Understanding Node Localizability of Wireless Ad-hoc Networks

Abstract—Location awareness is highly critical for wireless ad-hoc and sensor networks. Many efforts have been made to solve the problem of whether or not a network can be localized. Nevertheless, based on the data collected from a working sensor network, it is observed that the network is not always entirely localizable. Theoretical analyses also suggest that, in most cases, it is unlikely that all nodes in a network are localizable, although a (large) portion of the nodes can be uniquely located. Existing studies merely examine whether or not a network is localizable as a whole; yet two fundamental questions remain unaddressed: First, given a network configuration, whether or not a specific node is localizable? Second, how many nodes in a network can be located and which are them? In this study, we analyze the limitation of previous works and propose a novel concept of node localizability. By deriving the necessary and sufficient conditions for node localizability, for the first time, it is possible to analyze how many nodes one can expect to locate in sparsely or moderately connected networks. To validate this design, we implement our solution on a real-world system and the experimental results show that node localizability provides useful guidelines for network deployment and other location-based services. Index Terms—Localization, localizability, graph rigidity, wireless sensor networks, ad hoc networks. Ç