State propagation for targets moving in ground terrain

This paper addresses the problem of propagating the state for a target moving in terrain, as a part of a tracking problem. The propagation is based on the assumption that the target has a goal, unknown to the observer, and that it chooses the fastest or otherwise least costly path to the goal. This is handled as a variational calculus problem, and the corresponding Euler-Lagrange equations thus lead to the state propagation equations. It turns out that the motion is very similar to that of light in media with varying index of refraction. The applicability of the method is discussed with particle filtering in mind.