  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.
