ANALYTICAL SOLUTION OF 3D TRUE PROPORTIONAL NAVIGATION

The commanded acceleration appling in the direction normal to the Line of sight (LOS) between the interceptor and its target is called true proportional navigation (TPN). The main goal of this work is to derive the complete analytical solutions of three-dimensional (3D) TPN for n onmaneuvering and maneuvering targets. Three coupled nonlinear second- order state equations describing the relative motion are solved analyt ically without any linearization for performance and trajectory analys is. Properties of 3D TPN such as capture region, range-to-go, time-to- go, and two aspect angles within spherical coordinates are all obtaine d in closed form. Furthermore, the comparison between 3D TPN and 3D re alistic true proportional navigation (RTPN) is investigated analytical ly in the two-player game where a TPN-guided missile is commanded to p ursue a RTPN-guided target, and vice versa.