3 Daily processing

The processing was carried out using the Bernese GPS software V5.0 [Dach et al. 2007]. The strategy was based on the system developed at Geodetic Observatory Pecný (GOP) for the EUREF Permanent Network analysis. Only GPS data were used in the campaign, because only a few stations in the Czech Republic provide GPS+GLONASS observations and these are mostly equipped with problematic ASHTECH Z-18 receivers.

The main steps of the daily processing consist in:

Data and product conversion and a priori coordinates and input files preparation

Single point positioning based on pseudo-range observations (receiver clock synchronization)

Baseline definition using OBS-MAX strategy in clusters and baselines connecting the clusters

Triple-difference solution applied for data cleaning, cycle slip detection and ambiguity setting

Ambiguity-float solution for post-fit residual screening and outlier rejection

Iterative ambiguity-float solution for the selection of fiducial stations (datum definition)

Integer ambiguity resolution based on the QIF strategy

Ambiguity-fixed daily solution applying no-net translation (NNT) based on selected fiducial stations

3.1 Processing clusters

To complete data processing of 4 years within a few days a highly optimized processing scheme was prepared. This was achieved by splitting the network into clusters of a suitable size for parallel processing. Small clusters (4-8 stations) were designed for the ambiguity resolution and outlier rejection while large clusters (approximately 20 stations) usually for all others steps. Each processing step running in parallel ended with a combination, checking or summary extraction procedure.

3.2 A priori coordinates

A priori coordinates used in daily processing were prepared by merging the coordinates from three sources applied in a given order with an identification flag:

• Last IGS (or ITRF) realizations converted to the epoch of processed day using velocities consistent with coordinates
• Preliminary coordinates available from any previous solution (no velocities applied)
• Coordinates available in RINEX files (no velocities applied)

The coordinates were expressed in the epoch of processed day according to their velocities if available.

3.3 Orbits and Earth Rotation Parameters

Final IGS orbits and ERPs were fixed in the daily processing. The IGS final product is based on relative models of satellite and receiver antenna phase centre variations (PCV) before GPS week 1400 and on absolute PCV models starting with GPS week 1400. The absolute models were used in the campaign processing over the whole data span whereas the most important was to apply a consistent model for both satellite and receiver antennas. The satellites with zero accuracy codes (a few cases only) were a priori excluded from the processing. Nevertheless, our procedure independently checks residuals in order to identify any problematic satellite orbits.

3.4 Other external products and models

Applied models were consistent with the IERS 2003 conventions:

IGS final orbits and ERPs	ftp://cddis.gsfc.nasa.gov/gps/products/www/igswwwd.sp3.Z ftp://cddis.gsfc.nasa.gov/gps/products/www/igswww7.erp.Z
Ionospheric model	ftp://ftp.unibe.ch/aiub/CODE/yyyy/CODwwwwd.ION.Z
Antenna PCV	ftp://ftp.epncb.oma.be/pub/general/epn_05.atx http://czepos.cuzk.cz/_paramAnten.aspx
Ocean tide loading	http://www.oso.chalmers.se/~loading/ (model FES2004, no CMC corrections)
IGS05/ITRF2005	ftp://itrf.ensg.ign.fr/pub/itrf/itrf2005/ITRF2005.SNX.gz ftp://igscb.jpl.nasa.gov/pub/station/coord/IGS05.snx
EPN cumulative solution	ftp://epncb.oma.be/epncb/station/coord/EPN/EPN_A_ITRF2005.SSC (EPN_A_ITRF2005_C1570)

3.5 Observation sampling, weighting and elevation cut-off angle

The 3 degree elevation cut-off angle was applied in all steps of the processing, but 10 degrees in the step for integer ambiguity resolution. By including low-elevation angle observations the estimation of horizontal troposphere gradients was supported (see Troposphere modelling). Observations with 30 sec sampling interval and the elevation dependent weighting function were used in pre-processing and 180 sec in final processing.

