The increasing spreading of small commercial Unmanned Aerial Vehicles (UAVs, aka drones) presents serious threats for critical areas such as airports, power plants, 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 optimise 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, fault-tolerance. We focus on large, complex 3D regions, which exhibit obstacles (e.g., buildings), varying terrain elevation, different coverage priorities, 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 3D 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.

翻译：小型商用无人驾驶飞行器（UAV，又称无人机）的日益普及对机场、发电厂、政府和军事设施等关键区域构成严重威胁。事实上，此类无人机可能轻易干扰或阻塞无线电通信、与其他飞行物体碰撞、执行间谍活动，并携带攻击性载荷（例如武器或爆炸物）。在设计用于关键区域非法无人机定位的监控解决方案时，核心问题在于确定使用多少三角测量传感器，以及如何部署它们以优化覆盖范围和成本效益。本文针对无人机定位计算三角测量传感器的部署方案，优化一组特定指标组合，即：多感知质量级别下的覆盖范围、成本效益与容错能力。我们聚焦于大型复杂三维区域，这些区域存在障碍物（例如建筑物）、地形起伏变化、不同覆盖优先级以及传感器布设位置约束。我们提出的新方法依赖于计算几何与统计模型检验，并能够有效利用现成的基于人工智能的黑箱优化器。此外，该方法可计算传感器部署盲区的闭式解析表示，从而实现对部署质量进行严格的形式化认证。我们通过计算罗马莱昂纳多·达芬奇国际机场（FCO）和维也纳国际中心（VIC）这两个大型复杂三维关键区域的无人机定位最优传感器部署，验证了方法的实际可行性，其中使用NOMAD作为最先进的底层优化引擎。结果表明，我们能够在标准工作站上于数小时内、在小型并行基础设施上于数分钟内计算出最优传感器部署方案。