• Admissible region
• Attributable
• Initial orbit determination
• Orbit determination

In this thesis, we propose a new initial orbit method based on three observations of a Near-Earth
Object (NEO) or space debris. This method is based on the concept of the admissible region, defined
as the area in space where the object may plausibly be located. This region is defined by the
dynamical constraints on the position of the celestial body. We first define the admissible region for
solar system objects and then study the case of space debris based on TSA, using both optical and
radar observations. It has been demonstrated that, in all cases, the admissible region has at most two
connected components. By introducing certain constraints, a compact set can be obtained, allowing
for the admissible region to be sampled using a finite number of virtual asteroids (VAs) or virtual
space debris. The method has been implemented and to test its efficacy, we analysed 100 asteroids with observations from the same night, and 30 asteroids with observations from two different nights. All tests show that the method can compute a preliminary orbit, even in cases where classical methods, such as Gauss’s and Laplace’s, fail.