Analysis of 3D geometric guidance problem

Development of an easy to implement guidance law using differential geometric (DG) guidance commands is presented. To study the DG guidance commands in realistic engagement, they are transformed from the arc length system to time domain. A new necessary initial condition is developed to capture the high-speed target and the DG guidance commands are well defined over the guidance envelope. The study finds that the DG guidance commands would be effective and well defined only after the proposed initial condition is satisfied at the beginning of the guidance envelope. To illustrate the performance of the proposed guidance scheme, a comparison between the different guidance laws with regard to performance and characteristic responses is also presented. The results show that both the practical DG (PDG) and DG guidance laws compensate for the target's maneuvering at the beginning of the engagement, like the VPN guidance law.