Sparse multi-apparition linkages in large datasets

We present a new procedure to identify observations of known objects in large data sets of unlinked detections. It begins with a Keplerian integrals method that allows us to link two tracklets, computing preliminary orbits, even when the tracklets are separated in time by a few years. In the second step, we represent the results in a ‘graph’ where the tracklets are the nodes and the preliminary orbits are the edges. Then, acceptable ‘3-cycles’ are identified and a least squares orbit is computed for each of them. Finally, we construct sequences of n≥4 tracklets by searching through the orbits of nearby 3-cycles and attempting to attribute the remaining tracklets. We calculate the technique's efficiency at identifying unknown objects using real detections that attempt to mimic key parameters of the Minor Planet Center's (MPC) Isolated Tracklet File (ITF) and then apply the procedure to the ITF. This procedure enables the recovery of several orbits, despite some having few tracklets per apparition. The MPC accepted >95% of our linkages and most of the non-accepted linkages are 2-apparition linkages even when those linkages contained more than half a dozen tracklets.