Estimating the accuracy of satellite ephemerides using the bootstrap method

¹ Institut de Mécanique Céleste et de Calcul des Éphémérides, Observatoire de Paris, UMR 8028 CNRS, 77 avenue Denfert-Rochereau, 75014 Paris, France e-mail: desmars@imcce.fr
² Univ. Pierre & Marie Curie, 4 place Jussieu, 75252 Paris, France
³ CNRS, Willow Project-Team, Laboratoire d'Informatique de l'École Normale Supérieure (CNRS/ENS/INRIA UMR 8548), 45 rue d'Ulm, 75230 Paris, France
⁴ LAL, Univ. de Lille, 59000 Lille, France

Received: 12 December 2008
Accepted: 18 February 2009

Abstract

Context. The accuracy of predicted orbital positions depends on the quality of the theorical model and of the observations used to fit the model. During the period of observations, this accuracy can be estimated through comparison with observations. Outside this period, the estimation remains difficult. Many methods have been developed for asteroid ephemerides in order to evaluate this accuracy.

Aims. This paper introduces a new method to estimate the accuracy of predicted positions at any time, in particular outside the observation period.

Methods. This new method is based upon a bootstrap resampling and allows this estimation with minimal assumptions.

Results. The method was applied to two of the main Saturnian satellites, Mimas and Titan, and compared with other methods used previously for asteroids. The bootstrap resampling is a robust and practical method for estimating the accuracy of predicted positions.