Determination of predicted position of a satellite at limited errors of measurements

Abstract

Non-statistical formulation of the problem of determining the future position of an object in circumterrestrial space orbiting around the Earth is considered at some constraints on measurement errors. Criteria of optimality and the algorithms satisfying these criteria are presented. Computational schemes are given for the most interesting (for practical purposes) central and projective algorithms. Using mathematical simulation methods the precision characteristics of these algorithms are determined at different distributions of measurement errors for typical situations, arising when one supports a catalog of space objects. It is shown that the errors of determining the predicted position of a space object, obtained with the non-statistical approach, can be less than the errors of the least squares method.