Elliptic Localization With Imperfect Clock Synchronization for Known and Unknown Propagation Speed Scenarios

In this article, we address the elliptic localization problem in the presence of clock synchronization errors at the receivers and transmitters, when the propagation speed is known as well as not known. For the known propagation speed scenario, we first show that the clock synchronization errors, when modeled as Gaussian random variables, can be treated as part of the composite noise in the measurement model without incurring performance loss in localization. Motivated by this result, we propose a generalized trust region subproblem solution for estimating the object position. For the unknown propagation speed scenario, we first formulate a nonconvex weighted least-squares problem. Such a nonconvex problem is solved by either one of the two proposed methods, semidefinite relaxation or grid search, to jointly estimate the object position and the propagation speed. Furthermore, we conduct the mean square error analysis to show that the proposed methods are able to reach the Cramer–Rao lower bound accuracy under Gaussian noise, which is validated by using simulated and semireal data.