Integrated Probabilistic Engagement Modeling and Guidance Accuracy Optimization for Launch and Lethal Zone Construction

Abstract

This paper develops a unified probabilistic framework for missile–target engagement assessment integrating kinematic reachability, fragment-based lethality modeling, and stochastic terminal guidance uncertainty. Closed-form approximations for expected kill probability are derived under Rayleigh-distributed miss distance. Analytical asymptotic analysis reveals an exponential dependence of engagement effectiveness on inverse-squared guidance accuracy. A deterministic lethal-radius model is compared with the proposed probabilistic formulation, demonstrating significant overestimation by traditional methods. An optimization problem is formulated to determine the minimum required terminal guidance accuracy ensuring a prescribed kill probability threshold. The results provide quantitative design constraints for guidance and control system development.