3D guidance law modeling

Proportional navigation (PN) guidance laws (GLs) have been widely used and studied in the guidance literature. But most of the guidance literature on PN has concentrated on the evaluation of empirical PNGLs or GLs obtained from very specific optimality considerations. The authors present a novel approach (called guidance laws modeling) to derive new GLs. They consider the basic requirements of capture and define a complete class of GLs that meet these requirements. It is shown that PN is a natural candidate in this class. The main consequence of this modeling process is the definition of two new GLs: one in 2D space and the other in 3D space. These new GLs can be interpreted as new generalizations of the true proportional navigation (TPN) GL. Moreover, it is shown that these generalizations allow the TPNGL to match the capturability performance of the pure proportional navigation (PPN) GL in terms of initial conditions which allow the guided object to reach its target.