Under these hypothesis, the general transformation of the cartesian coordinates of any point close to the Earth from a TRS (1) to a TRS (2) will be given by a tri-dimensional similarity (T_1,2 is a translation vector, λ_1,2 a scale factor and R_1,2 a rotation matrix):

(2)

This concept can be generalized in the frame of a relativistic background model such as Einstein's General Relativity, using the spatial part of a local cartesian frame.

2. Conventional Terrestrial Reference System (CTRS).

Such a system designates the set of all conventions, algorithms and constants which determine the estimation of coordinates of points in a specific ideal TRS.

3. Conventional Terrestrial Reference Frame (CTRF).

A Conventional Terrestrial Reference Frame is defined as a set of physical points with precisely determined coordinates in a specific coordinate system as a realization of an ideal Terrestrial Reference System. Two types of frames are currently distinguished (this is also valid for celestial references), namely dynamical or kinematical ones, depending whether a dynamical model is applied in the determination process of these coordinates, or not.