Measurement-Based Modeling Methodology for Ballistic Missile Trajectory Simulation

Abstract

I N THE field of ballistic missiles, the problem of tracking the missile until the impact point is not only an important problem but also quite complex. The problem is made further complex by the approximations that are usually required to be introduced in the mathematical models, which are employed for predicting a reference trajectory for tracking. In addition, there are situations where an existing missile system needs to be redesigned/redeployed for a different mission scenario and thus needs tuning/modification of the trajectory simulation models. The present Note proposes a measurement-based model-updating strategy to create, as well as modify, the simulation models. In literature, there have been many studies [1–4] that have investigated the problem of creating a trajectory model using different philosophies and strategies. These include a conditional boost-phase trajectory-estimationmethod based on a ballistic missile information database and classification under an uncertain control environment, missile tracking using a priori information (e.g., launch position, launch time, burnout time, initial mass, and fuel burn rate), and posing of the trajectory estimation as a nonlinear parameter estimation problem. The previous studies have also shown that good trajectory estimates are possible with nonlinear filtering techniques [5–8]; for example, the unscented Kalman filter, the interactive multiple model filter, and the extended Kalman filter (EKF). Among these techniques, the EKF-based techniques are themostwidely used in nonlinear filtering algorithms for state estimation, including target tracking. However, none of the studies have addressed the issue of model building in the case when the missile data set is incomplete. Therefore, the aim of the present study is to evolve a trajectorymeasurement-based algorithm for arriving at a consistent and robust mathematical model for predicting the trajectories of a typical ballistic missile, for which some aspect of its description is either missing or known with poor accuracy. The proposed methodology makes use of a standard nonlinear dynamic model structure, along with the EKF algorithm, to establish a model evolution procedure. A typical ballistic missile configuration, along with outputs commonly measured during a realistic tracking scenario, is used to verify the feasibility of the proposed modeling strategy.