Microphone array position calibration in the frequency domain using a single unknown source

We study the problem of microphone array localization in a strongly reverberant room, where time of arrivals (TOA) or time difference of arrivals (TDOA) cannot always be measured precisely. Instead, we use frequency-domain measurements to calibrate the array position, based on the modes of the room, excited by a wide-band single source, that can be unknown. By using the fact that each measured mode can be decomposed as a sum of model-based polynomials, we build a cost function whose minimum indicates the positions of the microphones. A simple Block Coordinate Descent algorithm can be used to minimize this cost function. Numerical results indicate that this algorithm converges to the right solution, and therefore that using frequency measurements for position calibration is a valid concept for dense arrays, as an alternative to time-domain methods in reverberant domains.