Efficient semidefinite solutions for TDOA-based source localization under unknown PS

Abstract

Two efficient solutions via Semi-Definite Programming (SDP) are proposed for source localization problems using time difference of arrival (TDOA)-based ranging measurements when the propagation speed (PS) is unavailable and considered as a variable. For this problem, we propose a relaxed SDP (RSDP) solution, the performance of which is suboptimal. Accordingly, we propose a two-stage SDP method to improve the performance by applying the rank-reduction method. Besides, we also propose a penalty function-based SDP (PF-SDP) by introducing the penalty term. By doing so, the cost function becomes tighter so that the solution performs better. The simulated results show that the performance of two-stage SDP is sufficiently close to the Cramér-Rao Lower Bound (CRLB) accuracy at high noise levels. The PF-SDP outperforms the two-stage SDP in the presence of low noise levels.