Robust Microphone Placement for Source Localization from Noisy Distance Measurements

We propose a novel algorithm to design an optimum array geometry for source localization inside an enclosure. We assume a square-law decay propagation model for the sound acquisition so that the additive noise on the measured source-microphone distances is proportional to the distances regardless of the noise distribution. We formulate the source localization as an instance of the ``Generalized Trust Region Subproblem'' (GTRS) whose solution gives the location of the source. We show that by suitable selection of the microphone locations, one can tremendously decrease the noise-sensitivity of the resulting solution. In particular, by minimizing the noise-sensitivity of the source location in terms of sensor positions, we find the optimal noise-robust array geometry for the enclosure. Simulation results are provided to show the efficiency of the proposed algorithm.