- Published 2007

A large fraction of the asteroids have been lost shortly after discovery, thus the asteroid catalogs contain a large number of low accuracy orbits. Two of these inaccurate orbits can belong to the same physical object; the challenge is to nd e ective algorithms for identi cation. We give a new method to propose identi cations of orbits, applicable in the case where each of the two observed arcs provide enough information to solve for all the orbital elements by a least squares t to the observations. Even if the optimum t solution is unique, there is a con dence region in the space of orbital elements containing orbital solutions compatible with the observations: the identi cation of orbits is the search for an orbital solution in the intersection of the two con dence regions. In the linear approximation there is a rigorous and simple algorithm to nd the optimum joint solution and the increase in the RMS of the residuals relative to the two separate solutions. The linear approximation may fail if two poorly determined orbits are too far apart in the orbital elements space. In this case, the linear algorithm becomes more stable when restricted to only some of the orbital elements. Our procedure proposes orbit identi cation using a cascade of tests, all based upon identication metrics taking into account the di erence in the orbits weighted with the uncertainty. The rst test is based only upon the orbital plane; the couples of orbits compatible according to the rst test are submitted to further tests using identi cation metrics based upon 5 and 6 orbital elements. Finally, the couples passing all tests are submitted to an accurate computation, by di erential correction, of the orbit tting both sets of observations. This procedure has been tested on a set of 100 already known identi cations, and was found to be e ective in 99% of the cases. Finally we show that these methods have been used to obtain 150 previously unknown orbit identi cations.

@inproceedings{Milaniy2007TheAI,
title={The Asteroid Identification Problem Iii: Proposing Identifications},
author={Andrea Milaniy and Alessandra La Spinay and Maria Eugenia Sansaturioz and Steven R. Chesleyy},
year={2007}
}