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

Abstract

New PN guidance laws are developed to reduce sensitivity on heading errors at the initial homing phase. The key enabler to propose such guidance laws 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 new Proportional Navigation (PN) homing guidance law in two dimensional space is derived by applying the optimal control theory to the linear quadratic optimal problem with the new performance index. Unlike the conventional 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. Then, two extensions of the new PN homing guidance law to three-dimensional space are also proposed. The performance of the new guidance laws is analytically investigated. The main focus of the theoretical performance analysis is to provide lower bounds of the navigation gains in order to enable determination of appropriate design parameters in the new PN guidance laws.