An accurate algebraic closed-form solution for energy-based source localization

The localization of an acoustic source can be based on the energy measurements at a number of spatially separated microphones. This is because the amount of source energy attenuation at a microphone is proportional to the square of the distance between the source and the microphone. This paper develops an algebraic closed-form solution for the acoustic source localization problem using energy measurements, under the condition of direct line-of-sight and free space propagation. First-order analysis is applied to the proposed solution to study its performance, where only the linear noise terms are kept in obtaining the mean-square localization error. The first-order analytical results show that the proposed solution reaches the Cramer-Rao lower bound (CRLB) accuracy for Gaussian noise as the signal-to-noise ratio tends to infinity. In addition, the proposed solution provides much better accuracy than other closed-form solutions available in literature. Improvement on the proposed solution that extends its operating range beyond the threshold noise level was made by imposing non-negative constraints. Simulations are included to, corroborate the performance of the proposed method.