Algebraic Solution for Joint Localization and Synchronization of Multiple Sensor Nodes in the Presence of Beacon Uncertainties

This paper addresses the problem of joint localization and synchronization of multiple sensor nodes simultaneously using the time stamp information from message exchanges between the sensor nodes and beacons and among the sensor nodes. Through parameter transformation and multi-stage processing, two computationally efficient algebraic solutions are developed for this challenging non-linear estimation problem. One is without message exchanges among the sensor nodes and the other is with the exchanges. Theoretical analysis shows that the performance of the proposed solutions is able to reach the CRLB accuracy for the sensor node positions, as well as the clock parameters over the mild error region. Simulation results support very well the theoretical performance of the proposed solutions.