Relative kinematics of an anchorless network
Abstract
Estimating the location of N coordinates in a P dimensional Euclidean space from pairwise distances (or proximity measurements), is a principal challenge in a wide variety of fields. Conventionally, when localizing a static network of immobile nodes, nonlinear dimensional reduction techniques are applied on the measured Euclidean distance matrix (EDM) to obtain the relative coordinates upto a rotation and translation. In this article, we focus on an anchorless network of mobile nodes, where the distance measurements between the mobile nodes are timevarying in nature. Furthermore, in an anchorless network the absolute knowledge of any node positions, motion or reference frame is absent. We derive a novel data model which relates the timevarying EDMs to the timevarying relative positions of an anchorless network. Using this data model, we estimate the relative position, relative velocity and higher order derivatives, which are collectively termed as the relative kinematics of the anchorless network. The derived data model is inherently illposed, however can be solved using certain relative immobility constraints. We propose elegant closed form solutions to recursively estimate the relative kinematics of the network. For the sake of completeness, estimators are also proposed to find the absolute kinematics of the nodes, given known reference anchors. CramerRao bounds are derived for the new data model and simulations are performed to analyze the performance of the proposed solutions.
 Publication:

arXiv eprints
 Pub Date:
 July 2018
 arXiv:
 arXiv:1807.11296
 Bibcode:
 2018arXiv180711296T
 Keywords:

 Electrical Engineering and Systems Science  Signal Processing;
 Electrical Engineering and Systems Science  Systems and Control;
 Statistics  Applications
 EPrint:
 In submission, Elsevier signal processing