Asynchronous Time-of-Arrival-Based Source Localization With Sensor Position Uncertainties

This letter considers the problem of source localization from signal time-of-arrival measurements with unknown start transmission time and sensor position uncertainties. Under the standard assumption of uncorrelated Gaussian distributed measurement errors, we formulate the maximum likelihood estimator (MLE). It is well known that minimization of a nonlinear and nonconvex MLE cost function is not a trivial problem. We use the semidefinite programming (SDP) method to convert the nonconvex MLE problem into convex problem. However, it is shown that the original SDP algorithm is not tight and cannot provide a high-quality solution. Previous research call the untightness of the original SDP algorithm as ambiguity, and they propose to add a penalty term to avoid the ambiguity. In this letter, we show that jointly adding the second-order-cone constraints and penalty term can significantly improve the tightness of the original SDP algorithm. Simulation results are included to evaluate the localization accuracy of the proposed algorithms by comparing with the state-of-the-art methods and the optimality benchmark of Cramér-Rao lower bound.