New Result on Interception of Stationary Targets at Arbitrary Time-Varying Speed

Abstract

This paper develops a novel approach and some main results on the varying-speed missile guided by pure proportional navigation (PPN) against a stationary target in the planar interception problem. The missile kinematic equation is established in the arc-length domain based on the differential geometry theory, which eliminates the influence of time-varying missile speed. Then, the closed-form solutions of line-of-sight (LOS) rate, leading angle, closing speed, and curvature command are derived in the arc-length domain. The performance of the varying-speed missile is analyzed, including the maximum relative distance, maximum curvature command, accurate path-to-go, and curvature increment. Additionally, the capture region is obtained considering the missile maneuvering acceleration limit. These new theoretical results could be extended to improve the performance of existing guidance laws designed under the constant-speed assumption.