can be ignored and the obtained beam pattern approximates the theoretical beam pattern when the spacing of adjacent vector sensors is less than one-fifth of the signal wavelength. Compared to the three-dimensional beamforming based on the spherical harmonic decomposition of the sound field, the proposed method achieves comparable array gain with better robustness in the low frequency band. Therefore, a reliable approach for low-frequency three-dimensional target detection is provided.
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图 2 平面阵2阶振速差分示意图 (a)
${\partial ^3}p/\partial {x^3}$ ; (b)${\partial ^3}p/\partial {x^2}\partial y$ ; (c)${\partial ^3}p/\partial {x^2}\partial {\textit{z}}$ ; (d)${\partial ^3}p/\partial x{\partial ^2}y$ ; (e)${\partial ^3}p/\partial x\partial y\partial {\textit{z}}$ ; (f)${\partial ^3}p/\partial {y^3}$ ; (g)${\partial ^3}p/\partial {y^2}\partial {\textit{z}}$ ; (h) 阵列俯视图
图 4 本文所提方法三维波束图 (a) 指向方向
$ \left( {{{45}^ \circ },{{45}^ \circ }} \right) $ ; (b) 指向方向$ \left( {{0^ \circ },{0^ \circ }} \right) $ 
图 6 波束图随
$ {d \mathord{\left/ {\vphantom {d \lambda }} \right. } \lambda } $ 的变化 (a) 方位角${0^ \circ }$ 处切面图; (b) 俯仰角${90^ \circ }$ 处切面图
图 7 不同阶数下SHDSF和PABF法阵增益上限和白噪声增益随
$ {d \mathord{\left/ {\vphantom {d \lambda }} \right. } \lambda } $ (${{{r_s}} \mathord{\left/ {\vphantom {{{r_s}} \lambda }} \right. } \lambda }$ )的变化 (a) 阵增益; (b) 白噪声增益
图 9 水下环境参数及声线到达结构 (a) 水下环境参数; (b) 到达接收器的直达声线、海面反射声线、海底反射声线及海面−海底反射声线; (c) 各条声线的到达时间及幅度
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