This paper investigates a partial-information pursuit evasion game in which the Pursuer has a limited-range sensor to detect the Evader. Given a fixed final time, we derive the optimal evasion strategy for the Evader to maximize its distance from the pursuer at the end. Our analysis reveals that in certain parametric regimes, the optimal Evasion strategy involves a 'risky' maneuver, where the Evader's trajectory comes extremely close to the pursuer's sensing boundary before moving behind the Pursuer. Additionally, we explore a special case in which the Pursuer can choose the final time. In this scenario, we determine a (Nash) equilibrium pair for both the final time and the evasion strategy.

翻译：本文研究了一类部分信息追逃博弈问题，其中追踪者配备有限范围传感器以探测逃逸者。在给定最终时间条件下，我们推导了逃逸者最大化最终时刻与追踪者距离的最优规避策略。分析表明，在某些参数范围内，最优规避策略包含一种"冒险"机动——逃逸者轨迹会极度逼近追踪者感知边界，而后绕至追踪者后方。此外，我们探讨了追踪者可自主选择最终时间的特殊情形。在此场景中，我们确定了最终时间与规避策略构成的（纳什）均衡对。