Closed-Form Solution for Joint Localization and Time Synchronization in Wireless Sensor Networks

For Wireless Sensor Networks (WSNs), utilizing the same set of measurement data for joint localization and time synchronization is potentially useful for achieving higher estimation accuracy, lower communication overhead and power consumption. In this paper, we first formulate the Maximum Likelihood (ML) estimator, and then propose a Closed-form Weighted Least Square (CF-WLS) approach which can theoretically achieve the Cramer-Rao Lower Bound (CRLB) and is computationally efficient. Simulation results show that the performance of CF-WLS is similar to that of ML most of the time when a sufficient number of beacons are involved, and CF-WLS can attain the CRLB with only three-way message exchange when more than three beacons are present. CF-WLS offers reduced computational complexity over ML while maintaining similar estimation accuracy, and outperforms the Constrained Weighted Least Square (CWLS) approach, proposed in another paper, in higher estimation accuracy especially for timing parameters when only three-way message exchange is employed. The reduced complexity, communication overhead and power consumption make CF-WLS an attractive solution to the simultaneous localization and time synchronization problem in WSNs.