The asteroid identification problem III. Proposing identifications

A large fraction of 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 find effective algorithms for identification. We give a new method to propose identifications of orbits, applicable in the case where each of the two observed arcs provides enough information to solve for all the orbital elements by a least-squares fit to the observations. Even if the optimum fit solution is unique, there is a confidence region in the space of orbital elements containing orbital solutions compatible with the observations: the identification of orbits is the search for an orbital solution in the intersection of the two confidence regions. In the linear approximation there is a rigorous and simple algorithm to find 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 identification using a cascade of tests, all based upon identification metrics taking into account the difference in the orbits weighted with the uncertainty, The first test is based only upon the orbital plane; the couples of orbits compatible according to the first test are submitted to further tests using identification metrics based upon 5 and 6 orbital elements. Finally, the couples passing all tests are submitted to an accurate computation, by differential correction, of the orbit fitting both sets of observations. This procedure has been tested on a set of 100 already known identifications and was found to be effective in 99% of the cases. Finally we show that these methods have been used to obtain 152 previously unknown orbit identifications. (C) 2000 Academic Press.