This article presents a 3-D homing guidance law against a stationary target by using only bearing or angle measurement. The unobservable conditions of the 3-D bearing-only relative kinematics are derived and the weak observability under classical proportional navigation guidance (PNG) is revealed. An analytical observability-enhancement guidance law considering the energy consumption and interception accuracy is then designed based on the optimal control theory in the interception plane. To further improve the system observability, we develop a helical guidance law by artificially enforcing a rotating acceleration command. We show that the guidance command derived aligns with the PNG law under certain conditions. Both numerical simulations and physical experiments are provided to illustrate the characteristics of the proposed algorithm.

中文翻译：

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三维仅轴承螺旋归位引导


本文提出了仅使用方位或角度测量来针对静止目标的 3-D 寻的制导法则。推导了3D纯方位相对运动学的不可观测条件，揭示了经典比例导航制导（PNG）下的弱可观测性。然后基于拦截平面内的最优控制理论，设计了考虑能量消耗和拦截精度的解析可观测性增强制导律。为了进一步提高系统的可观测性，我们通过人为强制执行旋转加速度命令来开发螺旋制导律。我们表明，在某些条件下，得出的指导命令符合巴布亚新几内亚法律。提供了数值模拟和物理实验来说明该算法的特点。