Performance Analysis and Conversion Parameter Evaluation of
WGS84/ITRF Ephemeris Framework Implemented by NGA and IGS
Qinghua Zhang
1, 2, 3, 4
, Fengjuan Rong
4, *
and Zhengsheng Chen
2
1
Beijing Key Laboratory of Urban Spatial Information Engineering, Beijing, 100038, China;
2
State Key Laboratory of Geo-information Engineering, Xi’an, 710054, China.
3
College of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China
4
Army Engineering University of PLA, Nanjing, Jiangsu 210007, China
Email: lengyu880412@163.com.
Keywords: WGS84, NGA, ITRF, transformation
Abstract: The WGS84 coordinate system of GPS is dominated by the United States. At present, the ephemeris
framework of WGS84 is mainly established and maintained by NGA with precise ephemeris. However, the
IGS precise ephemeris usually adopted by navigation users is an ephemeris framework of ITRF. This paper
mainly evaluates the differences and transformation parameters between WGS84/ITRF. In the example of
this article, the WGS84/ITRF transformation parameter sequence is used daily from 2001 to the present. By
analysing the seven conversion parameters, it is found that only in a few days there are still wild values.
After eliminating field values, the three translation parameters are not more than 10cm, three rotation
parameters are no more than 0.1mas, and the scale parameters are not more than 0.1ppb.The characteristics
of conversion parameters in WGS84/ITRF can provide important reference for the GNSS users in the
precision positioning and orbit determination.
1 INTRODUCTION
In the field of satellite navigation, spatial datum and
time datum are the important foundation for the
establishment of navigation system. At present the
four satellite navigation system with different spatial
datum, the GPS by WGS84 (World Geodetic
System 84), GLONASS by PZ-90, BDS by
CGCS2000, Galileo by GTRF, and IGS by ITRF
(International Terrestrial Reference Frame)
framework. The definitions of these five spatial
datum traced to ITRS are basically the same, but
there are some differences in the implementation
(Janssen, 2009; Kotsakis, 2009; Zhang et al. 2015).
In practice, the coordinate framework is a form of
implementation of the coordinate system, including
the two forms of the T (Territorial) framework and
the E framework. Among them, the T frame is
represented by a series of core coordinates and speed
field locks of a series of GNSS ground tracking
stations, and the E framework is represented by the
satellite ephemeris. The use of the practical
application of the navigation satellite ephemeris
reference frame (E frame), the precise ephemeris or
(Jiao, 2003) broadcast ephemeris. As the GPS
system has accumulated a large amount of data
during the long run, the differences in the
WGS84/ITRF E framework will be evaluated and
analyzed in this paper.
GPS uses the WGS84 coordinate system, the
United States Department of Defense Agency NGA
to define and implement the specific realization
method including T framework and the E framework
in two forms, the E framework is the precise
ephemeris provided by the implementation (SP3)
broadcast ephemeris to achieve control and GPS
system. However, the precise ephemeris provided by
IGS (International GNSS Service) (SP3 format) is
used by users in PPP (Precise Point Positioning) or
post differential positioning, which is an
implementation of the ITRF E framework. This
article will analyze and evaluate the Helmert
conversion parameters for the WGS84 E framework
implemented by NGA and the ITRF E framework
implemented by IGS. At present, there have been
many research achievements on the GNSS
380
Zhang, Q., Rong, F. and Chen, Z.
Performance Analysis and Conversion Parameter Evaluation of WGS84/ITRF Ephemeris Framework Implemented by NGA and IGS.
In Proceedings of the International Workshop on Environment and Geoscience (IWEG 2018), pages 380-385
ISBN: 978-989-758-342-1
Copyright © 2018 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
coordinate transformation method in the world. The
layout of GLONASS completed a total of 24
constellations at the end of 1995 and began to run,
the German FAF Munich University Institute of
Geodesy and navigation in Germany and several
other research institutes in 1996 conducted a full
range of GPS/GLONASS stations in Europe, and the
conversion parameters of PZ-90 and WGS-84 are
estimated (Rossbceh, 1996; Misra, 1996). In 1997,
in order to determine the WGS84/PZ-90 coordinate
transformation parameters applicable to the Russian
region, the 29th Research Institute of the Russian
Ministry of Defense selected eight observation
stations in Russia for GPS/GLONASS joint survey
(Bazlov, 1999; Bazlov, 2002). In 1998, the
International Association of Geodesy (IAG) took the
lead in implementing the global GLONASS joint
test, namely IGEX-98 (International GLONASS
Experiment), and obtained worldwide conversion
parameters (Boucher and Alta, 2001). Nevertheless,
the existing research results are based on the T
framework to estimate the conversion parameters. In
this article, the differences and transformation
parameters between ITRF's E framework (IGS
precise ephemeris expression) and WGS84's E
framework (NGA precise ephemeris expression) are
deeply studied.
