Optimal Evasion Guidance Law Accounting for the Delay of Acceleration Estimation

This paper develops an analytical optimal evasion guidance law that explicitly accounts for the lag introduced by target acceleration estimation. The pursuer is assumed to employ augmented proportional navigation (APN), while the target acceleration available to the pursuer is generated through an arbitrary-order low-pass filter. Under this setting, an optimal control problem is formulated to maximize the terminal miss distance, and an analytical solution is derived via an infinite-series representation of the switching function. To facilitate real-time implementation, a unified finite-order polynomial approximation is further constructed for the key switching-function terms, and rigorous truncation-error bounds are established by exploiting the properties of transcendental functions and series convergence. As a representative practical case, a class of Kalman filters is incorporated to model target-acceleration estimation. Numerical simulations in both linearized and nonlinear engagement scenarios show that the proposed method accurately reproduces the numerical optimum while providing substantially higher computational efficiency and larger miss distances than APN-based evasion laws that neglect or oversimplify estimation delay.