隐蔽性的代价：对抗性感知下不确定流中的双控导航
The Price of Covertness: Dual-Control Navigation in Uncertain Flows under Adversarial Sensing
- University of California, Santa Barbara（加州大学圣塔芭芭拉分校）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究不确定流中车辆的隐蔽导航问题，通过将估计误差方差与路径规划耦合，建立HJB方程刻画泄漏率，并构建零和感知分配博弈，证明随机化极端分配的均衡性，揭示信息获取时序对泄漏的影响。
AI中文摘要：
在不确定流中的隐蔽导航将运动规划与信息获取耦合在一起。车辆必须估计局部流以进行导航，而估计误差会引发修正机动，从而增加统计可区分性（即泄漏），进而增加车辆的可探测性。我们通过将位置与估计误差方差（其演化取决于通过局部信息率的路径）相结合来建模这种耦合。小误差展开表明，估计不确定性对预期可探测率贡献了一个一阶修正项。由此产生的路径规划问题以一阶Hamilton-Jacobi-Bellman（HJB）方程为特征。截止时间索引值确定了隐蔽时间前沿，而关于感知质量的精确灵敏度公式表明，沿路径较早获取的信息可以减少较晚发生的泄漏，而较晚获取的信息则无法减少已经发生的泄漏。然后，我们构建了一个零和感知分配博弈，证明了泄漏率在感知分配上是凸的，并证明了防御者可以将注意力限制在极端单点分配的随机化上。由此产生的均衡通过列生成计算，车辆的最佳响应由HJB方程获得。数值实验展示了学习绕行、截止时间-泄漏权衡、空间排序效应以及随机感知分配的益处。
英文摘要：
Covert navigation in an uncertain flow couples motion planning with information acquisition. A vehicle must estimate the local flow to navigate, while estimation error induces corrective maneuvers that increase statistical distinguishability, or leakage, and hence the vehicle's detectability. We model this coupling by augmenting position with the estimation-error variance, whose evolution depends on the route through the local information rate. A small-error expansion shows that estimation uncertainty contributes a leading-order correction to the expected detectability rate. The resulting route-planning problem is characterized by a first-order Hamilton--Jacobi--Bellman (HJB) equation. The deadline-indexed value determines the covert-time frontier, while an exact sensitivity formula with respect to sensing quality shows that information acquired earlier along the route can reduce leakage incurred later, whereas information acquired later cannot reduce leakage already incurred. We then formulate a zero-sum sensing-allocation game, show that the leakage rate is convex in the sensing allocation, and prove that the defender may restrict attention to randomization over extreme single-site allocations. The resulting equilibrium is computed by column generation, with vehicle best responses obtained from the HJB equation. Numerical experiments illustrate the learning detour, the deadline--leakage tradeoff, the spatial-ordering effect, and the benefit of randomized sensing allocations.
