Three-Dimensional Bearing-Only Helical Homing Guidance

This paper presents a three-dimensional (3D) homing guidance law against a stationary target by using only bearing or angle measurement. The unobservable conditions of the 3D 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 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.