On a New SDP-SOCP Method for Acoustic Source Localization Problem

Acoustic source localization has many important applications. Convex relaxation provides a viable approach of obtaining good estimates very efficiently. There are two popular convex relaxation methods using either semi-definite programming (SDP) or second-order cone programming (SOCP). However, the performances of the methods have not been studied properly in the literature and there is no comparison in terms of accuracy and performance. The aims of this article are twofold. First of all, we study and compare several convex relaxation methods. We demonstrate, by numerical examples, that most of the convex relaxation methods cannot localize the source exactly, even in the performance limit when the time difference of arrival (TDOA) information is exact. In addressing this problem, we propose a novel mixed SDP-SOCP relaxation model and study the characteristics of the optimal solutions and its localizable region. Furthermore, an error correction scheme for the proposed SDP-SOCP model is developed so that exact localization can be achieved in the performance limit. Experimental data have been collected in a room with two different array configurations to demonstrate our proposed approach.