Using observations from the Global Position System (GPS), there are basically two ways to produce coordinates.
The first is by absolute point positioning using a GPS receiver and some a priori satellite orbit information. The reference frame of coordinates determined from point positioning will be identical to the reference frame of the satellite orbits, which is used to determine the satellite positions at signal emission time.
Stand-alone GPS code positioning, using the broadcasted satellite navigation message, is an example of this method. The satellites send their positions in the WGS84 reference as part of the broadcast signal recorded by the receiver. Consequently, the computed coordinates will be determined in WGS84.
The second method consists in GPS surveying relative to other GPS tracking stations (so called relative positioning"), whose coordinates are known in a particular reference system; these stations are commonly called "reference stations". Similar to the point positioning case, a priori satellite orbit information is necessary. If the coordinates of the reference stations refer to a different reference frame than the satellite orbits, then the relation between both references needs to be known.
Multiple examples of this second principle exist: static relative GPS positioning, real-time kinematic GPS, differential GPS,

In order to exactly determine the link between the Earth-centred (GNSS) frame and the previously used local datum, a rigorous definition of the Earth-centred frame is necessary. In this paper, we will define the different reference systems commonly used when computing positions based on GPS observations. In addition, each of these systems, consisting of a set of theoretical definitions, can only be used in practice if it has an associated reference frame. This reference frame consists of a set of markers on the Earth with known coordinates and velocities. We will show how coordinates, linked to each of these reference frames, can be obtained using GPS.

Satellite-positioning systems require a single global geodetic datum based on the Conventional Terrestrial Reference System (CTRS). The CTRS is geocentric and references north to the mean pole 1900-1905 and 0° longitude to the Greenwich Observatory, such as shown in Figure 1. The CTRS is Earth-fixed, and spins and revolves with the Earth.
Three particular relevant CTRS are: WGS84 as used for GPS, PZ90 as used for GLONASS and the International Terrestrial Reference System (ITRS). WGS84 and PZ90 are established and maintained by military organisations, while a scientific institution, the International Earth Rotation Service (IERS), produces the ITRS.



In the following, we will concentrate, in addition to the global systems WGS84 and ITRS, also on the European reference system ETRS89.
The International Astronomical Union (IAU) and the International Union of Geodesy and Geophysics (IUGG) established the International Earth Rotation Service (IERS) in 1987. The IERS began official operation on January 1st 1988. One of the primary objectives of the IERS is to provide the IERS Terrestrial Reference System (ITRS). The main characteristics of the ITRS are (see also http://www.iers.org/iers/earth/)

• The origin coincides with the geocentre
• The orientation of the fundamental plane coincides with the Earth's mean equator for the period 1900-1905
• The principal direction is the direction of the intersection of the plane through Greenwich and the equatorial plane

In practice, the IERS Terrestrial Reference Frame (ITRF) realizes the ITRS. The ITRF consists of estimates of the coordinates and velocities of a set of stations observed by VLBI (Very Long Baseline Interferometry), LLR (Lunar Laser Ranging), GPS, SLR (Satellite Laser Ranging) and DORIS (Doppler Orbitography and Radiopositioning Integrated by Satellite). Various realizations exist, called respectively ITRF88, ITRF89,...., ITRF2000. Each of them is an improvement with respect to the previous ones: more stations have been included and longer observation periods are used in order to obtain more reliable station coordinates and velocities ([2], [3] and [10]). Each ITRFyy can be transformed into another realization using a 7-parameter similarity transformation model whose parameters are made available by the IERS (http://lareg.ensg.ign.fr/ITRF/). It is also possible to have an ITRFyy propagated forward (or backward) in time using the station velocities. These velocities reflect the effect of the crustal motion.
The last ITRFyy, called ITRF2000, was issued in 2001 ( http://lareg.ensg.ign.fr/ITRF/ITRF2000/). It comprises about 500 "primary" sites distributed all over the world. More than 100 of these sites are in Europe from which four are located Belgium.
An ITRFyy is produced in its most raw form as Earth-centred Cartesian coordinates (X, Y, Z). Therefore, a reference ellipsoid must be used to convert to ellipsoidal coordinates (latitude, longitude and ellipsoidal height). The reference ellipsoid associated with recent ITRF is the Geodetic Reference System of 1980 (GRS80) ellipsoid (with a=6378137 m, 1/f=298.257222101 [13]).

