The standard relation of transformation between two reference systems is an Euclidian similarity of seven
parameters: three translation components, one scale factor, and three rotation angles, designated respectively,
T1, T2, T3, D, R1, R2, R3, and their first times derivations :
1, 2,
3, ,
1, 2,
3.
The transformation of coordinate vector X_{1}, expressed in a reference system (1), into a coordinate
vector X_{2}, expressed in a reference system (2), is given by the following equation:


(1) 
with :
It is assumed that equation (1) is linear for sets of station coordinates provided by space geodetic technique
(origin difference is about a few hundred meters, and differences in scale and orientation are of 10^{5} level).
Generally, X_{1}, X_{2}, T, D, R are function of time. Differentiating equation (1) with respect
to time gives :


(2) 
D and R are of 10^{5} level and is about 10 cm per year,
the terms D_{1} and R
_{1} are negligible which represent about 0.0 mm over 100 years. Therefore, equation (2) could be
writen as :


(3) 
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