Three plane approach for 3D true proportional navigation

A new three-dimensional (3D) guidance approach is proposed in this paper. It's called Three Plane Approach (TPA). The main goal of this work is to derive an effective and practical guidance solution for 3D missile-target engagement geometry. We propose our new law based on the True Proportional Navigation (TPN), but it diverges when computing accelerations special to TPN, and putting 3D acceleration commands into practice in Cartesian coordinates. Proposed algorithm works by separating 3D space with axes x, y and z to three perpendicular plane, xy, yz and xz respectively; after solving the pursuit-evasion problem analytically in these planes and computing the required accelerations, rejoining the solutions to three dimensional environment with respect to the geometric relationships. The performance of TPA has been tested both visually and analytically via developed simulation environment. The end-game scenario begins at the terminal guidance phase of the encounter. The missile guided with TPA and the target aircraft employing different evasion maneuvers are assumed to have initial velocities and some kilometers from each other. Trajectory and performance analysis are performed in our simulation software, VEGAS (Visual End-Game Simulation). In VEGAS, there are five objects: pursuer, evader, radar, aero, and main modules. In pursuer module, one degree-of-freedom modeling is taken into consideration and aerodynamic forces and constraints such as, thrust, drag, weight and maximum acceleration limits are included into missile equations of motion. The simulation environment has visual elements to see the end-game scenario from the observer point of view. It is verified that the performance of proposed approach is robust and effective in terms of the miss distance and interception time for high-g capacity aerial targets employing evasive maneuvers. The adaptive approach proposed here can be applied to other Proportional Navigation types.