The World Geodetic Reference System 84 (WGS84) has been established by the US National Imagery and Mapping Agency (NIMA) and the US Department of Defense (DoD). The initial realization of WGS84 was purely based on positions computed based on observations from the Transit satellite system and was only accurate at the one to two metre level.
Over the last 15 years, the quality of the successive realizations of the WGS84 has been considerably improved. A first step towards more consistency between the WGS84 and ITRS took place in 1993 when the complete WGS84 network was recomputed with respect to 8 GPS stations fixed to their ITRF91 position ([18]). This realization is known as WGS84 (G730),  "G730" indicates its official implementation on GPS week 730 (Jan. 2, 1994). The WGS84 (G730) realization is consistent with the ITRF92 at the 10 cm level ([11]).
Further improvements to the tracking station coordinates in 1996, led to WGS84 (G873). This realization consists of 13 sites (NIMA and Air Force sites); only one of them is located in Europe, namely in the UK ([14]). The WGS84 (G873) coordinates are consistent with the ITRF94 at a level better than 2 cm ([12]). As a consequence, for most practical applications, there is no difference between coordinates in the WGS84 or ITRS.
The WGS84 ellipsoid (a=6378137 m, 1/f=298.257223563) is identical to the GRS80 ellipsoid at the mm level.

The main disadvantage of the ITRS and WGS84 lies in the fact that they are global systems. This means that, due to the plate tectonics, the coordinates in the different continents move with respect to each other. For example, expressed in the ITRF2000, the coordinates of Brussels change with about 2.5cm/year. This time evolution makes these coordinates unsuitable for practical cartographic applications of cm-precision.
To remedy to this problem, the IAG and CERCO (Comité Européen des responsables de la Cartographie Officielle) decided, in 1987, to develop a new European Geodetic Reference Frame based on GPS. This reference should be a continent-wide modern reference for multinational Digital Cartographic Datasets, no longer derived from multiple national datums across Europe. It should unify national reference systems for surveying, mapping, GIS and navigation in Europe [16].
At that time, the IERS provided the best global realization of a geodetic reference system. Therefore, the IAG sub-commission EUREF and the CERCO WG VIII agreed to base the new European Terrestrial Reference System (called ETRS89) on the ITRF. They selected about 37 European SLR and VLBI sites whose ITRF-solution for the epoch 1989.0 would define the first realization of the ETRS89, called ETRF89. To avoid time varying coordinates, it was decided that the ETRS89 would rotate, together with the stable part of Europe, so that the station-to-station relations are kept fixed (see [9]). This is, of course, of huge importance for practical applications.
From that date, all successive realizations of the ETRS89 have been computed from the successive ITRFyy realizations by simply rotating the positions back to the place of the European plate at the epoch 1989,0. These ETRS89 realizations are known as ETRF90, ETRF91, ..., ETRF2000. Primary ITRFyy sites will automatically also be primary ETRFyy sites. They are defined to 1 cm accuracy and are consistent with the global ITRS. Coordinates and velocities in any given ITRFyy can be transformed in ETRFyy and vice versa using transformations formulae are available at: ftp://lareg.ensg.ign.fr/pub/euref/info/guidelines/REF.FRAME.SPECIFV4
The GRS80 ellipsoid was adopted in conjunction with ETRS89.

The transformation of national coordinates to other systems requires at least three, but better 6-8, identical points in both reference systems (e.g. national reference system and ETRS89). Taking into account that the ETRF89 only comprised 37 "primary" sites, EUREF decided already in the beginning that the ETRS89 had to be densified using GPS campaigns of finite duration. These campaigns, typically one or two weeks of GPS observations, were conducted from 1989 and are still now carrying on. Since the last ETRS89 realization (ETRF2000) comprises more than 100 sites, the number of densification campaigns has been reduced (see ftp://lareg.ensg.ign.fr/pub/euref/ ETRF2000.SSC).

On November 29 and 30, 1999 the EC organized a "Spatial Reference Workshop" in Marne-la-Vallée, France. The main topic was to examine the options and issues related to a European Reference System for spatial information. During this workshop, it became clear that the ETRS89 had been adopted by some European Agencies, Civil Aviation, industry, etc and is already part of the legal framework of some EU member states.
Some of the major conclusions of the workshop were the following recommendations to the EC:

• To adopt ETRS89 as the geodetic datum for the geo-referenced coordinates of its own data;
• To promote the wider use of ETRS89 within all member states;

