Results of GPS reprocessing campaign
(1996-2011) provided by Geodetic

observatory Pecný
Jan Douša, Pavel Václavovic

Research Institute of Geodesy, Topography and Cartography,
Geodetic Observatory Pecný
Ústecká 98, Zdiby 250 66

jan.dousa@pecny.cz

Abstract

The paper presents the GOP first reprocessing results, which officially contributed
to the EPN-repro1 project. It also describes the 15-year GOP cumulative so-
lution providing station coordinates, velocities and their discontinuities over the
period of 1996-2011. Repeatabilities estimated from cleaned long-term coordinate
time-series reached 1-2mm and 4-6mm in horizontal and vertical component, re-
spectively. We then showed the exploitation of GOP reprocessing results in the
assessment of the EUREF ITRF2005 densification and the latest ITRS realiza-
tion, ITRF2008. We identified and confirmed the North-South tilt (≈ 2mas) in
the currently available European reference frame based on the EPN cumulative
solution updated in GPS week 1600. The study showed a historical development
of the tilt and its close relation to a weak velocity datum definition of this real-
ization, which is very important for a long-term datum prediction. Selected EPN
station coordinates, velocities and discontinuities of the latest ITRS realization
(ITRF2008) were also assessed. Specific problems for some EPN stations were
identified in the global reference frame. This emphasized further necessity to check
all the stations before their use for datum definition for regional densifications.

Keywords: Global Positioning System, permanent network, reprocessing, terrestrial refer-
ence frame, cumulative solution, coordinates, velocities, discontinuities

1. Introduction

The EUREF (EUropan REference Frame, http://www.euref-iag.org) is one of the subcom-
misions for regional reference frames of the International Association of Geodesy (IAG). The
EUREF’s main goal is to define, to realize and to maintain terrestrial and vertical reference
systems in Europe. To serve both scientific and practical applications in positioning and nav-
igation, the European terrestrial reference system (ETRS89) has been realized mainly using
GPS observations as they became available at the beging of 90th. The EUREF permanent
network (EPN, e.g. [1]) was proposed by W. Gurtner in 1995 [2] in order to provide a con-
tinuously operating ground-based infrastructure for such realization of ETRS89. Since that
time EPN has developed from 40 stations (1996) to about 300 stations today (September,
2012), almost regularly distributed over Europe and the surrounding areas.

In order to handle a unique and common solution for all EPN stations, a distributed pro-
cessing scheme of GPS data was organized from the beginning. EUREF subnetworks, rou-
tinely processed by 17 local analysis centers (LACs) on a weekly basis, contribute to an EPN

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Douša J., Václavovic P.: Results of GPS reprocessing campaign (1996-2011)

weekly combined product. European terrestrial reference frame (ETRF), which represents a
realization of ETRS89, is based on a long-term combination of EPN weekly solutions. Such
combination includes the estimation of station coordinate changes per year (later referred
simply as ’velocities’) in addition to reference coordinates at a central epoch. Together with
a global terrestrial reference frame (labeled as ITRF<year>), which is maintained by the
International Earth Rotation and Reference Systems Service, IERS [3], European reference
frame (ETRF<year>) is established based on densification solutions provided by EPN.

During years, however, the GNSS data analysis of global (and regional) networks were affected
by different factors due the updates of reference system realizations, processing models, anal-
yses strategies and software packages. Precise products provided by the International GNSS
Services (IGS, [4]) – orbits, Earth Rotation parameters and clock corrections – are dependent
on the factors available at the time of generating these products. Thus the global products
are not consistent over the past period (1996-2012) and, consequently, also the coordinates
estimated by the EPN LACs. Inconsistencies in the time series of the coordinates appear
whenever reference frame or commonly adopted models were changed. Global reprocessing
activities were started by the Potsdam-Dresden Group [5] and later provided also by other
analysis centers in IGS-repro1 project [6] coordinated by IGS. The global reprocessing activ-
ities included the generation of improved global products labeled as IGS-repro1 products.

In the meantime some LACs of the EPN also started regional reprocessing activities in or-
der to provide initial solutions homogeneous over a whole period, i.e. without changes in
reference frames, global products, processing strategy or applied models. A plan of the co-
ordinated reprocessing activity, spanning over period 1996–2009, was agreed at the EUREF
LAC workshop in October 2008. The redistribution of EPN stations was organized (not all
LACs were able to contribute), historical archive established, benchmark campaign prepared
and evaluated and processing strategies agreed. The solutions of individual subnetworks were
then finished in 2011 and combined EPN weekly solutions prepared. The densification of
up-to-date global terrestrial reference frame (ITRF2008) could be thus based on a long-term
combination of all European stations.

