Ballistic missile defense is a major concern of the nation's armed forces, and it is a difficult problem. The Army's Patriot system had particular difficulty with the Scud missile during the Persian Gulf War. One of the difficulties was that the Scud flew 'corkscrew' trajectories. Another difficulty in using a missile to destroy another missile is that any sensor carried on the intercepting missile must be light, small, and expendable. Such sensors give limited information.
In order for the intercepting missile to determine the other missile's trajectory from limited data, it must maneuver non-trivially. In this work we show that simple maneuvers do not allow the intercepting missile to track its target and we define a maneuver which does. Then we define an algorithm for estimating the parameters of the target missile's trajectory and we test the algorithm in computer simulations.
Also in this work we present results on filtering theory. We show that the Kalman filter for continuous time systems can be obtained as the limit of the Kalman filter of discrete time systems. This is commonly believed to be true and there is a heuristic argument; we make it rigorous. This result will be used in the future to examine stochastic models for noise in missile defense.
Research supported by the Minnesota Center for Industrial Mathematics (MCIM)