This means that the ETRS89 has become de facto standard for the European Union, a major breakthrough in the promotion of a common reference system
The acceptance of ETRS89 ment that there was an even more urgent need for transformation formulae and the capability to compute transformations between the national systems and the ETRS89 standards, at least with an accuracy of 1 to 2 meters. A common initiative of EuroGeographics (former CERCO and MEGRIN, Europe's National Mapping Agencies working for the European Geographic Information Infrastructure) and EUREF was set up to collect, validate and make available these parameters. They asked the National Mapping Agencies to provide them with the information for the descriptions of the national Coordinate Reference Systems and for the transformation parameters between the national Coordinate Reference Systems and the European Coordinate Reference System ETRS89. The results of this query have been compiled in a web-based information system at http://crs.ifag.de. It also contains the parameters of the 7-parameter Helmert transformation between the Belgian national system (BE-BD72) and the ETRS89, and this with an accuracy of 30 cm.
More details about the Belgian contributions to EUREF can be found in [4], [5] and [6].

As explained in Section 2.2, the realizations of the ITRS are partly based on GPS. For this purpose, permanent GPS tracking stations distributed all over the world are used. These permanent GPS stations are part of global or regional GPS networks. This ensures that they all comply with similar standards for site monumentation, receiver and antenna equipment, data exchange format and maintain up to date auxiliary data.
For each ITRFyy realization, different scientific and governmental institutes submit to the IERS the position and velocity estimates for these stations and their covariances. The IERS then uses these estimates, together with position and velocity estimates obtained from other space geodetic techniques, to compute the "primary" ITRFyy coordinates and velocities for each of the sites included in the submitted solutions. In this way, the permanent GPS networks provide users with a direct link to the ITRFyy. They also form the backbone to compute densification points using the relative GPS surveying technique explained in the introduction. In what follows, we concentrate on permanent GPS networks contributing to the ITRS. The international scientific community has made, since 1991, a considerable effort to promote international standards concerning GPS data acquisition and analysis. This effort resulted in the creation of the International GPS Service (IGS). The IGS became a fully operational service in 1994, under the umbrella of the IUGG.
The primary purpose of the IGS is to make available the necessary products to allow high accuracy geodetic and geophysical applications using GPS. The IGS components are globally distributed permanent GPS stations (see Figure 2), data centres and data analysis centres. We refer the interested user to the web site of the IGS Central Bureau at http://igscb.jpl.nasa.gov/
Based on voluntary contributions from organisations all over the world, the main IGS products are:

• The data of the IGS tracking network
• Accurate positions and velocities for the IGS stations
• Precise satellite orbits
• Earth Rotation Parameters: polar motion and the Length of Day (LOD)

Table 1 gives a brief overview of the estimated quality of these different IGS products at the beginning of the year 2001.


Similar to the GPS broadcast navigation message which presently is given in the WGS84(G873) reference, the IGS orbits refer also to a specific reference frame, namely the ITRF. Throughout the years the IGS orbits have followed the different ITRF realizations as given in Table 2.





Since 1991, position and coordinate solutions obtained for IGS sites have been submitted and included in the ITRS realizations. Consequently, all stations belonging to the IGS network are "primary" ITRFyy reference stations.

In 1995, EUREF realized that the growing number of permanent GPS stations distributed all over Europe could be used (similar to what the IGS was doing) to submit solutions to the IERS. A direct result would be that all these stations would become "primary" ITRFyy and ETRFyy stations. It is clear that the accuracy of the "primary" reference stations, whose coordinates are based on permanent tracking, would be better than the accuracy of the densification sites based on EUREF densification campaigns of finite duration.
In accordance with the IGS, the EUREF organized its "EUREF Permanent GPS Network" (called EPN) consisting of the following components: permanent GPS stations, Local Data Centres, Regional Data Centre, Local Analysis Centres, Regional Analysis Centre and a Network Coordinator.
Today, the EPN comprises almost 130 GPS stations (see Fig. 3). The stations fulfil the EUREF specifications before they obtain the label of a permanent EUREF station. The criteria are strong in order to ensure data quality, the timeliness and the reliability of the provision of data, the stability of monumentation and the availability of documentation. The EPN has a full data handling service: GPS data provision is required on daily basis via local data centres to the regional data centre. Some stations provide data files every hour. Fifteen local analysis centres guarantee the routine processing of all GPS data. The coordinate results show an accurate and consistent network (+/- 3 mm in the horizontal component, +/- 6 mm in the height component).


