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

TL;DR

This paper develops new analytical results for intercepting stationary targets with missiles of time-varying speed using pure proportional navigation, including a closed-form solution and capture region analysis, verified through simulations.

Contribution

It introduces a novel arc-length based relative motion model and derives a closed-form solution for interception with time-varying missile speed, considering maneuvering limits.

Findings

Closed-form solution for interception with time-varying missile speed

Analysis of capture region considering missile acceleration limits

Verification of results through numerical simulations

Abstract

In this paper, some new results on time-varying missile against a stationary target using pure proportional navigation (PPN) are developed in the planar interception problem. First, the relative motion equation is established in arc-length domain based on the differential geometry theory, which eliminates the influence of time-varying missile speed. Then, the closed-form solution of time-varying speed missile intercepting stationary target with PPN is deduced, and the interception performance is analyzed. Additionally, considering the missile maneuvering acceleration limit, the capture region of time-varying speed missile is analyzed. Finally, the results derived in this paper are verified by numerical simulation analysis for various scenarios.