A Tractable Analysis of the Blind Spot Probability in Localization Networks Under Correlated Blocking

In localization applications, the line-of-sight between anchors and targets may he blocked by obstacles in the environment. If an insufficient number of anchors are visible (i.e., have line-of-sight) to a target, then the target cannot be unambiguously localized and is, therefore, said to be in a blind spot. In this paper, we analyze the blind spot probability of a typical target by using stochastic geometry to model the randomness in the obstacle and anchor locations. In doing so, we handle correlated anchor blocking induced by the obstacles, unlike previous works that assume independent anchor blocking. We first characterize the regime over which the independent blocking assumption underestimates the blind spot probability of the typical target, which in turn is characterized as a function of the distribution of the visible area surrounding the target location. Since this distribution is difficult to exactly characterize, we formulate the nearest two-obstacle approximation, which is equivalent to considering correlated blocking for only the nearest two obstacles from the target and assuming independent blocking for the remaining obstacles. Based on this, we derive an approximate expression for the blind spot probability, which helps to determine the anchor deployment intensity needed for the blind spot probability of a typical target to be bounded above by a threshold, mu.