Trajectory-Shaping Guidance for Interception of Ballistic Missiles During the Boost Phase

F OR many years now, the U.S. Department of Defense has expended great effort to develop an integrated intercontinental ballistic missile (ICBM) defense system through a layered, defense in depth strategy. An ICBM’s speed and altitude leave little room for error by the defender, and any strategy must include systems capable of defeating a ballisticmissile (BM) at each of its three distinct phases (boost, midcourse, and terminal), which theMissile Defense Agency labels the engagement sequence groups (ESG) [1]. It is the portion of the effort directed toward the boost phase of the Ballistic Missile Defense Programs that is the focus of this Note. The boost-phase ESG is concerned with developing methods and technologies to conduct boost-phase intercept (BPI). Intercepting a missile in its boost phase is the ideal solution for a ballistic missile defense, because the missile is very vulnerable during this phase of its flight. The missile is relatively slow while struggling to overcome gravity, has a very visible exhaust plume, and cannot deploy countermeasures. Yet, the challenges that need to be overcome are immense: countering the large and changing acceleration rates, reliable scanning and tracking, and very short reaction time are among the most daunting. A variety of weapon systems are under development for conducting BPI, including airborne lasers, spacebased intercept missiles, and ground-based intercept missiles. None of these systems is totally operational, though several look promising [1–3]. A missile’s guidance law is one of the largest single factors affecting its ability to intercept a target. Yet,when discussingmission success in the BPI ESG, intercepting the target is only one factor; another major consideration is the ability to kill the target, using the available kinetic energy as effectively as possible. This suggests the need to control the geometry of the interception [4]. The discussion of the existing approaches aswell as the genericmodels of ICBMand interceptor used in this study can be found in [5]. One of the findings of that paper is the constraint on the intercept altitude. As is well known, an endoatmospheric missile has a hard time maneuvering at high altitudes due to the low density of the surrounding atmosphere. Thus, the maximum allowable intercept value of 50–60 km is considered as the upper limit. The BM thrust model assuming the sharp drops at 130 and 240 s to represent the staging events suggests that 50–60-km altitude will be achieved between 130 and 140 s [5]. This is one of the most significant limitations on the BPI problem, because any station activelymonitoring the launch areawill still need 45–60 s to detect, track, analyze, and engage the target [3]. In the current study, simulations assume a 60-s delay in the interceptor launch, leaving about only 70–80 s for intercept per se. This Note does not address the question of achieving operationability for various engagement scenarios, but rather offers an approach to rapidly compute intercept trajectories in case it is possible in principle. To this end, Sec. II develops and describes the essence of a new direct-method-based guidance law continuously calculated onboard the missile as a complete solution of a two-point boundary-value problem (TPBVP), and Sec. III presents some simulation results and discusses the feasibility of employing the proposed guidance law in the real-world conditions.