Two Solutions to the Localization Using Time Difference of Arrival Problem

摘要

In this paper, two new solutions to the localization of an emitter using time difference of arrival (TDOA) measurements are proposed. The maximum likelihood estimation for this problem will result in a nonlinear and nonconvex optimization problem, which is very difficult to solve. The solutions presented in this paper consider an alternate formulation, which is based on the sensor-emitter geometry. This formulation results in quadratic (however, nonconvex) optimization problem. The first solution relaxes the original optimization problem into a semidefinite program (SDP). Using the solution to this relaxed SDP, emitter is localized using a randomization technique. The second solution forms the Lagrangian dual of the original problem, and it is shown that the dual problem is an SDP. From the solution to the dual problem a solution to the original problem is found. It has to be noted that the solution obtained using the optimal dual variable, is optimal to the original problem only if strong duality holds. This has not been proven in this paper analytically. Extensive simulations performed suggests that the strong duality may hold for this problem.