Joint TOA-based sensor synchronization and localization using semidefinite programming

In this paper, asynchronous sensor localization using time-of-arrival (TOA) measurements is studied. Accurate TOA-based localization requires perfect timing synchronization between the source and anchor nodes. In asynchronous networks, the anchor nodes are assumed to be synchronized, while the clock of the source node needs be synchronized with those of the anchor nodes. Although synchronization and localization are typically performed separately, in this work a joint synchronization and localization framework is considered, as it is expected to provide significant improvement over two-step approaches. The clock parameters (clock offset and skew) of the source node are estimated jointly with its location. The corresponding Cramér-Rao lower bound (CRLB) and the maximum likelihood (ML) estimator of the system model are derived. The ML estimator is highly nonlinear and nonconvex which must be solved with computationally complex algorithms. Alternatively, a novel semidefinite programming (SDP) estimator is introduced by relaxing the original ML minimization problem into a convex problem. Computer simulations show that the proposed SDP estimator outperforms other previously proposed estimators.