Establishment of Geodetic Coordinate Systems - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 355

the Earth's center of mass with fairly high precision. Thus, the coordinate origin of
ITRF can be determined by this technique, i.e., it can let the translation parameter of
a certain SLR network or the weighted sum of the translation parameters of several
SLR networks involved in the adjustment be zero.
The scale of ITRF, by definition, is that of the local Earth frame within the
meaning of a relativistic theory of gravitation. In practice, the scale is defined by
physical parameters like the speed of light c, the gravitational constant of the Earth
GM, and a certain model of relativistic correction adopted in data processing by the
analysis centers. If the above values and models are different, the scale of each
network will also be different. Currently, most analysis centers have adopted the
values recommended by IERS, so the difference in scale between various networks
is insignificant. The new ITRF scale is usually the scale of a certain network or the
weighted mean of the scales of several networks.
As to the orientation of ITRF, the orientation parameters are usually considered
to have known values.
The realization of ITRF of the present time, such as ITRF2000, ITRF2005, and
ITRF2008, in terms of their input data, mathematical models, solution parameters,
and solution methods is far more complex than that of earlier ITRFs. The underly-
ing concepts, however, are very much alike. To understand better the methods of
realizing the origin, scale, and orientation, we present here the establishment of the
early ITRF91 (which applied GPS data for the first time) as an example to illustrate
the process of ITRF realization.
Table 7.1 lists all the 16 networks involved in the establishment of ITRF91. The
serial numbers 1-5 are the VLBI networks, 6-12 are SLR networks, 13-15 are LLR
networks, and 16 is a GPS network. ITRF91 was eventually established by carrying
out combined adjustment of all the data (see Boucher et al. 1992).
In combined adjustment, the reference system is defined as: the origin of the
reference system as determined by SLR, the scale as determined by SLR coincident
with VLBI, and the orientation, which is consistent with ITRF90.
The methods for realizing this reference system by combined adjustment are:
1. The transformation parameters of SSC (CSR) 92L01 network (Table 7.1 , serial
No. 6) are all assigned to be zero, i.e., an adjustment in the reference system is
carried out to make the origin, scale, and orientation consistent with SSC (CSR).
This result is defined as the ITRF91A. Apparently, the origin and scale of
ITRF91A have satisfied the definition of ITRF91, but not the orientation.
2. The seven transformation parameters of ITRF91A and ITRF90 are solved to
obtain the orientation correction parameters (cf. Table 7.2 ).
3. Both the translation parameters and scale factors of SSC (CSR) are set to zero
and the rotation angles are R1, R2, and R3 as shown in Table 7.2 (cf. Table 7.1
serial No. 6). The transformation parameters obtained after the combined adjust-
ment of all the data can be seen in Table 7.2 .
For the datum definition adopted by ITRFyy (where yy is the annual series of this
frame, denoting the last year whose data were used in the realization of the frame) at
different dates, see Table 7.3 (Boucher et al. 1999, 2004; Altamimi et al. 2001,