  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.
