Analysis of proportional-navigation guidance law with delayed line-of-sight rate

This paper discusses the convergence analysis of proportional navigation (PN) guidance law in the presence of delayed line-of-sight (LOS) rate information. Delay in the LOS rate can be introduced by the missile guidance system that uses a low-cost sensor to obtain LOS rate information by image processing techniques. A Lyapunov-like function is used to analyze the convergence of the delay differential equation (DDE) governing the evolution of the LOS rate. Using a normalized linear engagement equation, general conditions on the delay for finite time convergence of the LOS rate are presented. As this method gives conservative bounds for convergence, numerical simulations are carried out to further analyze the effect of delay on the convergence and miss distance of the PN guidance law.