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.