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 without line-of-sight to enough 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 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 unshadowed area, as seen from 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 a closed-form (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, μ. Sundar Aditya and Andreas F. Molisch are with WiDeS, Ming Hsieh Dept. of Electrical Engineering, USC, Los Angeles, CA 90089, USA (Email:{sundarad,molisch}@usc.edu). Harpreet S. Dhillon is with Wireless@VT, Bradley Dept. of Electrical and Computer Engineering, Virginia Tech, Blacksburg, VA 24061, USA (Email: [email protected]). Hatim Behairy is with King Abdulaziz City for Science and Technology, P. O. Box 6086, Riyadh 11442, Saudi Arabia (Email: [email protected]) Revised: January 29, 2018. This work was supported by KACST under grant number 33-878. This paper was presented in part at the International Conference on Ubiquitous Wireless Broadband (ICUWB), 2016 held at Nanjing, China [1]. ar X iv :1 80 1. 08 56 0v 1 [ cs .N I] 2 5 Ja n 20 18