Time-to-go prediction for homing missiles based on minimum-time intercepts

Two minimum-time trajectories are developed for use as a time-to-go algorithm for a missile controlled by a linear-quadratic guidance law. The first algorithm is based on the minimum normal-acceleration-weighted final time trajectory for a constant speed missile, and the second algorithm is based on the minimum final time trajectory of an accelerating missile with bounded normal acceleration. Because the initial off-boresight angle is fixed, these algorithms are expected to work well for intercepts where large off-boresight angles occur. Both time-to-go algorithms are tested in a six-degree-of-freedom simulation of a bank-to-turn missile attacking a smart target, and their miss distances are compared with those obtained by time-to-go algorithms known as range over closing speed and accelerated range over closing speed. Both algorithms give low miss distances for a wide range of intercept geometries including those with large off-boresight angles. These results are substantially improved relative to those obtained with range over closing speed. However, the accelerated range over closing speed algorithm matches the minimum-time results and is the preferred algorithm because of its simplicity.