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. Existing Gaussian process (GP) based sensor placement approaches use GPs to model the phenomena and subsequently optimize the sensor locations in a discretized representation of the environment. In our approach, we fit an SGP 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 non-point sensors with an arbitrary field-of-view (FoV) shape using an efficient transformation technique. Finally, we leverage theoretical results from the SGP literature to bound the number of required sensors and the quality of the solution placements. Our experimental results on two real-world datasets show that our approaches generate solutions consistently on par with the prior state-of-the-art approach while being substantially faster. We also demonstrate our solution placements for non-point FoV sensors and a spatiotemporally correlated phenomenon on a scale that was previously infeasible.

翻译：我们提出一种基于稀疏高斯过程（SGP）的新方法，用于解决空间（或时空）相关现象（如温度）监测中的传感器布局问题。现有基于高斯过程（GP）的传感器布局方法利用GP对现象建模，随后在环境离散化表示中优化传感器位置。我们的方法将SGP拟合至环境中随机采样的未标记位置，并证明SGP学习到的诱导点天然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，并将计算复杂度从三次降至线性。当限定候选传感器布局位置集时，我们可利用SGP优化边界上的贪婪顺序选择算法寻找优质解。此外，我们提出一种通过指派问题将连续空间解高效映射至离散解空间的方法，从而获得协同优化的离散传感器布局。进一步，我们利用高效变换技术，将方法推广至具备任意视场形状的非点状传感器建模。最后，我们借助SGP文献的理论成果，界定了所需传感器数量及布局解质量的边界。在两组真实数据集上的实验表明，我们的方法在保持与现有最优方法一致性解的同时，计算速度显著提升。我们还展示了针对非点状视场传感器及大规模时空相关现象的布局解，此类场景此前难以实现。