Capturability of 3D PPN Against Lower-Speed Maneuvering Target for Homing Phase

The capturability of the two-dimensional (2-D) pure proportional navigation (PPN) guidance law against lower speed arbitrarily maneuvering target for homing phase had been thoroughly analyzed by using the nonlinear output regulation (NOR) method before. However, due to the complexity of the 3-D relative kinematics, the NOR method has not been applied to the capturability analysis of the 3-D PPN, which leads to the capturability discrepancy of the 2-D PPN and its 3-D extension. Thanks to the 3-D relative kinematic equation between the missile and target established in the rotating line-of-sight coordinate system, the capturability of the 3-D PPN against the lower speed arbitrarily maneuvering target for the homing phase is restudied by extending the NOR method of the 2-D PPN to the 3-D space. The necessary and sufficient condition for the missile guided by the 3-D PPN to intercept this type of target is obtained. It is proven that the capturability of the 3-D PPN is identical with that of the 2-D PPN.