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Multi-wavelength astronomical studies require cross-identification of detections of the same celestial objects in multiple catalogs based on spherical coordinates and other properties. Because of the large data volumes and spherical geometry, the symmetric N-way association of astronomical detections is a computationally intensive problem, even when sophisticated indexing schemes are used to exclude obviously false candidates. Legacy astronomical catalogs already contain detections of more than a hundred million objects while the ongoing and future surveys will produce catalogs of billions of objects with multiple detections of each at different times. The varying statistical error of position measurements, moving and extended objects, and other physical properties make it necessary to perform the cross-identification using a mathematically correct, proper Bayesian probabilistic algorithm, capable of including various priors.
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