Linking Sky-plane Observations of Moving Objects

Abstract The Asteroid Terrestrial-impact Last Alert System (ATLAS) observes the visible sky every night in search of dangerous asteroids. With four (soon five) sites ATLAS is facing new challenges for scheduling observations and linking detections to identify moving asteroids. Flexibility in coping with diverse observation sites and times of detections that can be linked is critical, as is optimization of observing time for coverage versus depth. We present new algorithms to fit orbits rapidly to sky-plane observations, and to test and link sets of detections to find the ones which belong to moving objects. The PUMA algorithm for fitting orbits to angular positions on the sky executes in about a millisecond, orders of magnitude faster than the methods currently in use by the community, without sacrifice in accuracy. The PUMA software should be generally useful to anyone who needs to test many sets of detections for consistency with a real orbit. The PUMALINK algorithm to find linkages among sets of detections has similarities to other approaches, notably HelioLinC, but it functions well at asteroid ranges of a small fraction of an astronomical unit. PUMALINK is fast enough to test 10 million possible tracklets against one another in a half hour of computer time. Candidate linkages are checked by the PUMA library to test that the detections correspond to a real orbit, even at close range, and the false alarm rate is manageable. Sky surveys that produce large numbers of detections from large numbers of exposures may find the PUMALINK software helpful. We present the results of tests of PUMALINK on three data sets which illustrate PUMALINK ’s effectiveness and economy: 2 weeks of all ATLAS detections over the sky, 2 weeks of special ATLAS opposition observations with long exposure time, and 2 weeks of simulated LSST asteroid observations. Detection probabilities of linkages must be traded against false alarm rate, but a representative choice for PUMALINK might be 90% detection probability for real objects while keeping the false alarm rate below 10% for a 100:1 population of false:real. Although optimization of the tradeoffs between detection probability, execution time, and false alarm rate is application specific and beyond the scope of this paper, we provide guidance on methods to distinguish false alarms from correct linkages of real objects.