Asymptotic Blind-spot Analysis of Localization Networks under Correlated Blocking using a Poisson Line Process

In a localization network, the line-of-sight between anchors (transceivers) and targets may be blocked due to the presence of obstacles in the environment. Due to the non-zero size of the obstacles, the blocking is typically correlated across both anchor and target locations, with the extent of correlation increasing with obstacle size. If a target does not have line-of-sight to a minimum number of anchors, then its position cannot be estimated unambiguously and is, therefore, said to be in a blind-spot. However, the analysis of the blind-spot probability of a given target is challenging due to the inherent randomness in the obstacle locations and sizes. In this letter, we develop a new framework to analyze the worst-case impact of correlated blocking on the blind-spot probability of a typical target; in particular, we model the obstacles by a Poisson line process and the anchor locations by a Poisson point process. For this setup, we define the notion of the asymptotic blind-spot probability of the typical target and derive a closed-form expression for it as a function of the area distribution of a typical Poisson-Voronoi cell. As an upper bound for the more realistic case when obstacles have finite dimensions, the asymptotic blind-spot probability is useful as a design tool to ensure that the blind-spot probability of a typical target does not exceed a desired threshold, $\epsilon$.