Geometric calibration of very large microphone arrays in mismatched free field

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.