Capture Region of a GIPN Guidance Law for Missile and Target with Bounded Maneuverability

In this paper, a novel method is used to analyze the capture area of three-dimensional general ideal proportional navigation (GIPN) guidance laws. Using a line-of-sight (LOS) fixed natural coordinate and three modified polar variables (MPVs), the expression of relative dynamics between target and missile becomes simple, and no trigonometric functions are involved, which makes possible the analysis of the capture region when both target and missile are subject to bounded maneuverability. It can be shown that the determination of the desired capture area requires only the first two of the MPVs no matter if the maneuverability of missile and target are bounded or not. For the case of unbounded missile acceleration and known target acceleration, the capture region can be found analytically, while for the other cases, the capture region can be obtained graphically in a two-dimensional phase plane. The boundaries of these capture regions are characterized by the stable and unstable manifolds of related equilibrium points, which can only be determined numerically in general at this moment. The results of this work indicate that knowing the target acceleration and utilizing larger navigation coefficients increase the area of the capture region, which agrees with known results in literature.