Iterative solution to three-dimensional differential geometric guidance problem

The application of three-dimensional (3D) differential geometric (DG) guidance commands is investigated. Also, the iterative solution to DG guidance law and the capture condition are studied. Classical differential geometry theory is utilized firstly to transform DG guidance commands from an arc-length system to the time domain. Secondly, the Newton iterative algorithm is introduced to derive an iterative solution in order to facilitate computation of angle of attack command and side slide angle command, which are designed to be output of 3D DG guidance system. Finally, the new necessary initial condition is developed to guarantee capture of high speed targets. Simulation results demonstrate that the DG guidance law is viable and effect in realistic missile defense scenario, and performs better than 3D proportional navigation guidance law. Also, the Newton iterative algorithm has sufficiently accuracy for missile guidance problems.