The Geodetic observatory Pecný (GOP) has contributed to EPN as a EUREF local analysis
center since January 1997, see [7]. In 2010-2011, GOP LAC processed an extended subnetwork
for the EPN reprocessing project. This paper describes daily/weekly GOP solutions and a
long-term cumulative (Sec. 2). The GOP-repro1 results were then exploited in the assessment
of European ITRF2005 densification based on the EPN cumulative solutions (Sec. 3) and in
the assessment of station discontinuities available from the latest terrestrial reference system
realization, ITRF2008 (Sec. 4). Section 5 sums up with concluding remarks.

2. GOP-repro1 solution

This section gives a brief summary of the GOP-repro1 solution which was prepared using
the Bernese GNSS software V50 [8] and an in-house developed processing engine. At the
first level the processing was carried out by analysing daily data batches and followed with
combinations of daily solutions into weekly ones. Figure 1 shows the EPN stations processed
by GOP for the EPN-repro1 project. The original subnetwork (stations marked in black) was
extended to support the EPN-repro1 requirements that each station is processed by three
analysis centres at least.

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Douša J., Václavovic P.: Results of GPS reprocessing campaign (1996-2011)

Figure 1: Map of GOP subnetwork extended for the EPN-repro1 project. Different colors
shows processing clusters and black color shows the stations from the routine GOP contribu-
tion to EPN.

2.1. Processing strategy

The global IGS-repro1 products (orbits and Earth rotation parameters) were estimated using
the IERS 2003 Conventions [9]. Fixing these global products in regional daily reprocessing,
consistent conventions and models needed to be applied, which was followed in most cases,
but these two: (1) models were not supported by the latest release of the software package
(e.g. the newest tropospheric models in the Bernese GNSS software V5.0), (2) individual
antenna calibration models used in EPN, while the IGS follows type-specific models only.

The daily processing consists of the following steps – converting input data and products;
preparing a priori coordinates and information; synchronizing receiver clocks; generating sin-
gle differences over baselines while keeping a maximum number of observations; cleaning data,
detecting cycle slips (based on triple-difference approach) and setting ambiguities; screening
post-fit residuals and detecting outliers; selecting fiducial stations for datum definition; re-
solving integer ambiguities; generating ambiguity-fixed daily solutions. The weekly products
then include combinations of correspoding daily solutions based on a normal equation stack-
ing procedure. The tropospheric products are finally generated for each day of a week based
on a fixing weekly coordinates in new daily adjustments.

The success of resolved integer ambiguities using the QIF strategy [10] is shown in Figure 2.
It is strongly seasonally dependent, however, a significant decrease of the percentage of fixed
ambiguities is also visible during 1997-2003 which could be partly attributed to the high solar
activity (with maximum in 2000) and partly to the lower quality of GPS observations and

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Douša J., Václavovic P.: Results of GPS reprocessing campaign (1996-2011)

Figure 2: Success of integer ambiguity resolution over processed period

products before 2000. The results of daily and weekly solutions (normal equations) providing
station coordinates were archived in the SINEX (Solution INdependent EXchange) format in
order to provide official contributions to EPN-repro1 project and in Bernese binary (NQ0)
format to support GOP long-term stacking of weekly normal equations.

2.2. Daily and weekly coordinate time-series

Daily and weekly solutions provide estimated coordinates of all processed stations in epochs of
minimum variance (in ideal case equal to a central epoch of processed data period). Because
the subnetwork has a regional extent only, a no-net translation (NNT) condition for a priori
coordinates of selected fiducial stations was applied for datum definition. For each daily
and weekly solutions, the individual set of consistent fiducial stations was iteratively selected
from the a priori list of reference stations. This enabled us to visualize coordinate time-
series in a single geodetic datum and to identify immediately most of the problems related
to indidivual station performances. Figure 3 gives only a few examples for six stations: (a)
GOPE – instrumentation change, (b) HFLK – seasonal variation probably due to a cumulating
snow/ice on top of the antenna radome, (c) OBE2 – a poor data quality, (d) DRAG - station
outside the Euroasian tectonic plate, (e) TUBI – non-linear post-seismic station movement and
(f) MAR6 – post-glacial uplift in Fennoscandia. These plots were useful for the preparation of
GOP long-term cumulative solution and in particular for the definition and revision of station
coordinate and velocity discontinuities.

