Tracking of goal seeking vehicles

In many competitive situations it is necessary to track an enemy vehicle on the basis of noisy measurements received at a tracking station. In such situations it is often not appropriate to model the enemy vehicle as a dynamic system subject to white noise inputs since the enemy may be moving toward some specific objective which is unknown or partially unknown to the tracker. The tracker should be able to incorporate this fact in computing his optimal estimate of the vehicle's position. A simple model of these competitive situations is proposed in which the enemy is assumed to be governed by a system of linear differential equations controlled so as to move optimally toward a goal unknown to the tracker. The optimal estimation equations for the tracker are derived, and it is shown that the tracker can use a linear dynamic system to form the best estimate of the enemy position and his goal.