Time-to-Go Prediction for a Homing Missile Based on Minimum-Time Trajectories

摘要

In two dimensions the trajectory of a constant velocity missile which intercepts a zero-acceleration target and which minimizes the weighted sum of the final time and the integral of the missile normal acceleration squared is derived. The launch angle of the missile is arbitrarily prescribed. The optimal control involves elliptic functions and requires the numerical solution of two non-linear algebraic equations for its calculation. This procedure is used to calculate the time-to-go in a six degree of freedom simulation in which the target performs maneuvers. The current missile velocity is projected on the plane of the line of sight vector and the target vector, and the time required to perform the two dimensional intercept is calculated and used as the time-to-go for the linear quadratic guidance law of the missile. Results show substantial improvement relative to the range-over-closing speed method of computing time-to-go. Keywords: Time-to-go; Guided missile trajectories; Intercept trajectories; Minimum-time trajectory; Reprints. (kt)