Problems in Estimation: Target tracking in missile defense and the limiting
case of the discrete time Kalman filter
Scott Michael Shald
Doctor of Philosophy in Mathematics (Industrial and Applied emphasis), March
1999
Temporary Control Number: ASG4613
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)
