Noisy localization over unit disk graphs: The shadow edge approach

Trilateration is an effective way to localize a sensor network based on relative distance measures, but the conditions that guarantee the existence of a solution are quite restrictive. If the network topology is a unit disk graph, however, the localization of the network can be achieved also when the standard trilateration fails, using a priori information about 'not being connected'. Such an information can be modeled as additional links, namely shadow edges, that can be used to localize also networks that are not localizable via trilateration. In this paper we inspect the applicability of shadow edge localization in the noisy setting, showing some conditions that guarantee the existence of solution and comparing the results of trilateration and shadow edge localization algorithms in a noisy setting, with respect to the error after a post processing done by means of a recursive least square algorithm. The results show that, besides localizing more nodes, the shadow edge approach has better results in terms of localization error.