The sensor placement problem is a common problem that arises when monitoring correlated phenomena, such as temperature and precipitation. Existing approaches to this problem typically use discrete optimization methods, which are computationally expensive and cannot scale to large problems. We address the sensor placement problem in correlated environments by reducing it to a regression problem that can be efficiently solved using sparse Gaussian processes (SGPs). Our approach can handle both discrete sensor placement problems-where sensors are limited to a subset of a given set of locations-and continuous sensor placement problems-where sensors can be placed anywhere in a bounded continuous region. We further generalize our approach to handle sensors with a non-point field of view and integrated observations. Our experimental results on three real-world datasets show that our approach generates sensor placements that result in reconstruction quality that is consistently on par or better than the prior state-of-the-art approach while being significantly faster. Our computationally efficient approach enables both large-scale sensor placement and fast robotic sensor placement for informative path planning algorithms.

翻译：传感器布局问题是在监测相关现象（如温度和降水）时常见的经典问题。现有方法通常采用离散优化技术，但这类方法计算成本高昂且难以扩展至大规模问题。本文通过将传感器布局问题转化为可基于稀疏高斯过程高效求解的回归问题，从而解决相关环境中的布局难题。我们的方法同时适用于两类场景：离散型布局（传感器只能部署于指定位置子集）与连续型布局（传感器可放置在有限连续区域内的任意位置）。此外，我们进一步泛化该方法，支持非点视场传感器及集成观测数据的处理。在三个真实世界数据集上的实验结果表明：本方法生成的布局方案在重构质量上始终与现有最优方法持平或更优，同时显著提升计算效率。这种高效的计算能力使其既能支撑大规模传感器布局，也能为机器人自主布局中的信息路径规划算法提供快速决策支持。