基于欧氏距离矩阵的三维单源定位
3D Single Source Localization Based on Euclidean Distance Matrices
摘要：
使用多个麦克风进行3D源定位的流行方法是转向响应功率方法，其中通过最大化三个连续位置变量的函数来直接估计源位置。而不是直接估计源的位置，在本文中，我们提出了一个间接的，基于距离的方法进行三维源定位。基于欧氏距离矩阵的性质，将三维声源定位问题转化为声源与参考麦克风之间的距离这一单变量的代价函数的最小化问题。使用已知的麦克风几何形状和麦克风之间的估计到达时间差（TDOA），我们展示了如何根据这个变量计算3D源位置。此外，而不是使用一个单一的TDOA估计每个麦克风对，我们提出了一个扩展，使选择最合适的估计从一组候选TDOA估计，这是特别相关的混响环境中具有较强的早期反射。针对不同声源和麦克风星座的实验结果表明，所提出的基于EDM的方法始终优于转向响应功率方法，特别是当声源靠近麦克风时。
英文摘要：
A popular approach for 3D source localization using multiple microphones is the steered-response power method, where the source position is directly estimated by maximizing a function of three continuous position variables. Instead of directly estimating the source position, in this paper we propose an indirect, distance-based method for 3D source localization. Based on properties of Euclidean distance matrices (EDMs), we reformulate the 3D source localization problem as the minimization of a cost function of a single variable, namely the distance between the source and the reference microphone. Using the known microphone geometry and estimated time-differences of arrival (TDOAs) between the microphones, we show how the 3D source position can be computed based on this variable. In addition, instead of using a single TDOA estimate per microphone pair, we propose an extension that enables to select the most appropriate estimate from a set of candidate TDOA estimates, which is especially relevant in reverberant environments with strong early reflections. Experimental results for different source and microphone constellations show that the proposed EDM-based method consistently outperforms the steered-response power method, especially when the source is close to the microphones.
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