Closed-Form Solutions of Miss Distance for Higher-Order Guidance System

In order to analytically evaluate the effects of different maneuvering strategies, we derive a series of closed-form solutions of the miss distance that are applicable to higher-order guidance system models. Instead of adopting the simplified zero-lag missile model, our solutions are closer to reality. First, based on the linearization of the guidance loop, the closed-form solutions of various guidance models are derived. For the first-order system, the confluent hypergeometric function is introduced to derive the solutions of the miss distance due to heading error and target maneuver; for the higher-order system in binomial form, the frequency and time domain expressions for the miss distance are obtained through frequency domain analysis and inverse Laplace transform; for the higher-order guidance systems with arbitrary forms, the power series solutions of the miss distance are given based on the adjoint system. Second, the effectiveness of step and weave maneuvers is analyzed based on the closed-form solutions, and the accuracy of these solutions is validated. Finally, an optimal maneuvering strategy based on the closed-form solutions is proposed. This strategy offers significantly better evasion performance than the conventional maneuvering strategy, as evidenced by both linear and nonlinear simulation results.