Optimizing Fault-Tolerant Quality-Guaranteed Sensor Deployments for UAV Localization in Critical Areas via Computational Geometry

The increasing spreading of small commercial unmanned aerial vehicles (UAVs, also known as drones) presents serious threats for critical areas, such as airports, power plants, and governmental and military facilities. In fact, such UAVs can easily disturb or jam radio communications, collide with other flying objects, perform espionage activity, and carry offensive payloads, e.g., weapons or explosives. A central problem when designing surveillance solutions for the localization of unauthorized UAVs in critical areas is to decide how many triangulating sensors to use, and where to deploy them to optimize both coverage and cost effectiveness. In this article, we compute deployments of triangulating sensors for UAV localization, optimizing a given blend of metrics, namely: coverage under multiple sensing quality levels, cost-effectiveness, and fault-tolerance. We focus on large, complex three-dimensional (3-D) regions, which exhibit obstacles (e.g., buildings), varying terrain elevation, different coverage priorities, and constraints on possible sensors placement. Our novel approach relies on computational geometry and statistical model checking and enables the effective use of off-the-shelf AI-based black-box optimizers. Moreover, our method allows us to compute a closed-form, analytical representation of the region uncovered by a sensor deployment, which provides the means for rigorous, formal certification of the quality of the latter. We show the practical feasibility of our approach by computing optimal sensor deployments for UAV localization in two large, complex 3-D critical regions, the Rome Leonardo Da Vinci International Airport (FCO) and the Vienna International Center (VIC), using NOMAD as our state-of-the-art underlying optimization engine. Results show that we can compute optimal sensor deployments within a few hours on a standard workstation and within minutes on a small parallel infrastructure.