Contents I. Introduction
Source location technique based on microphone array had widespread application in many areas, In a video teleconference, if can determine the location of the active speaker, This technique was also used in robot audition system, mobile navigation system, hearing aid system and etc Ye [1] classified approaches to the source location probiem into three classes, locators based on steered beam former, high-resolution spectral estimation locators, and locators based on Time Difference to), Arriva, (TDOA), TDOA method was often used because of, easy realization and small compulation, A lot of, mathematical model methods based on TDOA were presented, such as sphere cross(SX) method [2], sphere intersection(SI) method [3], tinear iniersection(LI) method [4], linear correction least square(LCLS) method [5] and linear correction total least square (LCTLS) method [6]. Reference [6] showed LCTLS method was better than SI and LCLS. However, the algorithm presented by reference [6] to solve the LCTLS model was just an approximation algorithm. The motivation of this paper is to present an exact algorithm for the LCTLS model and to show this model can be solvable in polynomial-time. One can obtain an optimal solution of the LCTLS model by semi-definite positive program (SDP) relaxation and rank-one decomposition of matrices. Numerical results show that the algorithm is indeed more effective than the algorithm in [6].
