Towards a new approach to model guidance laws

Proportional navigation laws have been widely used and studied. Nevertheless very few publications explain rigorously the origin of all these laws. For researchers who are starting to work on guidance laws, a feeling of confusion can result. For others, this lack of explanation can be, for example, the source of the difficulties to make the true proportional navigation become equivalent to the pure proportional navigation. The authors propose here a way to model guidance laws in order to fill this lack of explanation. The first consequence is a better exploration of the kinematic behaviors arising during the guidance process. The second consequence is the definition of a new 3D guidance law which can be seen as a generalization of the true proportional navigation. Moreover, this generalization allow this last law to become equivalent to the pure proportional navigation in terms of initial conditions which allow the object to reach its target