Asynchronous Microphone Array Calibration using Hybrid TDOA Information

TL;DR

This paper proposes to use TDOA-S and TDOA-M, called hybrid TDOA, together with odometry measurements for bath SLAM-based calibration of asynchronous microphone arrays, and shows that this method is more independent of microphone number, less sensitive to initial values, and has better calibration accuracy and robustness under various TDOA noises.

Abstract

Asynchronous microphone array calibration is a prerequisite for many audition robot applications. A popular solution to the above calibration problem is the batch form of Simultaneous Localisation and Mapping (SLAM), using the time difference of arrival measurements between two microphones (TDOA-M), and the robot (which serves as a moving sound source during calibration) odometry information. In this paper, we introduce a new form of measurement for microphone array calibration, i.e. the time difference of arrival between adjacent sound events (TDOA-S) with respect to the microphone channels. We propose to use TDOA-S and TDOA-M, called hybrid TDOA, together with odometry measurements for bath SLAM-based calibration of asynchronous microphone arrays. Extensive simulation and real-world experiments show that our method is more independent of microphone number, less sensitive to initial values (when using off-the-shelf algorithms such as Gauss-Newton iterations), and has better calibration accuracy and robustness under various TDOA noises. Simulation results also demonstrate that our method has a lower Cramér-Rao lower bound (CRLB) for microphone parameters. To benefit the community, we open-source our code and data at https://github.com/AISLAB-sustech/Hybrid-TDOA-Calib.

Figures (5)

• Figure 1: Differences between TDOA-M (a) and TDOA-S (b).
• Figure 2: Visualization of acquiring the rough delay: $T_{rough}$ (a) and precise delay: $T_{pre}$ (b). The red/green box represents the capture window obtaining the current/next recorded calibration signal.
• Figure 3: Box plot of estimation errors for microphone parameters in simulations: microphone locations (a),(d),(g), time offsets (b),(e),(h), and clock drift rates (c),(f),(i) under four microphone numbers, i.e. 4, 6, 8, and 10, four initial values noise SDs under three trajectories, i.e. 0m/0m, 1m/2m, 2m/4m, and 3m/6m, and three TDOA noise SDs, i.e. $5\times10^{-5}s$, $10^{-4}s$, and $5\times10^{-4}s$, respectively. Here, "$x$m/$y$m" means combining the estimation result of trajectory 1 under $\sigma_{init}=x$m and results of both trajectory 2 and 3 under $\sigma_{init}=y$m.
• Figure 4: The calibration scenario for real-world experiments.
• Figure 5: Box plot of results in real-world experiment: microphone location estimation errors under various microphone numbers (a), i.e. 4, 6, 8, and 10, initial values noise SDs (b), i.e. 0m, 0.5m, 1m, and 2m, and five cases of TDOA noises (c).