Improved bias proportional navigation with multiple constraints for guide ammunition

According to the infrared guidance ammunition (GA) attacking non-maneuvering targets on the ground or sea level, an improved bias proportional navigation (IBPN) is put forward, which can meet the constraints of the impact angle and the angle of attack (AOA). The motion equations and the collision triangle for the GA and the target are established in the two-dimensional plane. In accordance with the collision triangle, the integral value of the bias term is solved and BPN is designed on the basis of the relative velocity. To ensure the new method can be solved, closed-loop equation of the IBPN is deduced. Considering the limitation of the AOA and the seeker angle, a four-phase IBPN is improved by setting different phases of the bias term. At the same time, the guidance law will make the impact angle achieve the desired angle and the normal acceleration also converges to zero. The simulation results show that the improved guidance law can be applied to various flight tasks and has great potential for engineering applications.