Establishment of Geodetic Coordinate Systems - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 354

system. In practice the three axial directions of the reference system are determined
by the Earth Rotation Parameters (ERP) provided by BIH or IERS.
The terrestrial reference frame (TRF) can be established and maintained by SLR
techniques alone. Due to factors like variant models adopted, different numbers of
sites, and different amounts of data used in the solution, the reference frames
established by different SLR networks also differ to some degree.
The orientation and scale of the reference coordinate system can be determined
precisely using the VLBI technique, yet this technique cannot determine the origin.
Hence SLR is always used to determine a certain station coordinate as the initial
point; for instance, the VLBI network uses the American Westford station as the
initial point. Likewise, the reference systems established by different VLBI net-
works also differ from each other to some extent.
GPS and other technologies can also establish a TRF according to their own
technological characteristics.
The International Terrestrial Reference Frame (ITRF) can be established by
carrying out a combined adjustment between the above global SLR, VLBI, GPS
networks, and other spatial geodetic networks.
The equation of the combined adjustment is:

2
4

3
5 obs ﾼ

2
4

3
5 þ

2
4

3
5 CTRF þ

2
4

3
5 ,

X
Y
Z

ʴ X X

Y
Z

V x
V y
V z

ʴ Y ð 7 : 33 Þ

ʴ Z

T is the deformation displacement of the observation station,

where ﾽ ʴ X ʴ Y ʴ Z

T
obs

X 0 ,

ﾽ XYZ is the station coordinate vector corrected for translations ( Δ

Y 0 , Z 0 ), rotations ( m 0 ) of the observed coor-

Δ Δ ʵ

X ,

ʵ

Y ,

ʵ

Z ), and scale correction (

Δ

T defined in the terrestrial reference frame with respect to the
observational techniques “O” (such as SLR, VLBI, GPS, etc.), namely:

dinates X 0

Y 0 Z 0

2 3 2 3 2 3 2 3

X
Y
Z

X 0 X 0

Y 0
Z 0

X 0
Y 0
Z 0

Δ

Z Y X

4 5 obs ﾼ 4 5 þ 4 5 þ Δ 4 5 :

0 0 0

m 0

Y 0

R Z ʵ R Y ʵ R X ʵ ð 7 : 34 Þ

Δ

Z 0 Δ

Equations ( 7.33 ) and ( 7.34 ) are the observation equations used to realize CTRF.
The unknown parameters in the equations are XYZ

T
CTRF and

T ,

ﾽ ﾽ ʴ X ʴ Y ʴ Z

m 0 represent the relation-
ship between CTRF and the terrestrial reference frame relative to the observation
techniques “0”.
ITRF is an example of CTRF. In practical applications there will usually be
specific

X 0 , Y 0 , Z 0 ,

0 0 0

which define the CTRF. Δ Δ Δ ʵ

X ,

ʵ

Y ,

ʵ

Z , and

Δ

requirements of origin, scale, and orientation for the newly

established ITRF.
According to the definition of CTRS, the coordinate origin of ITRF is situated at
the center of mass of the whole Earth. As a dynamic technique, SLR can determine