Solution of Three-Dimensional Line-of-Sight Guidance with a Moving Tracker

The closed-form solution of a three-dimensional line-of-sight guidance with a moving tracker is derived for an ideal case, in which a pursuer is always on the instantaneous line between the target tracker and the target. The solution can be applied to both surface-to-air and air-to-surface applications. Some significant characteristics, such as intercept time, cumulative velocity increment, initial condition for interception, and the effect of acceleration limit, are also obtained and discussed. In addition, the equivalent effective navigation ratio for the line-of-sight guidance is introduced. Finally, solutions for a special case of maneuvering target are presented.