Ideal proportional navigation for exoatmospheric interception

Ideal proportional navigation (IPN) is a natural choice for exoatmospheric interception for its mighty capture capability and ease of implementation. The closed-form solution of two-dimensional ideal proportional navigation was conducted in previous public literature, whereas the practical interception happens in the three-dimensional space. A novel set of relative dynamic equations is adopted in this paper, which is with the advantage of decoupling relative motion in the instantaneous rotation plane of the line of sight from the rotation of this plane. The dimension-reduced IPN is constructed in this instantaneous plane, which functions as a three-dimensional guidance law. The trajectory features of dimension-reduced IPN are explored, and the capture regions of dimension-reduced IPN with limited acceleration against nonmaneuvering and maneuvering targets are analyzed by using phase plane method. It is proved that the capture capability of IPN is much stronger than true proportional navigation (TPN), no matter the target maneuvers or not. Finally, simulation results indicate that IPN is more effective than TPN in exoatmospheric interception scenarios.