Ballistic missile trajectory prediction using a state transition matrix

A method for the determination of the trajectory of a ballistic missile over a rotating, spherical Earth given only the launch position and impact point has been developed. The iterative solution presented uses a state transition matrix to correct the initial conditions of the ballistic missile state vector based upon deviations from a desired set of final conditions. A six-degree-of-freedom simulation of a ballistic missile is developed to calculate the resulting trajectory. Given the initial state vector of the ballistic missile, the trajectory is simulated and the state transition matrix propagated along the trajectory to the impact point. The error in the final state vector is calculated and elements of the initial state vector are corrected using the state transition matrix. The process is repeated until the ballistic missile impacts the target location within a predefined miss distance tolerance. The result of this research is an analysis tool which accurately solves for the initial state vector of the ballistic missile.