Abstract Source localization and quantification by an acoustic array of microphones depend to a great extent on an accurate knowledge of the antenna position towards the radiating device. The present work details a methodology to determine the location of the microphones in relation to an object of study, starting from its geometric shape and that of the array, in order to reproduce an experimental configuration in any retro-propagating method. A set of reference sources are placed on several prominent locations of the device to estimate the times of flight (ToF) (and distances) between them and the microphones, connecting the array and the object together. The overall geometric configuration is thus defined by an Euclidean Distance Matrix (EDM), which is basically the matrix of squared distances between points. First, MultiDimensional Unfolding (MDU) technique is used to reconstruct the point set from distances. Second, this point set is then aligned with the device, using reference sources as anchor nodes. This orthogonal Procustes problem is solved by the Kabsch algorithm to obtain the optimal rotation and translation matrices between the coordinate system of the array and that of the object of study. The methodology is detailed, validated first by a numerical simulation of a typical experimental set-up. An experimental campaign is finally carried out to assess the robustness of the method in a typical test case.

中文翻译：

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具有欧氏距离几何的麦克风阵列定位技术

摘要 麦克风声学阵列的声源定位和量化在很大程度上取决于对天线朝向辐射设备的位置的准确了解。本工作详细介绍了一种确定麦克风相对于研究对象的位置的方法，从其几何形状和阵列的几何形状开始，以便在任何反向传播方法中重现实验配置。一组参考源放置在设备的几个显着位置，以估计它们与麦克风之间的飞行时间 (ToF)（和距离），将阵列和物体连接在一起。因此，整体几何配置由欧几里得距离矩阵 (EDM) 定义，它基本上是点之间距离平方的矩阵。第一的，多维展开（MDU）技术用于从距离重建点集。其次，这个点集然后与设备对齐，使用参考源作为锚节点。该正交 Procustes 问题由 Kabsch 算法解决，以获得阵列坐标系和研究对象坐标系之间的最佳旋转和平移矩阵。该方法是详细的，首先通过典型实验装置的数值模拟进行验证。最后进行了一项实验活动，以评估该方法在典型测试案例中的稳健性。该正交 Procustes 问题由 Kabsch 算法解决，以获得阵列坐标系和研究对象坐标系之间的最佳旋转和平移矩阵。该方法是详细的，首先通过典型实验装置的数值模拟进行验证。最后进行了一项实验活动，以评估该方法在典型测试案例中的稳健性。该正交 Procustes 问题由 Kabsch 算法解决，以获得阵列坐标系和研究对象坐标系之间的最佳旋转和平移矩阵。该方法是详细的，首先通过典型实验装置的数值模拟进行验证。最后进行了一项实验活动，以评估该方法在典型测试案例中的稳健性。