Performance analysis of a three-dimensional geometric guidance law using Lyapunov-like approach

A three-dimensional (3D) geometric guidance law (GGL) was recently proposed based on the differential geometric curve theory, whose performance was thought to be better than that of 3D pure proportional navigation (PPN). In this paper, with the help of the dimension-reduction method and the Lyapunov-like approach, the performance of 3D GGL against a randomly maneuvering target with limited maneuverability is studied. The analysis in this paper proves that, for a certain initial heading error, if the navigation gain is large enough, a missile guided by 3D GGL can guarantee an intercept of the maneuvering target and keep the heading error in a certain range, as long as the missile has a speed advantage over the target. Moreover, if the navigation gain is sufficiently large, the LOS rate and commanded acceleration can also be limited in certain ranges. Finally, the performance of 3D GGL is demonstrated by numerical simulation results.