A linear estimator for joint synchronization and localization in wireless sensor networks

In this paper, joint sensor synchronization and localization using time-of-arrival measurements is studied. In wireless sensor networks, the accuracy of the clock synchronization among nodes has a great impact on the performance of the localization using time-based ranging methods. The clocks of the anchor nodes are typically synchronized with each other, while those of the source nodes must be synchronized with the anchor nodes. Each source node has its own clock characterized by clock offset and clock skew. Synchronization is the process of determining these clock parameters for the source node, while localization is the process of estimating its location. Generally, the estimation problem is broken down into two subproblems, where the synchronization is first performed and then the source node is localized. However, in this paper, a joint synchronization and localization framework is considered and examined, as it is expected to provide better accuracy, especially in dynamic networks. The system model for joint synchronization and localization is first introduced. The maximum likelihood (ML) estimator is then derived which is shown to be highly nonlinear and nonconvex. The ML estimator does not have a closed-form solution and must be solved by computationally complex and iterative algorithms. A novel linear estimator is derived which has a closed-form solution with significantly lower complexity. The performance of the proposed linear estimator is evaluated through computer simulations. Results show that the proposed linear estimator outperforms the previously considered estimators, especially in low signal-to-noise ratios.