Angle-Based Distributed Node Localizability and Localization.

To determine the positions of those free nodes in a wireless sensor network, angle-based localization approaches have been recently proposed. However, the existing angle-only localizability conditions are for the whole network, for which the existence of only one unlocalizable node implies that the whole network is unlocalizable. To efficiently obtain specific information on the nodes' localizability, this paper proposes to check each node's localizability in a distributed manner. First, we propose an algebraic condition for node localizability, based on which a distributed node-localizability checking algorithm is proposed. Then, a strategy on adding triangular angle measurements to those unlocalizable nodes is proposed, under which an unlocalizable network can become localizable. Finally, by using the local information of each node's triangle degree in the network, a fully distributed localization algorithm is designed, which does not require any graphic information or additional communication. Simulation examples are provided to validate the results.