Mathematical model of calculating metric tensor and GNSS-observations errors taking into account relativistic effects

Study of the trajectories of the motion of satellites remains an urgent task for modern science. This is especially true for GNSS systems and for satellites intended for Earth remote sensing. The basis of their operation is to accurately determine the position of the satellite, and the parameters of signal propagation. Considering the great distances and speeds of both satellites and the Earth in calculating these parameters, it is necessary to take into account the special and general theory of relativity. In the article formulas have been derived for calculating additional corrections for relativistic effects. A mathematical model for calculating the metric tensor was created. A sequence of correction was also proposed