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

Abstract

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 headpursuit 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 threedimensional acceleration, and also give the solution for calculating the impact angle from two-dimensional surface into three-dimensional space. Finally, the simulation results of UBPN compared with proportional navigation, retroproportional navigation, and bias proportional navigation guidance law are shown. It is demonstrated that the miss distance and impact angle error can meet the guidance law requirements. Capture region of UBPN is given by simulation, which indicates that it is almost two times than that of the guidance law in the head-on engagement for interception of high-speed target.

Three-dimensional impact angle guidance with coupled engagement dynamics

“…In Zhang et al 22 and Lei et al, 24 decoupled dynamics are used to derive the guidance laws. In Ghosh et al 26 and Yan et al, 27 impact angle guidance laws are designed based on generic PN and united biased PN, respectively, and are applicable even for higher speed targets.…”

“…[21][22][23][24][25][26][27] In Yoon, 21 a 3D impact angle constrained guidance law, based on a geometric approach, is proposed for non-maneuvering targets, which makes the interceptor follow a relatively circular trajectory, determined using the concept of a reference circle on a moving coordinate frame fixed to the target. In Zhang et al 22 and Ma et al, 23 the guidance laws are designed using optimal control and Lyapunov stability theory, respectively.…”

A blended control strategy for intercepting high-speed target in high altitude

“…The guidance concept was applicable in all aerial interception geometries namely, head-on, tail-chase, and the novel head-pursuit. Yan et al 5 proposed a new guidance law called united biased proportional navigation, which is applicable for head-pursuit engagement with negative time-varying navigation ratio.…”

Time-Varying Biased Proportional Guidance with Seeker’s Field-of-View Limit

“…In guidance law designs, not only achieving acceptable miss distance values, but also considering impact angles has become an increasingly important necessity. In some applications, it is desirable to control the path angle of missiles such as antitank missiles and antiship missiles to a proper impact angle to enhance warhead effectiveness and lethality [1]. On the other hand, maintaining missile seeker's lock-on during the engagement is critical for successful interception, especially for narrower FOV seekers such as strapdown seeker [2,3].…”