Beamforming using a circular array of hydrophones may be employed for the task of two-dimensional (2D) underwater sound-field visualisation. In this article, a parametric spatial post-filtering method is proposed, which is specifically intended for applications involving large circular arrays and aims to improve the spatial selectivity of traditional beamformers. In essence, the proposed method is a reformulation of the cross-pattern coherence (CroPaC) spatial post-filter, which involves calculating the normalised cross-spectral density between two signals originating from coincident beamformers. The resulting parameter may be used to sharpen another beamformer steered in the same look-direction, while attenuating ambient noise and interferers from other directions. However, while the original 2D version of the algorithm has been demonstrated to work well with second-order circular harmonic input, it becomes increasingly less suitable with increasing input order. Therefore, the proposed reformulation extends the applicability of CroPaC for much higher orders of circular harmonic input. The method is evaluated with simulated data of a 96-channel circular hydrophone array in three different passive sonar scenarios, where the proposed post-filter is shown to improve the spatial selectivity of both delay-and-sum and minimum-variance distortionless response beamformers.

中文翻译：

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利用高阶圆谐波的参数空间后置滤波在水下声场可视化中的应用

使用圆形水听器阵列的波束成形可用于二维 (2D) 水下声场可视化任务。在本文中，提出了一种参数空间后滤波方法，该方法专门针对涉及大型圆形阵列的应用，旨在提高传统波束形成器的空间选择性。从本质上讲，所提出的方法是对交叉模式相干 (CroPaC) 空间后置滤波器的重新表述，它涉及计算源自重合波束形成器的两个信号之间的归一化交叉频谱密度。所得参数可用于锐化在同一观察方向上操纵的另一个波束形成器，同时衰减来自其他方向的环境噪声和干扰。然而，虽然该算法的原始 2D 版本已被证明适用于二阶圆谐波输入，但随着输入阶数的增加，它变得越来越不适合。因此，建议的重新制定扩展了 CroPaC 对更高阶的圆谐波输入的适用性。该方法在三种不同的无源声纳场景中使用 96 通道圆形水听器阵列的模拟数据进行评估，其中表明所提出的后置滤波器可以提高延迟求和和最小方差无失真响应波束形成器的空间选择性。