A derivation of pure proportional navigation

There are two basic proportional navigation guidance laws in missile guidance: true proportional navigation (TPN), and pure proportional navigation (PPN). The missile command acceleration in TPN is defined to be perpendicular to the line-of-sight (LOS), and is proportional to the LOS rate and the closing velocity. While in PPN, the missile command acceleration is perpendicular to the missile speed vector, and is proportional to the LOS rate and the missile velocity. This paper presents a derivation of PPN, which is performed via Q-parametrization of stabilizing controllers to optimize the robust stability of the parameter-frozen system. The derivation provides an insight into PPN