A new homing guidance law to reduce sensitivity on initial heading errors

Abstract

In this paper, a new guidance law is developed to reduce sensitivity on heading errors at the initial homing phase. The key enabler to propose such a guidance law was to design a new performance index by introducing distribution functions to the input weighting. The distribution functions in the new performance index are expressed in terms of a second-order polynomial of time-to-go and inverse weighted time-to-go. This allows distribution of the relative input weighting over the entire homing phase. Then, a homing guidance law is derived by applying the optimal control theory to the linear quadratic optimal problem with the new performance index. Unlike the conventional proportional navigation (PN) guidance law with a constant navigation gain, the proposed guidance law has a time-varying gain to ease the heading error sensitivity at the initial homing phase. The characteristics of the proposed guidance algorithm are analytically investigated and its performance is demonstrated through numerical simulations.