SLAM-based Joint Calibration of Multiple Asynchronous Microphone Arrays and Sound Source Localization

Robot audition systems with multiple microphone arrays have many applications in practice. However, accurate calibration of multiple microphone arrays remains challenging because there are many unknown parameters to be identified, including the relative transforms (i.e., orientation, translation) and asynchronous factors (i.e., initial time offset and sampling clock difference) between microphone arrays. To tackle these challenges, in this paper, we adopt batch simultaneous localization and mapping (SLAM) for joint calibration of multiple asynchronous microphone arrays and sound source localization. Using the Fisher information matrix (FIM) approach, we first conduct the observability analysis (i.e., parameter identifiability) of the above-mentioned calibration problem and establish necessary/sufficient conditions under which the FIM and the Jacobian matrix have full column rank, which implies the identifiability of the unknown parameters. We also discover several scenarios where the unknown parameters are not uniquely identifiable. Subsequently, we propose an effective framework to initialize the unknown parameters, which is used as the initial guess in batch SLAM for multiple microphone arrays calibration, aiming to further enhance optimization accuracy and convergence. Extensive numerical simulations and real experiments have been conducted to verify the performance of the proposed method. The experiment results show that the proposed pipeline achieves higher accuracy with fast convergence in comparison to methods that use the noise-corrupted ground truth of the unknown parameters as the initial guess in the optimization and other existing frameworks.

Observability Analysis of Graph SLAM-Based Joint Calibration of Multiple Microphone Arrays and Sound Source Localization

Multiple microphone arrays have many applications in robot audition, including sound source localization, audio scene perception and analysis, etc. However, accurate calibration of multiple microphone arrays remains a challenge because there are many unknown parameters to be identified, including the Euler angles, geometry, asynchronous factors between the microphone arrays. This paper is concerned with joint calibration of multiple microphone arrays and sound source localization using graph simultaneous localization and mapping (SLAM). By using a Fisher information matrix (FIM) approach, we focus on the observability analysis of the graph SLAM framework for the above-mentioned calibration problem. We thoroughly investigate the identifiability of the unknown parameters, including the Euler angles, geometry, asynchronous effects between the microphone arrays, and the sound source locations. We establish necessary/sufficient conditions under which the FIM and the Jacobian matrix have full column rank, which implies the identifiability of the unknown parameters. These conditions are closely related to the variation in the motion of the sound source and the configuration of microphone arrays, and have intuitive and physical interpretations. We also discover several scenarios where the unknown parameters are not uniquely identifiable. All theoretical findings are demonstrated using simulation data.