2.3. GOP long-term solution (1996-2011)

A 15-year solution was based on a cumulative combination of weekly normal equations, where
only coordinates were kept in normal equations. The tropospheric parameters and ambiguities
were pre-eliminated during weekly combinations. However, we cannot keep the coordinates
constant over a long-term period and we need to apply at least a linear model (i.e. velocity)
for each coordinate component. In some cases where non-linear trend in individual coordinate
time-series exists (e.g. TUBI in post-seismic period, see Figure 3), a piece-wise linear model
need to be applied.

The velocity parameters for all stations are thus introduced into the normal equations just
before stacking weekly solutions and generating a unique cumulative one. The velocities can
be estimated thanks to the applying long period during which the coordinates significantly

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Figure 3: Example of coordinate time-series for six EPN stations from GOP daily solutions

Figure 4: Cleaned coordinate time-series from the final cumulative solution

Figure 5: Coordinate repeatabilities of the GOP final cumulative solutions

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Figure 6: Residuals velocities with respect to ITRF2005

change (decorrelating the velocity estimation from the coordinates). For the stations with
too short periods (usually less than a year), the velocities could be either constrained to some
well-known a priori values or they are estimated with large formal errors showing correctly
large uncertainties. A long-term solution was prepared based on the folowing steps, which
might be individually re-iterated if necessary:

• 1st step : check residuals and indentify bad data periods
• 2ndstep : setup discontinuities for coordinates and velocities
• 3rdstep : select the best set of fiducial stations and provide final solution

A final solution is achieved after a careful cleaning of all poor data (usually identified as
outliers or based on other external knowledges) and after setting discontinuities for all cases
when station coordinates or velocities show significant jumps. Cleaned coordinate time-series
(Figure 4) are results of such final solution, which already provides homogeneous repeatabil-
ities for all station coordinates (Figure 5). In our solution, the repeatability was 1-3mm and
4-6mm for the horizontal and vertical component, respectively. The highest repeatabilities
are clearly found at the station HFLK (on top of the Alp mountain) and those stations lo-
cated at the margins of the network (stations QAQ1, REYK, MORP, TRO1, KIR0, SVTL,
DRAG, NICO, TRAB, ZECK). This is due to their isolations (long-baselines) as well as less
contributing observations. The datum of the GOP final solution was defined using a set of 18
stations. The maximum residuals after applying Helmert transformation (using translations
only), between a priori and estimated coordinates, were below 5mm in horizontal and 15mm
in a vertical components.

The estimated velocity differences with respect to the motion of the Eurasian tectonic plate
(Figure 6) demonstrated stable changes of coordinates for most of the stations (usually below
1mm/year). This indicates a stability of the tectonic plate with respect to some others in

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Douša J., Václavovic P.: Results of GPS reprocessing campaign (1996-2011)

Figure 7: Residuals from the Helmert transformation at epoch of September, 7, 2010 (GPS
week 1600) between the EPN cumulative solution (EPNC, updated at GPS week 1600) and
EPN weekly solution (1600). Left: 7 parameters; Right: 3 translations (translation).

the world. However, we could clearly observe such geophysical phenomenas like: (a) post-
glacial uplift in Fennoscandia, which is of different magnitude for various stations, (b) a
single station in Greece representing a drift in the South–West direction common to most
of the Greek islands, (c) non-linear post-seismic relaxation (modelled by piece-wise constant
velocities) for TUBI station after the Izmit earthquake in 1999 (Mw 7.4).

3. Evaluation of European ITRF2005 densification

On November 5 2006, the IGS adopted new reference frame (ITRF2005) and new model
for antenna phase center offsets and variations (PCV, IGS08) for its global orbit and clock
products. This change caused jump at that epoch for almost all EPN station coordinates.
The velocity estimation should not be teoretically affected if discontinuities are correctly setup
and thus only velocities could provide a datum for the prediction of coordinates over a period
of 3-6 years later (i.e. before a new ITRS realization was available).

The preparation and maintenance of the ETRS89 realization is one of the tasks of the EUREF
Technical Working Group (TWG). Any further densification of ETRS89 on national level is
also usually validated by the EUREF TWG. During 2010, several national densifications cam-
paigns were validated: EUREF-2009-IR/UK, EUREF-2010-Czech and EUREF-2010-Serbia.
Except EUREF-2010-Czech, which concerned a solution over three years [11], the others
showed a North–South tilt from the coordinate residuals of Helmert transformation when
applying (a) 3 translations + 3 rotations + scale or (b) 3 translations only. The reason was
not known at that time, but the first impression was that the problem was not related to the
campaigns themselves, but to the cumulative EPN solution providing a last realizion of the
ETRS89. Consequently, an action item was raised to identify this problem.

