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 be blocked by obstacles in the environment. A target that is invisible (i.e., without line-of-sight) to a sufficient number of anchors 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 characterize exactly, 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 determine the anchor deployment intensity needed for the blind spot probability of a typical target to be at most a threshold, $\mu$.