Pursuing a maneuvering target which uses a random process for its control

Since a pursuer pursuing a maneuvering target does not know what maneuvers an evading target will make, the maneuvers (the target´s control law) appear as a random process to the pursuer. However, he has opinions about what the evader will do. From these, he can assign a prior probability distribution to the evader´s maneuvers. For a linear pursuit evasion problem in which the evader´s control law is modeled as a random process, in which the pursuer has partial noisy linear measurements of his own and the evader´s relative position, and a quadratic optimality criterion is used, past results of the authors imply that the optimal control is a linear function of the "predicted miss". Determining the predicted miss involves estimating the evader´s terminal position from past system measurements. Nonlinear filtering techniques are used to give expressions for computing the conditional expectation of the evader´s terminal position even in the presence of the random unknown maneuvers of the evader.