Performance of PPN Guided Missile with Arbitrary Time-Varying Speed against Stationary Targets: New Findings

The performance of the pure proportional navigation (PPN) guidance law against the stationary target is restudied, when the missile speed is arbitrarily time-varying. Based on the classical differential geometry theory, the analytical solutions of the line-of-sight (LOS) angle, LOS rate, missile lead angle, and closing speed of PPN are derived in the missile's arc-length domain. The capture condition of PPN against the stationary target is thoroughly analyzed, when the guided missile is with arbitrary-time-varying-speed. Some new theoretical findings are presented, such as the maximum relative range, maximum trajectory curvature, curvature integral, and missile flying range.