by W. Gurtner, Astronomical Institute - University of Bern

1. Introduction

With the results of the EUREF-89 GPS campaign, published in the proceedings of the EUREF Symposium 1992, Western Europe has now available for the first time a uniform set of some 100 reference sites with sub-decimeter accuracy that can be used :

  • for further densification, i.e. for making available the underlying European reference system to local users in a higher density
  • for the extension of the EUREF frame e.g. to Eastern Europe
  • for the determination of transformation parameters between local systems and the European reference system (EUREF-89).

The generation of smaller user networks compatible with or embedded in the (densified) reference frame can be just looked at as a further densification of the reference frame.

In the meantime the International Terrestrial Reference Frame ITRF (which was the "backbone" of EUREF-89) has been further improved. We know that the European SLR and VLBI reference sites are now determined in the ITRF (e.g. ITRF-91) with an (at least relative) accuracy of one centimeter in all three components!

We will focus in this paper on the problems related with the densifications and extension of the existing European reference frame using GPS techniques. A central issue will be the use of the products of the International GPS Geodynamics Service (IGS) for these purposes.

The reference frame issue is of utmost importance in geodynamics networks: The continuous maintenance of a reference frame and its consistent use in the processing of all epoch measurements is a prerequisite for success: Changes in the reference might easily be misinterpreted as crustal motions!

2. Densification of a Reference Frame Using GPS Techniques

Let's assume that we have a certain number of reference sites at our disposal, the coordinates of which define our reference frame.

For its densification by GPS we basically need three things:

a) Observations

We must have GPS phase observations available on the densification sites as well as on at least one of the given reference sites.

b) Software

We need a processing software capable of handling baselines of the actual length with the proper accuracy: The physical and mathematical models used have to be such that remaining modelling errors do not create important errors in the resulting coordinates. Aiming at a uniform one-centimeter accuracy we have to ask for a maximum error of a very few millimeters only.

c) Orbits

We need orbits given in the same reference system as the reference sites or, if this is not the case, at least the transformation parameters between these two systems to be able to perform the necessary transformation. The accuracy of the orbits of course has to be high enough to guarantee the desired accuracy of the resulting coordinates.

Ad a):

Provided no orbit improvement has to be performed we only need observations on one of the reference sites. In order to minimize errors in the baseline we would select a reference site as close by as possible. Using more than one reference site (e.g. 3 to 4 sites surrounding the densification sites) might lead to a certain improvement, both in reducing effects from observation errors on the reference sites as well as from residual errors in the coordinates of the reference sites.

Ad b):

The degree of complexity of the software heavily depends on the actual length of the densification baselines. Commercial dual frequency software (like PRISM, SKI, TRIMVEC) is certainly good enough for short (< 10 km) baselines. The use of this kind of software for medium range baselines (< 100 km) has first to be checked very carefully. The points of concern might be:

  • Cycle slip detection and repair
  • Troposphere (height component of the baselines)
  • Use of "precise ephemerides", i.e. orbits provided by some external source
  • Network capabilities if more than one reference site and/or several densification sites are to be processed simultaneously

High-accurate baselines need special attention if on the two ends different receiver/antenna types are used. This might well be the case if the observations of the permanently operating receivers on some of the reference sites are used! We and others (e.g. [ROCKEN, 1992]) have recently indentified differences in the elevation-dependent phase center variations between different antenna types that may lead to errors in the vertical baseline components of as much as 10 centimeters.

Several groups are currently trying to compile such (at least elevation-dependent) correction tables for the different antenna types. Applying these corrections to the L1 and L2 phase observations will remove or at least considerably reduce such errors. The software used has to be capable of using such correction tables or the data would have to be corrected beforehand (which would need a special program as the elevation values have to be available for the corrections!).

Ad c):

In order to reach the goal of a uniform accuracy of about one centimeter in the three-dimensional position we have to have orbits available with an accuracy mostly depending on the actual baseline lengths between the reference and densification sites:

Baselines of 1000 km ask for an average orbit accuracy of about 1 over 10^8 or about 20 cm. More precisely: The ensemble of the orbits has to be capable of yielding results in the 10-8 order of magnitude. Periodic orbit errors with periods short in comparison with the session lengths might be less dangerous than actual biases or long-term errors.

