Fundamentos matemáticos envolvidos na realização do ITRS

The mathematical fundamentals involved in the realization of a high precision reference system, taking into account solutions from VLBI, SLR, GPS and DORIS are presented. Each individual solution has its own deficiencies in providing a global reference system. But combining all solutions together, and by the introduction of the no net rotation condition (NNR), a solution that reflects the nowadays precision of the available spatial techniques for the determination of position and velocity of stations located on the Earth crust is obtained. Whilst the origin is provided by SLR, the scale is introduced by SLR and VLBI. The orientation and its temporal evolution are introduced via internal constraints, in accordance with the NNR condition.