2 THE DEFINITION OF WGS84
AND ITRF
WGS84 (World Geodetic System 84), also known as
the 1984 World Geodetic Coordinate System, was
established back in the 1960s. At that time, the
National Imagery and Mapping Agency (NIMA)
was commissioned by the U.S. Department of
Defence (DoD) to establish the Global Geodetic
Coordinate System, including WGS60, WGS66, and
WGS72. WGS84 is refined and enhanced by NIMA
and produces WGS84 (G730) and WGS84 (G873).
After that, WGS84 (G1150) and WGS84 (G1674)
were introduced in 2002 and 2012 respectively.
The WGS 84 T frame is the ground reference
station coordinate and velocity field in Figure 1, and
its E Frame is implemented with a sophisticated
ephemeris provided by the NGA.
ITRF is the International Geo-Reference Frame,
which is the realization of ITRS (International
Terrestrial Reference System). With the
development of observational techniques such as
GPS, VLBI(Very Long Baseline Interferometry),
SLR(Satellite Laser Range) and DORIS(Doppler
Orbitography and Radio positioning Integrated by
Satellite), and the need for a series of earth science
research at the time, the IERS Center is responsible
for establishing ITRF. It is an integrated, global,
highprecision geocentric reference frame. ITRF is
implemented by globally distributed observatories,
which are usually equipped with observational and
solution equipment’s such as VLBI, SLR, GPS and
DORIS.And since 1988, there were a total of 15
Version of the framework, namely ITRF0, ITRF88,
ITRF89, ITRF90, ITRF91, ITRF92, ITRF93,
ITRF94, ITRF96, ITRF97, ITRF2000, ITRF2005
and ITRF2008.
The ITRF TFramework is realized with the
ground reference station coordinates and velocity
fields in Figure 2 in significantly greater numbers
and types than the WGS84. In this paper, the ITRF
EFramework is implemented with the final
ephemeris provided by IGS.
Figure 1: WGS 84 (G1762) Reference Frame Stations
(http://earth-info.nga.mil/GandG/wgs84)
Performance Analysis and Conversion Parameter Evaluation of WGS84/ITRF Ephemeris Framework Implemented by NGA and IGS
381
Figure 2: ITRF (2008) Reference Frame Stations (http://www.iers.org/IERS/EN/DataProducts/ITRF/itrf).
3 HELMERT COORDINATE
TRANSFORMATION MODEL
AND ESTIMATION OF E -
FRAME CONVERSION
PARAMETERS
3.1 Helmert Coordinate
Transformation Model
The seven-parameter Helmert Transformation, also
known as the Bursa-Wolf model (Závoti, 2012),
contains seven parameters, of which three are
translation parameters; three are rotation parameters
and onescale parameters (Figure 3). In the figure
below, for two different spatial Cartesian coordinate
frames (in this paper, the WGS84 E frame
implemented by NGA and the ITRF E frame
implemented by IGS). Seven parameters contain
three translation parameters, three rotation
parameters and one scale parameter.
Figure 3: Seven parameters Helmert transform of two
coordinates.
It can be expressed as
12
12
12
zy
zx
yx
Xdxdm X
Ydy dm Y
Z
dz dm Z
ωω
ωω
ωω
⎡⎤
⎤⎡⎤
⎢⎥
⎥⎢⎥
=+
⎢⎥
⎥⎢⎥
⎢⎥
⎥⎢⎥
⎦⎣⎦
⎣⎦
(1)
In the ideal case, the classical least-squares
method is used, that is, under the least squares
criterion, where is the inverse of the coordinate
covariance matrix (i.e., the weight matrix) of each
point. The conversion parameters between the two
coordinate bases are as follows (classical least
squares solution):
PLAPAA
TT 1
)(
=
β
v
(2)
3.2 E Framework Conversion
Parameter Estimation
Framework conversion parameters usually include
the ground common point method and ephemeris
method. The ground point method is the most
common method for solving the different coordinate
reference transformation parameters. Its principle is
to select some GNSS ground observation stations
(the best global distribution), and the precise point
positioning method is used to estimate the
coordinate values of the stations in different GNSS
coordinate data, and further obtain the
transformation parameters. The essence of the
ephemeris method is the same as that of the
terrestrial common point method, except that the
position of the satellite is regarded as a common
point. The principle of the ephemeris is to estimate
the transformation parameters by estimating the
IWEG 2018 - International Workshop on Environment and Geoscience
382
values of the satellites in different GNSS coordinate
frames.
