Reference-distance estimation approach for TDOA-based source and sensor localization

In this paper, we present a new method to find solutions to the time difference of arrival (TDOA)-based source and sensor localization problem. This paper is a continuation of [1], in which sources and sensors are localized on the basis of time of arrival (TOA) measurements. Generally, the TOA is known if the TDOA and reference-distances with the sound velocity are given, where the reference-distances are defined as the distances from the first (reference) sensor to the sources. We show that when the numbers of sources and sensors are at least six and eight, respectively, the reference-distances can be computed directly from TDOA measurements. This means that in such cases, the positions of the sources and sensors can be directly estimated in closed-form solutions, except for one reference-distance, which is estimated by a grid search. The validity of our algorithm is evaluated by synthetic experiments in noise-free and noisy cases.