Theoretic analysis of unique localization for wireless sensor networks

Node self-localization has become an essential requirement for realistic applications over wireless sensor networks (WSNs). Although many distributed localization algorithms have been proposed, fundamental theoretic analysis of unique localization is still in its early stage of development. This paper aims at a synthetic and homogeneous survey of the theoretical basis on WSN localization problem carried out thus far. Specifically, subsequent to establishing a technological context of relevant terms, we construct a graph and then a formation for each WSN to present current state-of-the-art by analyzing possible conditions for unique localization, as well as corresponding verification algorithms, by drawing on the powerful results from rigidity theory, distance geometry, geometric constraints in CAD, and combinatorial theory. We show that the unique localization problem is well understood in two-dimension, however, only partial analogous results are available in three-dimension.