Such biases might come from differences between the reference system used to determine the orbits and the one of the reference sites. Therefore we have to make sure that the two references are in fact identical. We can achieve this by using the (top level) reference sites with the appropriate coordinates for the orbit improvement, too.

3. Processing of Local Networks

If we want to keep the uniform accuracy of the reference frame even after piecewise densification or after having observed and processed different local networks in adjacent regions we have to make sure that also local networks are processed in a correspondingly consistent way:

We can either look at the processing of a local network as a further step in the densification of the reference frame. By applying the respective rules we can guarantee that the accuracy between neighbouring sites will never exceed the "absolute" accuracy of say one centimeter postulated above.

If we look at the processing of the local network as a sort of independent task we have to look at the following two major error sources in a GPS network:

a) Coordinates of the "fixed station(s)"

Usually one (sometimes several) of the local sites is introduced into the processing with given coordinates. Depending on the error of these coordinates (with respect to the orbit system) the resulting local network may be more or less distorted. The rule of thumb tells us that this error also grows with the size of the local network. If we want to guarantee the centimeter in a 100 km network we have to know the fixed station coordinates relative to the satellite orbits with an accuracy of 1 to 10^7 or roughly two meters. A mere single-point positioning solution using code observations will not be good enough. So, we have to determine the "fixed site" beforehand with an appropriate accuracy. As we want to link afterwards the local network to the reference frame anyway we would better determine the "fixed site" using the densification rules right away!

b) Orbits

In order to guarantee the geometrical accuracy of the network we need orbits with the corresponding accuracy, which again depends on the actual size of the local network, according to the same rule of thumb: One centimeter on 100 km corresponds to about 10^-7 or 2 meters in the orbit. That is an order of magnitude that is hardly reached by the broadcast orbits (it is of no use to split the local network into many short baselines: Although the relative accuracy between neighbouring sites will increase the full network will not be improved at all).

Of course it helps if the orbits are already given in the same reference system as the reference sites. Otherwise we would have to translate/rotate the resulting local network into our reference system using either known parameters or enough common sites.

To conclude: To process the local network before the proper determination of the "fixed sites" (= densification of the reference frame into the local region) only makes sense if the approximate coordinates and the available orbits are checked to be good enough.

4. The International GPS Geodynamics Service (IGS)

An initiative of Prof. Ivan Mueller, Ohio State University, in the year 1990 and subsequent activities of several institutions and individuals lead to the planning and finally to the execution of a global GPS test campaign in 1992 with the goal to test the feasibility of a continuously operating civil service providing the scientific community with high-quality GPS orbits accurate enough to perform geodynamic geodesy everywhere on Earth.

The 3-months test campaign (IGS'92) had some 30 P-code receivers permanently operating on all 6 continents the data of which was daily collected in compressed RINEX files by special data centers and forwarded to about 7 processing centers in the US, Canada, and Europe.

Processing Centers during the IGS Testcampaign
Name Location Software
CODE Berne "Bernese"
EMR Ottawa, Canada Gipsy
GFZ Potsdam EPOS.P

CODE (Center for Orbit Determination in Europe) is a joint project of

  • Astronomical Institute, University of Berne
  • Institut Geographique National, Paris
  • Institut für Angewandte Geodäsie, Frankfurt
  • Bundesamt für Landestopographie, Wabern

Most of the sites have been part of already existing tracking networks as e.g. CIGNET, PGGA (California), Canadian ACPs, JPL's DSN and FLINN). Other sites came into operation just shortly before or even during the campaign.

The processing centers computed orbits, earth rotation parameters (ERPs), and coordinates of non-fixed permanent sites and made available the products to the user community directly or again through the special data centers. The ERPs have also been sent to the International Earth Rotation and Reference Systems Service (IERS) for inclusion into their compilation of the ERP series.

