Minimal solutions for dual microphone rig self-calibration

In this paper, we study minimal problems related to dual microphone rig self-calibration using TOA measurements from sound sources with unknown positions. We consider the problems with varying setups as (i) if the internal distances between the microphone nodes are known a priori or not. (ii) if the microphone rigs lies in an affine space with different dimension than the sound sources. Solving these minimal problems is essential to robust estimation of microphone and sound source locations. We identify for each of these minimal problems the number of solutions in general and develop non-iterative solvers. We show that the proposed solvers are numerically stable in synthetic experiments. We also apply our method in a real indoor experiment and obtain accurate reconstruction using TOA measurements.