Joint relative position and velocity estimation for an anchorless network of mobile nodes

Localization is a fundamental challenge for any network of nodes, in particular when the nodes are in motion and no reference nodes are available. Traditionally, the Multidimensional scaling (MDS) algorithm is employed at discrete time instances using pairwise distance measurements to find the relative node positions (with arbitrary rotation). In this paper, we present a novel framework to localize an anchorless network of mobile nodes given only time-varying inter-nodal distances. The time derivatives of the pairwise distances are used to jointly estimate the initial relative position and relative velocity of the nodes. Under linear velocity assumption for a small time duration, we show that the combination of the initial relative positions and relative velocity beget the relative motion of the nodes at discrete time instances. The proposed approach can be seen as an extension of the classical MDS, wherein Doppler measurements, if available, can be readily incorporated. We derive Cramér Rao bounds and perform simulations to evaluate the performance of the proposed estimators. Furthermore, the computational complexity and the benefits of the proposed algorithms are also presented.