Ad-hoc microphone array calibration from partial distance measurements

Abstract

We address the problem of ad hoc microphone array calibration where some of the distances between the microphones can not be measured. The conventional techniques require information about all the distances for accurate reconstruction of the array geometry. To alleviate this condition, we propose to exploit the properties of Euclidean distance matrices within the framework of low-rank matrix completion to recover the missing entries. We provide rigorous analysis to bound the calibration error using noisy measurements. This study elucidates the links between the performance and the structure of the missing distances, along with the size of the network. The experiments carried out on real data recordings demonstrate these theoretical insights. A significant improvement is achieved by the proposed Euclidean distance matrix completion algorithm over the state-of-the-art techniques for ad hoc microphone array calibration.

Distributed Microphone Arrays, Emerging Speech and Audio Signal Processing Platforms: A Review

“…For microphone array calibration, some advanced mathematical methods use joint source and microphone localization methods [62] and incorporate matrix completion constrained by Euclidean space properties [63,64]. Such methods require partial knowledge of pairwise microphone distances [65].…”

“…For microphone array calibration, some advanced mathematical methods use joint source and microphone localization methods [62] and incorporate matrix completion constrained by Euclidean space properties [63,64]. Such methods require partial knowledge of pairwise microphone distances [65]. It has been shown that using sound emissions for self-calibration can result in a calibration method more robust to sampling frequency mismatch [66]; however, the method is only applicable to devices that have both recording and sound emitting capabilities.…”

Spatial Sound Localization via Multipath Euclidean Distance Matrix Recovery

“…Unless Ξ π consists of correct order of images, theM π does not correspond to a Euclidean distance matrix, so we propose to projectM π on to the cone of Euclidean distance matrices, EDM N . To this end, we apply a projection, P : S N h −→ EDM N and measure the distance between the estimated matrix and the EDM cone [26,27].…”