Equilibrium radar-target interactions in an ATR scenario: A differential game

In this work, we pose a two-player differential game in which a mobile Radar attempts to gather sufficient information to identify a mobile Target in minimum time. Simultaneously, the Target attempts to maneuver in such a way to maximize the identification time. We introduce a general sensing model inspired by the ATR literature to capture the benefits of both angular and temporal sensing diversity, while providing a suitable framework from which to optimize the trajectories in a game-theoretic sense. This model captures two key features of an engagement: geometric dependence and the value of multiple measurements. We develop the regular optimality conditions for the game and examine two singular surfaces that are a result of symmetry of the cost function and nonlinearities of the dynamics. Using the regular and optimality conditions and singular characteristics, we construct the equilibrium control strategies for both the Radar and Target as well as the resulting equilibrium trajectories.