2. The filtering procedure

To give a global view of the way our three stage procedure operates, Table 1 shows an example (referring to the April 2000 update) of the number of pairs passing through the stages of our filtering procedure. For the four classes of orbits, corresponding to arcs longer than 180 days, between 20 and 180 days, between 4 and 20 days, and between 2 and 4 days, respectively, we give the number of orbits available, which is multiplied by the number of attributables to give the number of pairs, the number of pairs passed by each filtering stage, the number of submissions and the number of attributions published.

   

Table 1: The attribution filtering efficiency. Data are from the Apr 18, 2000 MPC observational dataset update. The number of attributables was 74656.

Arc length (days)	> 180	20 - 180	4 - 20	2 - 4
Number of orbits	20872	18179	24188	4085
Number of pairs	$1.56\times 10^9$	$1.36\times 10^9$	$1.81\times 10^9$	$0.30\times 10^9$
Number passing 1st filter	978903	691076	1420594	203150
Number passing 2nd filter	374	7026	396795	97744
Number passing 3rd filter	183	1208	7010	1701
Number submitted	68	40	101	23
Number published	67	40	83	22

Given the large number of orbit-attributable pairs, the first stage of the filtering procedure needs to be as computationally simple as possible. It does not matter if the first filtering stage selects a large number of ``false positives'', provided this number is anyway much smaller that the total number of pairs being examined. From Table 1 we can see that the number of pairs passed by the first filter (described in Section 2.1) is less by more than a factor 1,000 with respect to the total number of pairs entering the filter. The second stage of filtering, described in Section 2.2, is also effective in reducing the number of pairs to be considered, but in a very uneven way. The predictive value of the quantity $\sigma$ we compute as a measure of similarity in the observations space is very good for long arc orbits (180 days and more, in most cases this means multi-opposition) and is satisfactory for medium arc orbits (between 20 and 180 days, in most cases this means extensive observation during one opposition). For short arc orbits the second filter is not very effective and, as discussed in Section 4, this is likely to be a point on which further improvements are possible. The results of the third stage, described in Section 2.3, are more difficult to assess in a quantitative way because, out of the successful differential corrections, only a fraction are submitted as identifications to the MPC. The attributions passed by the three selection stages still need to be assessed, by means of a formally defined protocol, discussed in Section 3.1; in many cases a visual inspection of the residuals is also necessary to evaluate the reliability of the proposed identification. The submissions also depend upon the outcome of the competition with other groups of identifiers; that is, an identification we have found is not submitted if it has been already found by someone else. On the other hand, the speed of the computation is an achievement in itself: if others are faster in submitting identifications, they deserve the credit.