Vanwynsberghe Charles, Challande Pascal, Ollivier François, Marchal Jacques, Marchiano Régis
Lab-STICC UMR 6285, CNRS, ENSTA Bretagne, 2 rue François Verny, 29200 Brest, France.
Sorbonne Université, CNRS, Institut Jean Le Rond d'Alembert, 4 place Jussieu, 75005 Paris, France.
J Acoust Soc Am. 2019 Jan;145(1):215. doi: 10.1121/1.5083829.
Large microphone arrays are an efficient means for source localization thanks to a wide aperture and a great number of sensors. When such arrays are deployed in situ, accurate geometric calibration becomes essential to obtain the microphone positions. In free field, the classic procedures rely on measured Times of Arrival (TOA) or Time Differences of Arrival (TDOA) between the microphones and several controlled sources. However, free field model mismatches, such as reflectors, generate outliers which severely deteriorate the positioning accuracy. This paper introduces a unified framework for robust calibration using TOA or TDOA by exploiting an outlier-aware noise model. Thanks to the largeness of the array, the existing outliers are sparse and can be identified by a Lasso regression. From this, three iterative robust solvers are proposed: (i) for TOA by Robust Multi Dimensional Unfolding, a particular variation of Robust Multi Dimensional Scaling, (ii) for TDOA by data predenoising based on sparse and low-rank matrix decomposition, and (iii) for TDOA by jointly identifying the outliers and the geometry. The relevance of outlier-aware approaches is asserted by numerical and experimental tests. Compared with the baseline least-square approaches, the proposed robust solvers significantly improve the positioning accuracy in a free field mismatched by reflectors.
大型麦克风阵列由于孔径大且传感器数量众多，是一种高效的声源定位手段。当此类阵列现场部署时，精确的几何校准对于获取麦克风位置至关重要。在自由场中，经典方法依赖于测量麦克风与多个受控声源之间的到达时间（TOA）或到达时间差（TDOA）。然而，自由场模型不匹配，如反射器，会产生异常值，严重降低定位精度。本文通过利用一种考虑异常值的噪声模型，引入了一个使用TOA或TDOA进行鲁棒校准的统一框架。由于阵列规模较大，现有的异常值较为稀疏，可以通过套索回归进行识别。据此，提出了三种迭代鲁棒求解器：（i）通过鲁棒多维展开（Robust Multi Dimensional Unfolding）求解TOA，它是鲁棒多维缩放（Robust Multi Dimensional Scaling）的一种特殊变体；（ii）基于稀疏和低秩矩阵分解的数据去噪求解TDOA；（iii）联合识别异常值和几何形状求解TDOA。数值和实验测试证明了考虑异常值方法的相关性。与基线最小二乘法相比，所提出的鲁棒求解器在存在反射器导致不匹配的自由场中显著提高了定位精度。
