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）时常见的一个问题。现有方法通常采用离散优化方法，这些方法计算成本高昂且难以扩展至大规模问题。我们通过将相关环境中的传感器布局问题简化为一个可使用稀疏高斯过程（SGP）高效求解的回归问题来解决该问题。我们的方法既能处理离散传感器布局问题（即传感器只能放置在给定位置集合的某个子集中），也能处理连续传感器布局问题（即传感器可放置在有限连续区域内的任意位置）。我们进一步推广该方法，使其适用于具有非点视场角及集成观测的传感器。在三个真实世界数据集上的实验结果表明，与先前最先进的方法相比，我们的方法生成的传感器布局在重建质量上始终持平或更优，同时计算速度显著更快。这种计算高效的方法使得大规模传感器布局以及用于信息路径规划算法的快速机器人传感器布局成为可能。