A pursuit-evasion differential game in relative polar coordinates with state estimation

The application and usefulness of solutions to pursuit-evasion differential games depend upon a player´s knowledge of the states of the system. In most practical cases, a player will not have exact knowledge of the states of the system, but will need to estimate them based on noisy measurements. To prevent implementation difficulties it is important that the game be played and the subsequent state estimates be obtained in the same coordinate system that the measurements are made in. Typical measurements are range, range rate; and bearing. These are made in a relative polar coordinate system. Therefore, a solution to the pursuit-evasion differential game needs to be developed in a relative polar coordinate system. This paper presents a closed-form solution to this game. The pursuit-evasion differential game is solved in relative polar coordinates using a feedback linearization technique. Measurement models and an extended Kalman filter are developed to obtain the state estimates. The solution is demonstrated by use of simulation results