Speaker locations from inter-speaker range measurements: closed-form estimator and performance relative to the Cramer-Rao lower bound

The problem of determining the relative positions of speakers in an array given noisy measurements of inter-speaker ranges is considered. A closed-form position estimator which minimizes a weighted equation error norm is presented. The information inequality is used to bound the position estimate mean square error and to gauge the accuracy of the closed-form estimator, which is shown to be nearly efficient.