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

Beijing Key Laboratory of Urban Spatial Information Engineering, Beijing, 100038, China;

State Key Laboratory of Geo-information Engineering, Xi’an, 710054, China.

College of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China

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

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

Xdxdm X

Ydy dm Y

dz dm Z

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

)(

−

(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.

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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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