无人水下航行器对抗导航目标的策略推理
Strategic Inference of Adversarial Navigation Objectives for Unmanned Underwater Vehicles
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中文总结 AI 辅助
研究无人水下航行器对抗导航目标推理，推导连续时间似然模型及相关估计器，分析费希尔信息敏感性，建立流场几何与目标可识别性联系，扩展框架到依赖扫描观测模型并进行数值实验验证。
中文摘要 AI 辅助
我们研究了在空间变化流场中对抗性无人水下航行的目标推理问题。红色航行器被建模为大致沿着一条哈密顿 - 雅可比（HJ）时间最优路径驶向未知目的地，而蓝色航行器观测到该轨迹的有噪声实现。我们为该问题推导了连续时间似然模型，并得到了闭式局部最大似然估计器、常记忆多周期估计器以及渐近克拉美 - 罗效率结果。费希尔信息由一个具有两个加性分量（策略均值敏感性和参考路径敏感性）以及一个乘性漂移敏感性的组合得分核控制，其主要几何贡献是当前海森矩阵与HJ特征流的雅可比场的收缩。所有这三种敏感性都由该雅可比场诱导，在流场几何与目标可识别性之间建立了可计算的联系。我们进一步将框架扩展到依赖扫描的观测模型，并为蓝色团队制定了主动扫描设计问题。在涡旋和通道剪切流中的数值实验验证了克拉美 - 罗预测，并说明了流场几何如何决定哪些目的地可以可靠推断。
英文摘要
We study destination inference for adversarial unmanned underwater navigation in a spatially varying current field. The red vehicle is modeled as approximately following a Hamilton-Jacobi (HJ) time-optimal path toward an unknown destination, while a blue vehicle observes a noisy realization of that trajectory. We derive a continuous-time likelihood model for this problem and obtain a closed-form local maximum likelihood estimator, a constant-memory multi-period estimator, and an asymptotic Cramér-Rao efficiency result. The Fisher information is governed by a combined score kernel with two additive components, a policy-mean sensitivity and a reference-path sensitivity, and a multiplicative drift sensitivity whose leading geometric contribution is a contraction of the current Hessian with the Jacobi field of the HJ characteristic flow. All three sensitivities are induced by that Jacobi field, yielding a computable link between current-field geometry and destination identifiability. We further extend the framework to a sweep-dependent observation model and formulate an active sweep-design problem for the blue team. Numerical experiments in vortex and channel-shear currents validate the Cramér-Rao prediction and illustrate how current geometry determines which destinations can be reliably inferred.
