Effect of Collaboration on Localizability in Range-Based Localization Systems

In this paper, we examine, via analysis, the improvement in device localizability through collaboration. Depending on the sensitivity of the receivers in the devices, it is not unusual for an unlocalized device to lack a sufficient number of detectable positioning signals from localized devices to determine its location without ambiguity (i.e., to be uniquely localizable). This occurrence is well-known to be a limiting factor in localization performance, especially in communications systems. In cellular positioning, for example, cellular network designers call this the hearability problem. In this work, we employ tools from stochastic geometry to derive accurate approximations for the probabilities of unique localizability in the noncollaborative and collaborative cases. We consider range-based positioning scenarios with and without shadowing. The results are very promising and motivate further research into enhancing cellular positioning with small-scale collaboration (e.g., using D2D in LTE).