The sensor placement problem is a common problem that arises when monitoring correlated phenomena, such as temperature, precipitation, and salinity. Existing approaches to this problem typically formulate it as the maximization of information metrics, such as mutual information~(MI), and use optimization methods such as greedy algorithms in discrete domains, and derivative-free optimization methods such as genetic algorithms in continuous domains. However, computing MI for sensor placement requires discretizing the environment, and its computation cost depends on the size of the discretized environment. This limitation restricts these approaches from scaling to large problems. We have uncovered a novel connection between the sensor placement problem and sparse Gaussian processes~(SGP). Our approach leverages SGPs and is gradient-based, which allows us to efficiently find solution placements in continuous environments. We generalize our method to also handle discrete environments. Our experimental results on four real-world datasets demonstrate that our approach generates sensor placements consistently on par with or better than the prior state-of-the-art approaches in terms of both MI and reconstruction quality, all 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：传感器布局问题是监测温度、降水、盐度等关联现象时常见的典型问题。现有方法通常将该问题表述为互信息等信息度量的最大化问题，并在离散域采用贪心算法等优化方法，在连续域采用遗传算法等无导数优化方法。然而，计算传感器布局所需的互信息需要对环境进行离散化，其计算成本取决于离散化环境的规模。这一局限使得这些方法难以扩展至大规模问题。我们发现传感器布局问题与稀疏高斯过程之间存在新颖的关联。本方法利用稀疏高斯过程并采用梯度制导，能够高效求解连续环境中的最优布局方案。我们还将该方法推广至离散环境。在四个真实世界数据集上的实验结果表明：无论从互信息还是重建质量角度评估，本方法生成的传感器布局均与现有最优方法持平或更优，同时计算速度显著提升。这种高效的计算方法不仅支持大规模传感器布局，还能为信息路径规划算法实现快速机器人传感器部署。