Biased Proportional Navigation with Decaying Error for 3D Impact Angle Control

A guidance law for impact vector control in 3D engagements is derived without linearization or decoupling of engagement kinematics. The proposed method, which requires neither the range to go nor the time to go but only a rough estimate of the engagement duration, is in vector form and composed of biased proportional navigation and plane pursuit guidance laws applied in a continuous form with no switching. The plane pursuit aims to bring the velocity vector of the missile into the impact plane, which is defined by the line of sight and the desired impact vectors. On the other hand, the bias is designed using an angular error defined in the impact plane, which is regulated with a proportional and integral controller, where it is possible to exploit the initial value of the integrator to shape the acceleration response. The performance is demonstrated through simulation studies.