Three-dimensional united biased proportional navigation law for interception of maneuvering targets with angular constraint

Studying a guidance law, which can intercepts not only high-speed targets, but also low-speed targets with impact angle constrains, is a challenging task. In this paper, a new guidance law called united biased proportional navigation (UBPN) is proposed. The guidance law uses time-varying bias and navigation ratio, and incorporates the advantages of head-on and head-pursuit engagement. UBPN with positive time-varying navigation ratio can intercept low-speed targets which is a head-on engagement, while with negative time-varying navigation ratio can intercept high-speed targets, which is a head-pursuit engagement. To begin with, planar UBPN guidance law is proposed and exact time-varying bias is derived. Moreover, the solution to the singularity in time-varying navigation ratio is given. Secondly, in order to realize the guidance law in three-dimensional space, we derive the relation between two-dimensional acceleration and three-dimensional acceleration, and also give the solution for calculating the impac...