发表机构
Georgia Southern University; Virginia Tech; Johns Hopkins University Applied Physics Laboratory（佐治亚南方大学; 弗吉尼亚理工大学; 约翰斯·霍普金斯大学应用物理实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出 Gamma-Laplace 代理函数，在分布层面近似空隙概率目标，实现方差感知的传感器布置，并通过单调子模性质支持高效贪心优化，在中等不确定性下提升选点稳健性。
AI 中文摘要
针对随机到达目标的传感器布置问题，本文采用空隙概率目标函数进行研究，该函数定义为在有限时间范围内没有目标保持未被检测到的概率。直接优化是不可行的，因为它需要对随机强度场进行期望计算。基于 Jensen 不等式的常见代理函数将随机场替换为其均值，从而得到可处理的目标函数，但丢弃了分布信息。所提出的 Gamma-Laplace 代理函数用矩匹配的 Gamma 分布近似单元暴露变量，并利用其闭式 Laplace 变换评估目标函数。与标量矩校正或局部展开不同，该方法在分布层面运作，并在独立 Gamma 近似下保留 Laplace 变换结构。对数变换和常数平移产生一个被证明是单调子模的目标函数，从而能够进行具有性能保证的高效贪心优化。在真实船舶交通数据上的数值实验表明，在低不确定性区域中，该方法与 Jensen 代理函数结果一致。在中等不确定性下，该方法改善了候选位置排名，从而带来更稳健的传感器选择，并降低了对目标到达变异性敏感度。
英文摘要
Sensor placement for stochastically arriving targets is studied using a void probability objective, defined as the probability that no target remains undetected over a finite horizon. Direct optimization is intractable because it requires an expectation over a random intensity field. A common surrogate based on Jensen's inequality replaces the random field with its mean, yielding a tractable objective but discarding distributional information. The proposed Gamma Laplace surrogate approximates cellwise exposure variables with moment matched Gamma distributions and evaluates the objective using their closed form Laplace transforms. Unlike scalar moment corrections or local expansions, this approach operates at the distribution level and retains a Laplace transform structure under an independent Gamma approximation. A log transformation and constant shift yield an objective shown to be monotone submodular, enabling efficient greedy optimization with performance guarantees. Numerical experiments on real ship traffic data show consistency with the Jensen surrogate in low uncertainty regimes. Under moderate uncertainty, the method improves candidate location rankings, leading to more robust sensor selections and reduced sensitivity to variability in target arrivals.
Comments(This paper is accepted by conference on decision and control/CDC 2026)