Since 1997, the EPN has been submitting coordinate and velocity solutions for its network to the IERS. As a result, the EPN stations are included in the ITRF97 and ITRF2000 realizations and they form a European network of "primary" ITRS reference stations. Additionally, as explained in Section 2.4, they will, by removing the rotation of the European plate since 1989, form the "primary" ETRS89 network.
All information related to the EPN is available at the web site of the EPN Central Bureau: http://www.epncb.oma.be, maintained by the Royal Observatory of Belgium (ROB) (see also [7]). As EPN Central Bureau, the ROB is responsible for the long-term day-today management of the EPN. In addition, the ROB also operates an EPN Local Data Centre (ftp://epncb.oma.be/gps_rob/data) and an EPN Local Analysis Centre (see [17]).
In 1989, a EUREF densification campaign (introduced in Section 2.4), called EUREF-89, covered Western Europe and included also the Belgian territory. Three sites (Brussels, Oostende and Arlon) were observed by the NGI (National Geographic Institute) and the ROB. This campaign was a densification of the original ETRF89 and had a 5cm coordinate accuracy.
In 1993, the Royal Observatory of Belgium installed four permanent GPS stations located in Brussels, Dourbes, Dentergem and Waremme. These GPS tracking stations have been observing in permanence since that time and have been included in several campaigns and international permanent networks.
One of these stations, the one in Brussels, has been included in the IGS since November 1993. As a consequence, it has been a "primary" ITRFyy station since the ITRF93 realization.

In 1994, a second EUREF densification campaign covered Belgium, the LUXBD94 campaign. The campaign included the four ROB permanent tracking sites and also the sites included in the EUREF-89 campaign (Arlon and Oostende). LUXBD94 was carried out to improve the poor results of the EUREF-89 campaign. This campaign was a densification of the ETRF92 and the resulting site coordinates showed 1cm accuracy. The campaign coordinates, together with the coordinates of all other EUREF campaigns, are available at http://www.geo.tudelft.nl/mgp/euref/

In March and April 1994, the BEREF network, consisting of 36 markers (from whom 4 permanent ROB tracking stations), was observed by the NGI (see Fig. 4). The BEREF network coordinates have been tied to the ETRF92 coordinates from the LUXBD densification campaign ([19]) for the 6 Belgian sites and one additional Dutch site. The standard deviation of the resulting ETRS89 coordinates is 1 cm.
With precise observations, 33 of the 36 markers were tied to first order triangulation points. To all the BEREF markers high precision spirit levelling was conducted to determine the height above sea level. Finally, both precise ETRS89 coordinates and high order Lambert 72 coordinates (the national grid based on the international ellipsoid) were obtained. The knowledge of both sets made it possible to derive the seven parameters needed for transformation between the two reference systems.
As a second application the NGI integrated the BEREF points in the network of geodetic ground markers ( about 4000 points) which led to a set of ETRS89 coordinates for all of them. However, this is a temporary solution, since it has been carried out in different parts (of about a province each, as soon as all observations became available during the densification of the national geodetic network). By mid 2002 the network densification will be completed and a complete readjustment of the whole network at once will be computed. This should lead to the final and most homogeneous ETRS89 coordinates for the geodetic ground markers (P. Voet, personal communication).



In 1996, at the start of the EPN, the four permanent ROB stations were included in the EPN network. Thanks to EUREF's submissions to the IERS, these stations have become "primary" ITRS and ETRS89 stations and this from the 1997 realizations on.

For comparison, we have displayed in Table 3 the coordinates of Brussels in the different ITRFyy. Since for each of the ITRFyy the station coordinates and velocities refer to a specific epoch, we have used the velocities to extrapolate them to a common epoch, January 1st 2002. All ITRFyy, except for the ITRF93, agree at the 1-3 cm level.





In Table 4, we have shown the coordinates of the station Brussels in the different ETRS89 realizations: except for the ETRF93, they all agree at the 1-3 cm level.



For Brussels, the difference between the present-day ITRFyy and ETRFyy coordinates, comprises respectively -21.1, 17.3 and 17.3 cm in the (X, Y, Z) components. Taking into account that ITRFyy coordinates are moving due to the motion of the Eurasian plate, this difference grows each year with about -1.2, 1.7 and 0.9 cm in the (X, Y, Z) components.

Each of the different realizations of the ITRS and ETRS89 forms a consistent frame at the 1cm level. However, as seen from Table 3 and 4, the different frames, even referring to the same system show coordinate differences up to 4 cm. Therefore they may not be mixed, e.g. do not mix ETRF_BEREF with ETRF2000.
When coordinates from frames relating to different systems, such as ITRS and ETRS89 are used in the same network adjustment, then high accuracy applications (mm-cm) are not possible.


