Z. Knežević

Contemporary observational surveys provide a huge number of detections of small solar system bodies, in particular of asteroids. These have to be reduced in real time in order to optimize the observational strategy and to select the targets for the follow-up and for the subsequent determination of an orbit. Typically, reported astrometry consists of few positions over a short time span, and this information is often not enough to compute a preliminary orbit and perform an identification. Classical methods for preliminary orbit determination based on three observations fail in such cases, and the new approach is necessary to cope with the problem.

In this paper, the basic principles of the classical methods of orbit determination are reviewed and the problems that lead to the failure of the classical algorithms are briefly addressed. The new paradigm is next described and the concept of an attributable (two angles and two angular velocities at a given time) introduced. It is then shown that the missing values (geocentric range and range rate), necessary for the computation of an orbit, are constrained to a compact set, the so-called admissible region. The latter is defined on the basis of requirements that the body belongs to the solar system, that it is not a satellite of the Earth, and that it is not a "shooting star" (very close and very small).

A mathematical description of the admissible region is given, and its properties, like the existence of no more than two connected components, demonstrated. Sampling of the admissible region can be performed by using the Delaunay triangulation. A finite number of six-parameter sets of initial conditions are thus defined, with each node of triangulation representing a Virtual Asteroid for which it is possible to propagate the corresponding orbit and predict ephemerides. For subsequent instants in time we can then compute an image of the original triangulation and use it as nominal ephemerides (with their confidence regions) for a full least square orbit.