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On an array localization technique with Euclidean distance geometry


The localization of sources by an acoustic array of microphones depends to a great extent on an accurate knowledge of the antenna position in its environment. From the geometric data of the array and the object of study, the present work details a methodology to determine the location of the microphones in relation to the object and reproduce the experimental configuration. Reference sources are placed on the object in order to measure 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 Scaling (MDS) technique is used to reconstruct the point set from distances. Second, this point set is then aligned with the sources whose coordinates are known. This orthogonal Procustes problem is solved by the Kabsch algorithm to obtain the rotation and translation matrices between the coordinate system of the array and the object of study. In addition, a low rank property of Euclidean distance matrices is exploited to evaluate in situ the speed of sound. The main theoretical and algorithmic elements are exposed and a numerical simulation of a geometric configuration, representative of a typical experimental set-up, is carried out. The robustness of the method is finally discussed.
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Dates et versions

hal-01820078 , version 1 (21-06-2018)


  • HAL Id : hal-01820078 , version 1


Simon Bouley, Charles Vanwynsberghe, Thibaut Le Magueresse, Jérôme Antoni. On an array localization technique with Euclidean distance geometry. Euronoise 2018, May 2018, Hersonissos, Greece. ⟨hal-01820078⟩
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