Efficient Sensor Placement from Regression with Sparse Gaussian Processes in Continuous and Discrete Spaces

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.