Analytical investigation of intersection based range-free localization

By range-free localization, the positions of a mobile device can be limited to the coverage area of a radio access network cell. The drawback of such approach is the coarseness of the corresponding information. This can be refined by computing the intersection area of all cells that can provide access for the device at its current position. The computation of the intersection area can be a complex task. Thus, one would like to have an estimate about the possible gain that can be achieved. In this paper, we present an analytical and numerical investigation of the problem. Several approaches are presented for the computation of the information gain, based on stochastic geometry and on a Monte-Carlo method. We show that simple scaling arguments can be used in order to estimate the order of magnitude of the average information gain, while more complex approximations based on Voronoi cells lead to relatively good results.