Presentations at special IGS sessions of the DOSE meeting in Greenbelt in October 1992 and of the fall'92 AGU meeting in San Francisco and then at the IGS workshop in Berne in March 1993 showed that the quality of the orbits leads to daily repeatabilities on long baselines (> 1000 km) of a few millimeters to one or two centimeters only. The agreement of GPS solutions in Europe with the SLR/VLBI-derived coordinates (ITRF-91) turns out to be in the one-centimeter region!

The campaign was such a success that the IGS oversight committee and the participating organizations decided to continue operation without interruption under the name "IGS Pilot Service". Later this year IAG will be proposed to establish a permanent service (IGS). It is expected that IGS may start operation under the final status early 1994.

End of March 1993 the US National Geodetic Survey joined the group of the IGS Pilot Service Processing Centers.

The products of the test campaign and the Pilot Service are available for scientific users, national geodetic surveys, and other interested parties directly at the processing centers or at some of the data centers. They can be downloaded in most cases through Internet using the FTP file transfer protocol.

The products are stored in ASCII files with the following naming conventions:

Naming conventions for the IGS products
Ephemeris Files : cccwwwwd.EPH
ERP Files : cccwwwwd.ERP
Summary Files : cccwwwwd.SUM
ccc : 3-character code for the processing center
wwww : GPS week
d : Day of the week
(0=Sunday,...,6=Saturday,7=whole week)

The ephemeris files contain earth-fixed positions of the GPS satellites, either in the well-known SP1 format of the "NGS precise ephemerides" or in the newer version SP3. The reference frame upon which the satellite positions are based should be ITRF-91 at the epoch of the observation.

IfAG Frankfurt also makes available some of the products at their GIBS bulletin board.

The products of the CODE are available in Berne through anonymous ftp at the internet address in the directory [ASTRONOMY.CODE].

The compressed RINEX observation files are also available to interested users. European users address themselves to the Regional Data Center IfAG for European data or to the IGS Global Data Center at IGN, Paris for non-European data.

The use of the IGS products, especially of course the high-precision orbits, will

  • remove the burden of individual orbit improvements
  • lead to high-precision large to medium size densifications or other geodetic/geodynamic applications
  • guarantee the adherence to a stable reference system, thanks to the long-term maintenance of ITRF by the IERS / IGS activities.

5. How to Use the IGS Products for EUREF Densifications

In order to properly use the IGS products for EUREF densification purposes we have to observe a few rules or principles:

Phase center variations
  • A densification should be done only if the differences in the elevation-dependent phase center variations are known to be small enough to be neglected or if they are known and can be taken into account by the processing software.

The orbits are given in earth-fixed coordinates, based on ITRF-91, at the actual epoch:

  • All reference sites the coordinates of which will be kept fixed during the densification process may have to be shifted into the proper epoch first. We therefore have to know their velocities in the respective reference frame.
  • The resulting coordinates of the densified sites belong to the actual epoch. They may only be transfered back to a common epoch (such as 1989 in the case of EUREF-89) if their velocity vector can be assumed to be known.
Earth Rotation Parameters

The orbits are given in earth-fixed coordinates. Software that merely interpolates the ephemerides to the proper epochs does not need additional Earth rotation information. Software however (such as the "Bernese") that transforms the ephemerides into the inertial space and performs the interpolation using dynamical models needs to know the current coordinates of the Earth's pole and UT1-UTC in order to be able to do the transformation correctly.

Theoretically the values to be used should be the same ones used by the processing centers when they created the earth-fixed ephemerides. In practice however it is not too critical:

  • We recommend to use the official IERS Bulletin B values. ERP files compatible with the "Bernese GPS Software" are available, together with the orbits, at CODE.
Proposed Procedure for the Densification of ETRF coordinates
a) IGS orbits
  • refer to ITRF-TI (TI being the ITRF realisation the processing centres have been using, such as '91) and
  • refer to the epoch TO, i.e. to the actual epoch of the observations (such as 1993.4)
  • the coordinates of the reference stations have been previously shifted from the reference epoch of ITRF-TI to the epoch TO using velocities contained in ITRF-TI (e.g. ITRF-91 from 1988.0 to 1993.4)
b) Densifications/Extensions using IGS orbits:
  • Convert all reference sites to be used for the densification given in ETRF-TE from the reference epoch TR of ETRF-TE to the epoch of densification TO, using given velocities in ETRF-TE! (e.g. ETRF-89 from 1989.0 to 1993.4)

The velocities of sites in the rigid part of Europe should be nearly zero.

