AI 中文总结
针对水下防御穿越问题，提出联合传感器布局与检测阈值分配方法，利用凹最大最小分配和透视重构优化，在深水案例中提升目标14.9%并提供连续场屏障强度下界证书。
AI 中文摘要
我们研究了联合传感器布局与探测器工作点分配问题，以防御对抗性穿越来守卫某一区域。每个传感器可调整其检测阈值，而所有传感器共享一个网络级的虚警预算。对于平方律探测器的高斯信号超量模型，我们给出了传感器虚警概率下负对数漏报风险为凹函数的充要条件。在固定部署下，这产生了一个凹的最大最小分配，其鞍点在最坏情况占据测度下使每单位报警的边际屏障增益相等。一个透视重构为混合整数联合问题提供了线性割，而一个独立的证书则在不依赖于路径搜索所用图的情况下，对连续屏障强度给出下界。在基于典型Munk剖面的深水案例研究中，重新分配固定报警预算在传感器数量和报警负载不变的情况下将图设计目标提高了14.9%，并且该证书在插值连续场上确立了屏障需求，而仅凭图值无法做到这一点。
英文摘要
We study joint sensor placement and detector operating-point allocation for guarding a region against an adversarial crossing. Each sensor may adjust its detection threshold, while all sensors draw on a shared network-level false-alarm budget. For a Gaussian signal-excess model of a square-law detector, we give a necessary and sufficient condition for the negative-log miss hazard to be concave in a sensor's false-alarm probability. At fixed deployment, this yields a concave max-min allocation whose saddle point equalizes marginal barrier gain per unit alarm against a worst-case occupation measure. A perspective reformulation supplies linear cuts for the mixed-integer joint problem, and a separate certificate lower-bounds the continuum barrier strength independently of the graph used for path search. On a deep-water case study based on the canonical Munk profile, reallocating a fixed alarm budget raises the graph design objective by 14.9% at unchanged sensor count and alarm load, and the certificate establishes the barrier requirement on the interpolated continuum field, which the graph value alone cannot.
