The Price of Covertness: Dual-Control Navigation in Uncertain Flows under Adversarial Sensing
Abstract
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.
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BibTeX
@misc{hu2026price,
title = {{The Price of Covertness: Dual-Control Navigation in Uncertain Flows under Adversarial Sensing}},
author = {Ruimeng Hu and Botao Jin and Xu Yang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24225},
eprint = {2609.24225},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24225},
}
RIS
TY - UNPB
TI - The Price of Covertness: Dual-Control Navigation in Uncertain Flows under Adversarial Sensing
AU - Ruimeng Hu
AU - Botao Jin
AU - Xu Yang
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24225
UR - https://arxiv.org/abs/2609.24225
AB - 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.
ER -