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This paper addresses the problem of ad hoc microphone array calibration whereonly partial information about the distances between microphones is available.We construct a matrix consisting of the pairwise distances and propose toestimate the missing entries based on a novel Euclidean distance matrixcompletion algorithm by alternative low-rank matrix completion and projectiononto the Euclidean distance space. This approach confines the recovered matrixto the EDM cone at each iteration of the matrix completion algorithm. Thetheoretical guarantees of the calibration performance are obtained consideringthe random and locally structured missing entries as well as the measurementnoise on the known distances. This study elucidates the links between thecalibration error and the number of microphones along with the noise level andthe ratio of missing distances. Thorough experiments on real data recordingsand simulated setups are conducted to demonstrate these theoretical insights. Asignificant improvement is achieved by the proposed Euclidean distance matrixcompletion algorithm over the state-of-the-art techniques for ad hoc microphonearray calibration.

Ad Hoc Microphone Array Calibration: Euclidean Distance Matrix Completion Algorithm and Theoretical Guarantees