If the precision ephemeris is used to estimate the
datum conversion parameters, a set of parameters
can be estimated by the precision of a day. The
interval between precise ephemeris is 15 minutes,
and there are 96 groups of parameters every day.
The least square method is used to deal with the
superfluous observation data and finally get a set of
estimation parameters. Using the ephemeris method
we can calculate a set of conversion parameters
every day. Its flow is as follows (Figure 4):
Figure 4: Flowchart of conversion parameters estimation
using ephemeris.
4 CALCULATING RESULTS
From the Helmert transformation model in Section
3, the transform seven parameters of the WGS84 /
ITRF E frame can be obtained by using GPS final
precision ephemeris (* .sp3) provided by NGA and
IGS. In this study, the author selected a total of 6005
transform parameters (one set per day) from 2001 to
2017. This study not only analyzed the time series of
seven conversion parameters, but also calculated the
average daily transform parameters. Based on this,
the impact of the WGS84 / ITRF E framework
implemented by NGA and IGS Precise Ephemeris
on user positioning is analysed. The detailed results
are as follows.
The evolution of the three translational
parameters is analysed in Figure 5. From the
analysis of the graph, it can be found that after the
first day of 2012, the translation parameters
decreased significantly in the direction of X and Y.
On the 344th day of 2010, the translation parameters
appeared abnormal in X and Y directions. In Z
direction, the translation parameters had 5 abnormal
jumps. For the same result of each year, see Figure
6, we can find that in recent years the values of the
three translation parameters become smaller and
smaller, and closer to zero.
Figure 5: Time series of DX, DY and DZ.
Figure 6: Annual mean statistics of DX, DY and DZ.
In Figure 7, the evolution of three rotation
parameters is depicted. The unit of rotation angle is
mas. From the following analysis, it can be found
that after the first day of 2012, the three rotation
parameters changed a lot. On the twentieth day of
2002, the rotation parameters of Y appeared
Performance Analysis and Conversion Parameter Evaluation of WGS84/ITRF Ephemeris Framework Implemented by NGA and IGS
383
abnormal jump. On the ninety-ninth day of 2002, the
rotation parameters also had 1 abnormal value. From
the analysis of the annual average in Figure 8, it is
found that in recent years, the three rotation
parameters all jerk up and down near zero, and there
is no obvious trend deviation.
Figure 7: Time series of RX, RY and RZ.
Figure 8: Annual mean statistics of RX, RY and RZ.
In Figure 9, the scale parameter is plotted in
units of ppb, and it can be found that there is no
obvious trend change before and after 2012001.
However, we can see from Figure 10 that the scale
parameter shows a shrinking trend in the past three
years. Throughout the daily scale parameters, a total
of three numerical abnormalities occurred.
Figure 9: Time series of scale factor.
Figure 10: Annual mean statistics of scale factor.
The precise ephemeris of NGA and IGS are
obtained by using different observation station data,
precise orbit determination and time synchronization
strategy, so there are certain differences between
them. This difference can be unified by a set of
conversion parameters. But if the user uses their
precise ephemeris to determine the point position of
the ground receiver, how much error can be caused?
Figure 11 shows the user range error (URE) caused
by the E framework difference of WGS84/ITRF. We
can find from Figure 12 that user location error
caused by the two frame difference at about 0.05m.
In 2009-2012 years, the value of URE is relatively
large, and the standard deviation is larger too. After
2012, the E framework difference between WGS84
and ITRF kept a stable and low level.
IWEG 2018 - International Workshop on Environment and Geoscience
384
Figure 11: Annual mean values of URE.
Figure 12: Time series of URE.
5 CONCLUSIONS
Over the past decade, WGS84 E framework
(implemented by NGA ephemeris) and ITRF E
framework (implemented by IGS final ephemeris)
have been used to analyze time series, including
three translational parameters, three rotation
parameters and a scale parameter evolution. The
analysis results show that the difference between
WGS84 (NGA E framework) and ITRF (IGS E
framework) is very small (the influence on user
location is less than 5cm), and the difference is not
constant. Therefore, when the user is in decimeter
navigation scenes, systematic errors need not be
considered. While precise positioning is carried out,
such as plate motion, systematic errors need to be
estimated .
ACKNOWLEDGMENTS
This work was carried under funding from The
National Natural Science Foundation of China
(Grant no. 41604024), China Postdoctoral Science
Foundation (Grant no. 2016M601815), Beijing Key
Laboratory of Urban Spatial Information
Engineering with NO. 2017210 and the State Key
Laboratory of Geo-information Engineering
(SKLGIE2016-Z-1-3).
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