The paper applies the framework of general relativity to the problem of reduction of high-precision astrometric observations of the order of 1 microarcsec. Theoretical methods making it possible to construct astrometric reference systems involving the barycentric, geocentric, and satellite (observer) systems are described. Relativistic transformations between the reference systems employed are derived. Equations of geometric optics for the nonstationary gravitational field of the solar system are deduced. The effects of relativistic deflection of the light due to monopole and quadrupole components of the sun's gravitational field and the planets are calculated, with their motions and rotations taken into account. Transformations between the reference systems are used to calculate the light aberration occurring when passing from the satellite system to the geocentric system and from the geocentric system to the barycentric systems. Aberrational corrections are applied to transform the observed position of a celestial object to the barycentric system, taking the relativistic light deflection into account.
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Klioner et al. (1992) studied this question.