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

TL;DR

This paper introduces a novel Euclidean distance matrix completion algorithm for ad hoc microphone array calibration, providing theoretical guarantees and demonstrating significant improvements over existing methods through experiments.

Contribution

It proposes a new EDM completion algorithm with theoretical performance guarantees, enhancing calibration accuracy in ad hoc microphone arrays.

Findings

The algorithm outperforms state-of-the-art calibration techniques.

Calibration accuracy improves with more microphones and lower noise.

Theoretical analysis links calibration error to noise and missing data ratio.

Abstract

This paper addresses the problem of ad hoc microphone array calibration where only partial information about the distances between microphones is available. We construct a matrix consisting of the pairwise distances and propose to estimate the missing entries based on a novel Euclidean distance matrix completion algorithm by alternative low-rank matrix completion and projection onto the Euclidean distance space. This approach confines the recovered matrix to the EDM cone at each iteration of the matrix completion algorithm. The theoretical guarantees of the calibration performance are obtained considering the random and locally structured missing entries as well as the measurement noise on the known distances. This study elucidates the links between the calibration error and the number of microphones along with the noise level and the ratio of missing distances. Thorough experiments on real data recordings and simulated setups are conducted to 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.