Reachable Sets for Tracking

In many aircraft-tracking systems the following problem is of importance in correlating radar returns with tracks: Given the aircraft position and velocity at time t − Δt and the limits on the ability of the aircraft to maneuver and/or change speed, what is the set of all possible aircraft positions at time t? We call this set the reachable set (or set of attainability) at time t. This paper uses the Pontryagin maximum principle to derive a set of equations for describing the reachable set.