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 :
The transformation of coordinate vector X1, expressed in a reference system (1), into a coordinate
vector X2, expressed in a reference system (2), is given by the following equation:
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, X1, X2, T, D, R are function of time. Differentiating equation (1) with respect
to time gives :
D and R are of 10-5 level and is about 10 cm per year,
the terms D1 and R
1 are negligible which represent about 0.0 mm over 100 years. Therefore, equation (2) could be
writen as :
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