A relativistic definition of the physically adequate proper reference system of a test observer is suggested within the framework of the parametrized post-Newtonian formalism. According to the nomenclature accepted within the GAIA project this reference system is called the center-of-mass reference system (CoMRS). The interrelation between the suggested definition of the CoMRS and the International Astronomical Union (IAU) Resolutions 2000 on relativity are elucidated. The tetrad representation of the CoMRS at its origin is also explicated. It is demonstrated how to use this tetrad representation to calculate the relation between the observed direction of a light ray and the corresponding coordinate direction in the barycentric celestial reference system of the IAU. It is argued that the kinematically nonrotating CoMRS is the natural choice of the reference system where the attitude of the observer (e.g., of the GAIA satellite) should be modeled. The relativistic equations of rotational motion of a satellite relative to its CoMRS are briefly discussed. A simple algorithm for the attitude description of the satellite is proposed.