Placement and Concise MSE Lower-Bound for UAV-Enabled Localization via RSS

Abstract

We consider an unmanned-aerial-vehicle (UAV) enabled localization system with one typical ground user in a circular area under non-line-of-sight channels, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> UAVs are deployed as anchors to localize the user via received signal strength. Our objective is to minimize the average (localization) mean-square-error (MSE) in the area by optimizing the anchors’ placement. To this end, we first derive a concise lower-bound of MSE with fixed user position. Then, for the user uniformly distributing in the circular area, we prove that deploying the UAV anchors with symmetrical horizontal-angles and same distance to the area center can minimize or almost minimize the MSE lower-bound, whereas such distance needs to be determined, neither increasing nor decreasing it can always improve the average MSE. A problem to find such distance is formulated and furthermore converted to a form that can be solved by one-dimensional search, based on which, we propose to deploy the anchors where the minimum MSE lower-bound is achieved for minimizing MSE. The effectiveness of the proposed placement is verified by numerical studies.