We could use the GOP-repro1 as an existing historical homogeneous solution for more deep
study, however, at the first stage we tested for which EPN stations the North–South tilt can be

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Figure 8: time-series of estimated Helmert parameters between EPN weekly and EPN cumu-
lative solutions. All stations used; x-axis represents time in GPS week.

observed. We compared one of the latest combined weekly EPN solutions with respect to the
latest update of the EPN cumulative solution. We used GPS week 1600 and all EPN active
stations from which we iteratively selected a set of ’consistent’ stations to be used as fiducials
for the Helmert transformation. We applied 3 (translations) and 7 (translations, rotations
and scale) parameters in the transformation between coordinates at a reference epoch in the
middle of GPS week 1600 (September 8, 2010). Figure 7 shows the results, which clearly
confirmed a common North–South tilt over all stations between the two solutions of about 2
mas (and additionally a small scale difference). This corresponds to about ±1 cm for heigh
component for stations in North and South Europe for given epoch. Our expectation that
the problem exists in the cumulutive solution was confirmed.

We have then run a similar test for every solution over a whole EPN period of GNSS ob-
servations (1996-2010) with a 10-week step. We should emphasize that the EPN cumulative
solution provided coordinates, velocities and discontinuities at the common central epoch
2000.0, while the EPN weekly solutions provided coordinates at a central epoch of each week.
Before applying Helmert transformations the coordinates of the EPN cumulative solution
were firstly converted (by applying velocities) to the central epoch of EPN weekly solution.
In order to provide a robust estimation of Helmert parameters, all available EPN stations
were set a priori as fiducials while during an iterative procedure all those not consistent were
temporarily excluded. Discontinuities defined in the EPN cumulative solution was necessary
to take into account as well as to apply renaming scheme to compare theoretically identical
stations only.

Time-series of 7 Helmert parameters between the two coordinate sets are depicted in Figure
8. The figure clearly shows jumps in the time-series due to existing inconsistencies in EUREF
weekly solutions over the entire period. The inconsistencies are related to reference frame
changes and different models applied (e.g. at GPS week 1400 antenna PCV model was
switched from relative to absolute calibrations). The figure also shows time-series of Helmert
parameters estimated in a local reference system centered at the geometrical centre of the EPN
network. The North–South tilt, which is represented by the rotation around the East axis in
the local system, has been clearly observed since GPS week 1400. In the global system the
tilt is represented by X- and Z-translations and Y-rotation (not shown here). The figure was
important to prove that we are able to reconstruct Helmert parameter time-series estimated

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Douša J., Václavovic P.: Results of GPS reprocessing campaign (1996-2011)

Figure 9: time-series of estimated Helmert parameters between GOP-repro1 and EPN cumu-
lative solutions. GOP-repro1 stations used only; x-axis represents time in GPS week.

by the CATREF software [12] used during the combination of EPN weekly solutions into a
cumulative one.

Additionally the figure demonstrated that our strategy developed for automated selection of
fiducials was enough robust to achieve the same results as with datum uniquely defined during
the EPN cumulative solution. The same strategy could be then used for the estimating tran-
formation parameters for GOP-repro1 weekly solutions with respect to the EPN cumulative
solution and plotting corresponding time-series. Being a homogeneously reproccessing the
GOP-repro1 solution enabled to reconstruct a full history of estimated Helmert parameters
in a consistent way. Figure 9 shows such smooth time-series not affected by regular updates
of reference frame or antenna calibration model.

The GOP-repro1 weekly products didn’t include all EPN stations, but well covered the ter-
ritory of Europe. We could guarantee the possible replacement of a complete EPN-repro1
solution, which was not available at that time, with the GOP-repro1 since reaching a good
agreement of Helmert parameters estimated for both solutions after GPS week 1400. All
comparisons before GPS weeks 1400 for GOP-repro1 (Figure 9) thus represents a successful
reconstruction of the full historical development of Helmert parameters and also the devel-
opment in the trend of the North–South tilt. From the clear linear trend, the tilt can be
understood as a product of the weak velocity datum definition in original and European
ITRF2005 densifications. And this further resulted in the North–South tilt increasing with
the lenght of the coordinate prediction.

4. ITRF2008 discontinuities assessed using GOP cumulative solutions

The GOP-repro1 cumulative solution gave us an opportunity to assess the latest ITRS realiza-
tion, ITRF2008. The motivation was raised again during the validation of national ETRS89
densification campaigns. The question was wheather the station REYK can be used as fidu-
cial due to a significant coordinate jump in the ITRF2008. Such jump was, however, not
visible in the EPN cumulative solution although an earthquake occured on September 11,
2008 close to the station.

