Abstract:The dimension reduction method of the true proportional navigation (TPN) guidance law is proposed. Firstly, the rotation principle of the line of sight (LOS) was investigated, two kinds of angular velocities of LOS were presented, and so were their calculation methods. Then, the LOS kinematic equation was advanced, and the new relative dynamic equation between interceptor and target was proposed. It was found that there is an instantaneous rotation plane of LOS (IRPL) in the three dimensional (3D) space, in which two dimensional (2D) guidance laws can be constructed to serve for 3D interception guidance. The spatial 3D true proportional navigation (TPN) guidance law was directly introduced into IRPL without any approximation and linearization to transform into dimension reduced 2D TPN, and the characteristics were studied. Finally, an exoatmospheric interception was taken for simulation to demonstrate the effectiveness of the theory presented in this paper.