  • Transform these coordinates to ITRF-TI using given transformation parameters between ETRF-TE and ITRF-TIat epoch TO (e.g. ETRF-89 to ITRF-91, both at 1993.4).

These parameters are time-dependent, they reflect e.g. the fact that the ETRF is tied to the rigid part of the European plate.

  • The immediate results of the densification/extension process are given in the same reference (ITRF-TI at epoch TO, as above). (e.g. ITRF-91 at 1993.4)

In order to be able to express the results in the European Reference Frame TE (e.g. in ETRF-89) we have to:

  • transform the results from ITRF-TI at epoch TO to ETRF-TE (e.g. from ITRF-91 to ETRF-89, both at 1993.4)
  • shift the ETRF-TE coordinates from TO to the desired reference epoch TR (such as 1989.0) using velocities given for ETRF-TE (e.g. ETRF-89 from 1993.4 back to 1989.0)
d) Rigid Plate Model

According to a EUREF resolution the ETRF is locked to the "rigid" part of Europe. Therefore EUREF has to define what part of Europe this is. Such a definition certainly is only valid for a limited time. ETRF has to move with this part of Europe. To attenuate the effects of noise in the individual velocities a best-fitting motion of a rigid plate model should be computed. What comes out of it is part of the time-dependent transformation parameters between ETRF-TE and ITRF-TI.

e) Necessary Parameters

The user who wants to perform densifications/extensions needs concrete in structions how to perform all the above transformations and shifts:

  • Time-dependent transformation parameters between each ITRF-TI and ETRF-TE
  • Transformations between different ITRF solutions might be necessary, too.
  • Coordinates and velocities of the reference sites (including the IGS tracking sites) in the ETRF-TE reference frames.

The EUREF-89 set of coordinates are expected to have an accuracy of about 2 cm for the SLR/VLBI sites and about 4 centimeters horizontally and 6 centimeters vertically for the GPS sites (the EUREF-89 coordinates of the SLR/VLBI sites are identical with ITRF-89 at epoch 1989.0). From investigations with the IGS data set we know that the ITRF-91 are definitely better than the former ITRF-89 set.

In order to transfer the higher quality of the newer ITRF reference frame into the densification process we recommend using as fixed sites for the first densification level the permanently operating or regularly re-visited SLR/VLBI sites within the range of about 1000 km around the densification sites together with their ITRF-91 (or later) based ETRF. Therefore we also need such a list of improved initial ETRF coordinates. It can be generated by transforming the latest ITRF coordinates to ETRF and shifting them to the proper reference epoch using the above-mentioned transformation parameters and velocities.


Boucher C., Altamimi Z., Duhem L.: ITRF-91 and its associated velocity field (IERS Technical Note 12, Oct 1992, Observatoire de Paris).

Brockmann E., Beutler G., Gurtner W., Rothacher M., Springer T.: European solutions and results at the Center for Orbit Determination in Europe (CODE) during the 1992 IGS Campaign (Proceedings of the IGS Workshop, March 24-27 1993; Bern).

Gurtner W., Fankhauser S., Ehrnsperger W., Wende W., Friedhoff H., Habrich H., Botton S.: EUREF-89 GPS Campaign - Results of the Processing by the "Berne Group" (Report on the Symposium of the IAG Subcommission European Reference Frame - EUREF - in Berne, March 4-6, 1992; Section: Reports of the International Computing Centres - ICC's).

Mueller I., Beutler G.: The International GPS Service for Geodynamics - Development and Current Status (Proceedings 6th International Geodetic Symposium on Satellite Positioning, March 1992, Columbus, Ohio).

Rocken Ch.: GPS Antenna Mixing Problems (Nov 1992, UNAVCO Memo).