Derivation of flip ambiguity probabilities to facilitate robust sensor network localization

Erroneous local geometric realizations in some parts of the network due to their sensitivity to certain distance measurement errors is a major problem in wireless sensor network localization. This may in turn affect the localization of either the entire network or a large portion of it. This phenomenon is well-described using the notion of "flip ambiguity" in rigid graph theory. In this paper we analytically derive an expression for the flip ambiguity probabilities of arbitrary neighborhoods in two dimensional sensor networks. This probability can be used to mitigate flip ambiguities in two ways: 1) If an unknown sensor finds the probability of flip ambiguity on its location estimate larger than a predefined threshold, it may choose not to localize itself 2) Every known neighbor can be assigned with a confidence factor to its estimated location, reflecting the probability of flip ambiguity; a sensor with an initially unknown location can then choose only those known neighbors with a confidence factor greater than a predefined threshold. A recent study by co-authors have shown that the performance of sequential and cluster based localization schemes in the literature can be significantly improved by correctly identifying and removing neighborhoods with possible flip ambiguities from the localization process. One motivation of this paper is to enhance the performance of the robustness criterion presented in that study by accurately identifying the flip ambiguity probabilities of arbitrary neighborhoods. The various simulations done in this study show that our analytical calculations of the probability of flip ambiguity matches with the simulated detection of the probability very accurately.