As explained in the Introduction, GPS-based coordinates can be computed using absolute positioning and relative positioning.

In the case of absolute positioning, the reference frame of the a priori orbits used will determine the reference frame of the surveyed point. In practice, satellite orbits are available in the WGS84 (broadcast navigation message) and the ITRS (IGS orbits).
Using the broadcast navigation message, the accuracy of the absolute code point positioning, even with Selective Availability (SA) off, will be limited to +/- 15 to 25 m at the 95% confidence level [8]. Tests, using a 24-hour data set, have shown that by averaging the results, the accuracy of the WGS84 coordinates can be further reduced to 6.3 m at the 95% confidence level [15].
When computing ITRS coordinates, the IGS orbits should be used. Based on one year of daily code observations at Brussels, our experiments have shown that the most accurate absolute point positions are obtained using the IGS precise orbits and 24-hour data sets and this by processing the ionospheric free code observables. These daily coordinate solutions have sub-m repeatabilities and a comparison with the known "primary" ITRFyy coordinates of Brussels shows also an agreement better than 1 m.
We know that on one hand, the ITRFyy agrees with the last realization of the WGS84 at the few cm level, and on the other hand, the ITRFyy can be transformed into the ETRFyy without altering the accuracy. Consequently, the method used in our test, will give sub-m absolute positions in WGS84, ETRS89 and ITRS.

When applying the relative positioning method, the quality of the computed coordinates will depend upon:

• The proximity of stations with known coordinates;
• The quality of the a priori orbits used;
• The quantity of the submitted data;
• The quality of the submitted data.

In Belgium, a surveyor will always be within a range of 100 km from one of the four "primary" ITRFxx or ETRFxx stations. If we consider that high quality GPS data are used and 24-hour observation sessions are available, then the orbits error will be of the utmost importance. Using broadcast satellites orbits, with a typical accuracy of 5 m (SA off), the error on the estimated base length will be 2.10-7. This corresponds to 0.2 cm for a 10 km baseline and 2 cm for a 100 km baseline. Using the IGS precise orbits, with an accuracy of 5 cm, the error will be 2.10-9, which is negligible (sub-mm) for all baselines on the Belgian territory. Similar to absolute positioning, using the IGS orbits will always give better results than the broadcast orbits.

If the coordinates at the decimetre level are required, then both broadcast and IGS orbits can be used; additionally, the distinction between the WGS84 and ITRS system is not necessary.

To compute WGS84 coordinates it is necessary to survey relative to the US DoD's GPS tracking stations, which are the only sites with known WGS84 coordinates. However, the GPS data from those DoD stations is not typically available to civilians, which makes it for civilian users impossible to compute WGS84 coordinates from relative positioning.
If WGS84 coordinates are required with an accuracy better than that available from point positioning, we will need to pass through an intermediate reference system. Realizations of this intermediate reference system should coincide with the WGS84(G873) at a level better than the accuracy of the required WGS84 coordinates. A candidate reference system is the ITRS.

The EUREF Technical working group has issued guidelines for the computation of densification points in the ETRS89 (see [1]). These guidelines allow computing coordinates in any of the ETRFyy realizations and guaranteeing the highest homogeneity of different ETRS89 densifications all over Europe; they are as follows: For the computation of coordinates in the NGI realization of the ETRS89, ETRF_BEREF, it will be necessary to replace the ITRF reference stations by one (or several) of the 4000 NGI markers known in the ETRS89 and perform relative GPS surveying with respect to these points. The inconsistency between the reference frame of the satellites orbits (WGS84 or ITRS) and the reference station coordinates (ETRS89) will cause some network distortions of the order of 8.10 ^-9 they are sub-mm for all baselines smaller than 125 km. If the observations are tied to more than one point (known in ETRS89), this small inconsistency will be reflected anyway in, and absorbed by the scale factor estimated during compensation (P. Voet, personal communication). Taking into account that more than 4000 NGI markers are known in the ETRS89, the reference frame inconsistency is negligible in Belgium. This is not always the case in other part of Europe where access to the ETRS89 is limited.

When applying Steps 1 to 5 as given in the theoretical method to compute ETRS89 coordinates, the coordinates computed from step 4 for the densification point will be given in the ITRFyy (at the epoch of observation). This is the reference frame of the precise IGS orbits used at the epoch of observation (see Table 2). As explained in Section 2.2, these coordinates can be transformed in any other ITRFyy. In most cases, no velocity information for the densification point will be available, which means that the ITRFyy coordinates cannot be propagated forward (or backward) in time.


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