A method for target acquisition and tracking of a moving station or target (e.g., an unmanned aerial vehicle) for carrying out free space optical communications uses an "elapsed time"-based approach to determine the position of the moving station at any future time, based on the time difference since the moving station's last known position. For example, the vehicle may be for purposes of reconnaissance, where the optical link provides a secure and high-bandwidth communications pathway between the moving station and a ground station. A mathematical model of the moving station's expected periodic flight path is combined with position and time elements to accurately predict the future position of the moving station for target re-acquisition. The model is a cubic spline interpolation of known flight path waypoints. The system may also employ multiple waypoints in initial acquisition, by alternating acquisition attempts over several waypoints instead of "staring" at a single waypoint.