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We investigate the behaviour of two recent methods for the computation ofpreliminary orbits. These methods are based on the conservation laws ofKepler's problem, and enable the linkage of very short arcs of opticalobservations even when they are separated in time by a few years. Our analysisis performed using both synthetic and real data of 822 main belt asteroids. Thedifferences between computed and true orbital elements have been analysed forthe true linkages, as well as the occurrence of alternative solutions. Somemetrics have been introduced to quantify the results, with the aim ofdiscarding as many of the false linkages as possible and keeping the vastmajority of true ones. These numerical experiments provide thresholds for themetrics which take advantage of the knowledge of the \emph{ground truth}: thevalues of these thresholds can be used in normal operation mode, when we do notknow the correct values of the orbital elements and whether the linkages aretrue or false.

Numerical behavior of the Keplerian Integral methods for initial orbit determination