Joint Ranging and Synchronization for an Anchorless Network of Mobile Nodes

Synchronization and localization are critical challenges for the coherent functioning of a wireless network, which are conventionally solved independently. Recently, various estimators have been proposed for pairwise synchronization between immobile nodes, based on time stamp exchanges via two-way communication. In this paper, we consider a network of mobile nodes for which a novel joint time-range model is presented, treating both unsynchronized clocks and the pairwise distances as a polynomial functions of true time. For a pair of nodes, a least squares solution is proposed for estimating the pairwise range parameters between the nodes, in addition to estimating the clock offsets and clock skews. Extending these pairwise solutions to network-wide ranging and clock synchronization, we present a central data fusion based global least squares algorithm. A unique solution is nonexistent without a constraint on the cost function e.g., a clock reference node. Ergo, a constrained framework is proposed and a new Constrained Cramér-Rao Bound (CCRB) is derived for the joint time-range model. In addition, to alleviate the need for a single clock reference, various clock constraints are presented and their benefits are investigated using the proposed solutions. Simulations are conducted and the algorithms are shown to approach the theoretical limits.