This paper addresses the challenges of optimally placing a finite number of sensors to detect Poisson-distributed targets in a bounded domain. We seek to rigorously account for uncertainty in the target arrival model throughout the problem. Sensor locations are selected to maximize the probability that no targets are missed. While this objective function is well-suited to applications where failure to detect targets is highly undesirable, it does not lead to a computationally efficient optimization problem. We propose an approximation of the objective function that is non-negative, submodular, and monotone and for which greedy selection of sensor locations works well. We also characterize the gap between the desired objective function and our approximation. For numerical illustrations, we consider the case of the detection of ship traffic using sensors mounted on the seafloor.

翻译：本文研究了在有界区域内，为检测服从泊松分布的目标而最优部署有限数量传感器所面临的挑战。我们力求在整个问题中严格考虑目标到达模型中的不确定性。传感器位置的选择旨在最大化未遗漏目标的概率。尽管这一目标函数非常适用于遗漏目标的检测极不可取的应用场景，但它并未形成计算效率高的优化问题。我们提出了一个非负、子模且单调的目标函数近似形式，在此近似下，贪婪的传感器位置选择策略表现出良好性能。同时，我们刻画了期望目标函数与所提近似之间的差距。在数值示例中，我们考虑了利用海底安装的传感器检测船舶交通的情况。