On Using the Relative Configuration to Explore Cooperative Localization

Cooperative localization differs from conventional localizations in using the measurements between the unknown nodes, which provide the relative location information of the nodes. This paper investigates cooperative localization by adopting the concept of relative configuration that describes the “shape” of the node network, without considering its absolute location, orientation, and/or scaling. Since the relative configuration is a non-Euclidean object, we introduce the Procrustes coordinates as a coordinate representation, suggest using the relative error as a coordinate independent error metric, and then derive the Cramér-Rao lower bound (CRLB) and a CRLB-type bound for the Procrustes coordinates and the relative error respectively. Three applications of the relative configuration are demonstrated: the first one gives the CRLB analysis for anchor-free localization; the second one discusses the optimal minimally constrained system (MCS) for deriving the absolute locations; and the third one refers to the anchor selection with consideration of anchor location uncertainty. These applications show the advantages of using the relative configuration to investigate cooperative localization.