In previous works, it has been shown that the estimation problem of a thrusting/ballistic object in the three-dimensional space can be solved with two-dimensional measurements (azimuth and elevation angles starting from the launch time) assuming the launch point is perfectly known. In this paper, the problem is extended to estimate the target's trajectory with measurements starting after the launch time, i.e., delayed acquisition. Compared to the situation of acquisition at launch time, one has an additional unknown speed (magnitude of the velocity vector) and the unknown acquisition location. The 2D angle measurements are all obtained from a single fixed passive sensor. The parameter vector, in this case, has dimension 8 (velocity vector azimuth angle and elevation angle, drag coefficient, specific thrust, target speed and 3D acquisition position). The invertibility of the Fisher Information Matrix (FIM) of the parameter vector is investigated to test the observability (estimability) of the system. The simulation results prove the statistical efficiency and unbiasedness of the Maximum Likelihood estimator, that is, the Cramer-Rao lower bound (the inverse of the FIM if it is invertible) can be used as the actual covariance.

The camera in video conference systems is typically positioned above, or below, the screen, causing the gaze of the users to appear misplaced. We propose an effective solution to this problem that is based on replacing the eyes of the user. This replacement, when done accurately, is enough to achieve a natural looking video. At an initialization stage the user is asked to look straight at the camera. We store these frames, then track the eyes accurately in the video sequence and replace the eyes, taking care of illumination and ghosting artifacts. We have tested the system on a large number of videos demonstrating the effectiveness of the proposed solution.