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

We present a novel approach based on sparse Gaussian processes (SGPs) to address the sensor placement problem for monitoring spatially (or spatiotemporally) correlated phenomena such as temperature and precipitation. Existing Gaussian process (GP) based sensor placement approaches use GPs with known kernel function parameters to model a phenomenon and subsequently optimize the sensor locations in a discretized representation of the environment. In our approach, we fit an SGP with known kernel function parameters to randomly sampled unlabeled locations in the environment and show that the learned inducing points of the SGP inherently solve the sensor placement problem in continuous spaces. Using SGPs avoids discretizing the environment and reduces the computation cost from cubic to linear complexity. When restricted to a candidate set of sensor placement locations, we can use greedy sequential selection algorithms on the SGP's optimization bound to find good solutions. We also present an approach to efficiently map our continuous space solutions to discrete solution spaces using the assignment problem, which gives us discrete sensor placements optimized in unison. Moreover, we generalize our approach to model sensors with non-point field-of-view and integrated observations by leveraging the inherent properties of GPs and SGPs. Our experimental results on three real-world datasets show that our approaches generate solution 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 approaches will enable both large-scale sensor placement, and fast sensor placement for informative path planning problems.