Joint non-linear ranging and affine synchronization basis for a network of mobile nodes

Synchronization and localization are critical challenges for the coherent functioning of a wireless network of mobile nodes. In this paper, a novel joint non-linear range and affine time model is presented based on two way time stamp exchanges, extending an existing affine time-range model. For a pair of nodes, a closed form pairwise least squares solution is proposed for estimating pairwise range parameters, namely relative range, range rate and rate of range rate between the nodes, in addition to estimating the clock skews and the clock offsets. Extending these pair wise solutions to network wide ranging and clock synchronization, we present a central data fusion based global least squares solution. Furthermore, a new Constrained Cramer Rao Bound (CCRB) is derived for the joint time-range model and the proposed algorithms are shown to approach the theoretical limits asymptotically.