An efficient convex constrained weighted least squares source localization algorithm based on TDOA measurements

• We explore the source localization problem using noisy TDOA measurements in the presence of random sensor position errors.
• By exploiting the hidden convexity, the formulated non-convex localization problem is transformed to a convex optimization problem.
• The proposed convex localization algorithm analytically achieves the CRLB under some mild approximations.
• The proposed algorithm can efficiently avoid the ill-conditioning problem.

This paper investigates the source localization problem based on time difference of arrival (TDOA) measurements in the presence of random noises in both the TDOA and sensor location measurements. We formulate the localization problem as a constrained weighted least squares problem which is an indefinite quadratically constrained quadratic programming problem. Owing to the non-convex nature of this problem, it is difficult to obtain a global solution. However, by exploiting the hidden convexity of this problem, we reformulate it to a convex optimization problem. We further derive a primal-dual interior point algorithm to reach a global solution efficiently. The proposed method is shown to analytically achieve the Cramér-Rao lower bound (CRLB) under some mild approximations. Moreover, when the location geometry is not desirable, the proposed algorithm can efficiently avoid the ill-conditioning problem. Simulations are used to corroborate the theoretical results which demonstrate the good performance, robustness and high efficiency of the proposed method.