The GOP-repro1 proved that the REYK position was not disrupted by the earthquake and
relevant discontinuity in the coordinate time-series is not necessary. For visualization, we have

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developed a plot schemes showing clearly all instrumentation and reference frame changes at
each station. Additionally, these plots include all setup discontinuities (coordinate offsets)
as they were estimated in various reference frame realizations. Finally, the GOP-repro1
cumulative solution residuals are plotted to show all remaining (unmodeled) effects in the
coordinate time-series. Figure 10 shows an example for station REYK with the specific jump
(September 11, 2008) in coordinates from ITRF2008. The GOP-repro1 residuals before and
after this epoch are smooth although a discontinuity was not setup for this epoch. Another
station showing unrealistic discontinuities of several centimeters was TRDS (Figure 11) from
those included in GOP-repro1 solution.

Besides discontinuities and their comparisons the plots clearly display the inconsistencies in
station availability in various solutions. A limited validity of a coordinate prediction exists
whenever the discontinuities were recently defined and observations from later period were
not available. Figure 10 (REYK) and Figure 11 (TRDS) can represent typical, but not
worst examples. Other examples are MAR6, RIGA and JOEN (not shown) providing an
uninterrupted coordinate time-series over a whole period, but with missing first three years
in ITRF2008.

The above assessments were important to demonstrate the necessity of the careful ITRF2008
station selection for their use as fiducials for regional or national densifications. It also shows
some weak points of a global GNSS solution when considering aspect of regional permanent
stations. The IGS-repro1, which was a basis for a global GNSS contribution to the ITRF2008,
didn’t provide the best solutions for at least the following cases: (1) for stations with missing
data when compared to their official validity (and availability) within the EPN or, opposite,
stations with data excluded from this period (both affecting the quality of estimated velocities)
(2) for stations which discontinuties were not properly handled and, consequently, the station
can not be considered as fiducial for this period or later (meaning that coordinates for specific
periods were not correctly estimated).

5. Conclusion

The paper presented the GOP first reprocessing results, which officially contributed to the
EPN-repro1 project. Additionally, the 15-year GOP cumulative solution was described pro-
viding long-term station coordinates, velocities and their discontinuity estimation. Repeata-
bilities estimated from cleaned long-term coordinate time-series reached 1-2mm and 4-6mm
in horizontal and vertical component, respectively. We then showed the exploitation of GOP
reprocessing results in the assessment of the EUREF ITRF2005 densification and the latest
ITRS realization, ITRF2008.

We identified and confirmed the North-South tilt (≈ 2mas) in the currently available Eu-
ropean reference frame based on the EPN ITRF2005 densification solution (e.g. last EPN
cumulative solution updated in GPS week 1600. The study showed a historical development
of the tilt and its close relation to a weak velocity datum definition in this frame. The
velocity datum is particularly important for a long-term datum prediction when for most
stations discontinuities were setup due to changes in processing strategy. The results of the
tilt study were presented at the EUREF Technical Working Group meeting (Padua, March
2011) and confirmed by new European ITRF2008 densification already based on solutions
from the EPN-repro1 project.

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Figure 10: Coordinates discontinuities for station REYK for various solutions (ITRF2005,
ITRF2008, EPN cumulative solution updated in 1600 and GOP-repro1 for which also residuals
are shown). The changes in reference frames are marked in magenta besides the station specific
instrumentation updates.

Figure 11: Coordinates discontinuities for station TRDS for various solutions (ITRF2005,
ITRF2008, EPN cumulative solution updated in 1600 and GOP-repro1 for which also residuals
are shown). The changes in reference frames are marked in magenta besides the station specific
instrumentation updates.

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Douša J., Václavovic P.: Results of GPS reprocessing campaign (1996-2011)

Finally, selected EPN station coordinates, velocities and discontinuities of the latest ITRS
realization (ITRF2008) were assessed using GOP-repro1 results. Specific problems for some
EPN stations were identified in the global reference frame. This emphasized a further necessity
of careful revision of all ITRF2008/IGS08 stations before their use for datum definition in
regional densifications.

Acknowledgements

This work was partly supported by the Technology Agency of the Czech Republic (TB01CUZK006)
and by the European Regional Development Fund (ERDF), project ’NTIS – New Technologies
for Information Society’, European Centre of Excellence, CZ.1.05/1.1.00/02.0090.

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