On the value of collaboration in multidimensional location estimation

In this paper, we investigate the benefit of inter-node collaboration in multidimensional location estimation. In particular, for networks with reference nodes at known locations and source nodes whose locations are unknown and to be estimated, we establish the value of collaboration for source node position estimation by presenting proof of a decreasing Cramér-Rao lower bound as additional source nodes (meeting some minimum connectivity requirements) are introduced into the collaborative position estimation problem. Prior work has shown this for one-dimensional location estimation; however, the previous proof as presented is not easily extendable to multidimensional location estimation. Following the completion of the proof, the minimum connectivity conditions for two-dimensional positioning using time-of-arrival and received-signal-strength ranging information are discussed. Lastly, the theoretical result is verified with numerical results through simulation.