A rank-one decomposition algorithm for robust 3D acoustic source localization problem

For the 3D acoustic source localization problem (3DASLP) based on time difference of arrival (TDOA) technique, this paper shows that SDP relaxation of the 3DASLP is tight to the original problem. One can obtain an optimal solution of the 3DASLP by rank-one decomposition of matrices. So the 3DSLP based on TDOA is solvable in polynomial-time. Moreover, an algorithm based on semi-definite positive program (SDP) relaxation and rank-one decomposition of matrices has been presented. Numerical results show that the algorithm is indeed efficient.