TDOA-based acoustic source localization in the space–range reference frame

In this paper we consider a class of geometric methods for acoustic source local- ization based on range differences (or time differences of arrival), and we offer a new and unifying perspective on such methods based on the adoption of a multidimensional refer- ence frame obtained by adding the range difference coordinate to the spatial coordinates of the source. In this extended coordinate system the working principles of a wide range of source localization methods becomes clear and immediate. The space–range reference frame, however, has a practical purpose as well, as it can be used for gaining insight on why some configurations of microphones lead to better localization performance than others and it suggests methods for improving existing localization techniques. In particular, we derive a closed-form solution of the constrained least-squares localization problem for linear arrays of microphones