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.

翻译：我们提出一种基于稀疏高斯过程（SGPs）的新方法，用于监测温度、降水等空间（或时空）相关现象的传感器布局问题。现有基于高斯过程（GP）的传感器布局方法需已知核函数参数的GP对现象建模，并在环境的离散化表征中优化传感器位置。我们的方法将已知核函数参数的SGP拟合到环境中随机采样的未标记位置，并证明SGP学习到的诱导点内在解决了连续空间中的传感器布局问题。使用SGP可避免环境离散化，并将计算复杂度从立方级降至线性级。当传感器布局位置限定于候选集时，可在SGP优化边界上应用贪心顺序选择算法获得优质解。我们还提出通过指派问题将连续空间解高效映射到离散解空间的方法，从而获得协同优化的离散传感器布局。此外，我们利用GP和SGP的固有属性，将方法推广至具有非点视场和非点积分观测的传感器建模。在三组真实数据集上的实验表明，我们的方法生成的布局解在重建质量上持续达到或优于现有最优方法，同时显著提升计算速度。这种高效计算方法将支持大规模传感器布局，以及信息路径规划问题中的快速传感器部署。