Robust Estimates of Orientation between Astrometric Catalogs

Abstract

Accurately comparing two celestial reference frames based on the observed position of a number of common objects requires to detect and appropriately process outliers, lest they spuriously influence the results. It is thus of practical importance to use algorithms able to minimize the impact of those outliers when comparing radio and/or optical astrometric catalogs. In this paper, we investigate and compare the performances of some well-established and more recent robust algorithms when fitting a simple rotation vector between two reference frames. We particularly focus on two aspects: the variance of the resulting estimates, and the ability of the estimators to deal with outlying leverage points. We ran a number of Monte Carlo simulations with synthetic objects, varying their number, as well as the fraction and dispersion of outliers. Since the distribution of catalog objects in the sky is sometimes markedly nonuniform as in the case of the ICRF3 catalog, and because the position of outliers in the sky might cause issues when fitting rotation models, we also ran simulations representative of the observed distribution of objects. We compare the ICRF3 S/X, ICRF2 and Gaia EDR3 reference frames. Our results, based on the synthetic simulations and the comparison between the existing celestial frames, show that the M estimator, with a scale obtained from a least absolute deviations estimate, is the best among all the robust estimators compared.