3.6 Ionosphere modelling

Wherever possible the first-order effect of the ionosphere was eliminated using ionosphere-free linear combination (single point positioning based on code observations, pre-processing for the cycle slip detection and outlier rejection and final modelling of the GPS observations for normal equation generation). The second- and third-order effects were neglected in the processing. While the estimation of the ionosphere model is also a part of our routine system, in this campaign the final CODE model was introduced to support the ambiguity resolution (see Ambiguity resolution).

3.7 Troposphere modelling

In pre-processing steps the troposphere effects were modelled with site-specific station parameters applying a simple tropospheric model and mapping function. In all steps requiring the highest accuracy of observation modelling, the following parameterization was applied (gradients were estimated only in the ambiguity-fixed solution):

• A priori model by Saastamoinen (1972), standard atmosphere and Niell dry mapping function (Niell, 1996). Loose constraints (5m) were applied for a priori values.
• Corrections estimated for each station and 60-min interval applying Niell wet mapping function (Niell, 1996). Loose relative constraints (1 m) were applied to subsequent values.
• Tropospheric horizontal gradients estimated for each station and 24-hour interval.

The troposphere parameters were pre-eliminated before saving daily normal equations. Thus, their connection at daily boundaries was not possible in the final combination. Whereas the effect on coordinate estimates in long-term combination is negligible, this approach significantly reduces requirements for the disk space and combination time.

3.8 Data cleaning

Detection of cycle-slips, removal of incomplete data and setting new ambiguities were done in several clusters using a triple-difference solution. Ambiguity-float solution was then used for post-fit residual screening and outlier detection. A problematic station or satellite could be detected during this step, followed by removal of all relevant data and jump back to the step of baseline definition. The last feature was practically not used in this processing campaign.

3.9 Datum definition

Figure 3. Datum realization during daily processing

After data cleaning and outlier rejection, the daily combination of ambiguity-float solution was used for fiducial station selection. Stations used as fiducials in the IGS05 reference frame (BOR1, BRUS, GLSV, GRAS, JOZE, MATE, ONSA, POTS, WTZR, ZIMM) were used to define an initial set, while the selection procedure was based on a minimum constrained solution (NNT), which was repeated until the set of fiducial stations provided sufficiently small residuals. Only in a few cases in the whole period an additional iteration was used. The RMS of residuals for the fiducial stations were 2.4, 4.4 and 5.0 mm on average for North, East and Up, respectively. The RMS time-series are plotted in Figure 3.

3.10 Ambiguity fixing

Figure 4. Success of integer ambiguity resolution with QIF strategy

The length of all baselines in the network was below 2000 km so that the QIF ambiguity resolution strategy (Mervart, 1996) could be generally applied. The ionospheric model was ready to be estimated within the campaign processing scheme, but finally this was not applied in order to minimize the time for a single day processing. The ionospheric product from the Centre of Orbit Determination in Europe (CODE) was introduced instead, which slightly increased the rate of fixed ambiguities by about 2-3% with respect to the estimated model. Apart from a priori ionosphere model, stochastic ionospheric parameters were estimated during the ambiguity fixing. The tropospheric parameters and a priori coordinates from daily ambiguity-float solution were introduced from the last iteration of the datum definition. The coordinates of one station were constrained for each cluster during the ambiguity resolution. On average 84% ambiguities were fixed. Figure 4 shows seasonal variation of the total number of fixed ambiguities per each day over the whole period.

3.11 Daily solutions

The final solution of daily processing consists of two steps:

• Correct correlation and modelling in 3-4 clusters (approx. 20 stations) with saving normal equations for each cluster
• Daily normal equation combination into a network solution (neglecting correlations across different clusters) and saving daily network normal equations

These normal equations from the network solution were input in the final 4-year combination. Nevertheless, thanks to well defined datum in daily solutions, we could directly plot daily coordinate differences with respect to simple mean values and immediately identify significant jumps and problems with daily solutions. Typical examples are given in Figure 5. Most of the coordinate differences are within ±1 cm with a standard deviation below 5 mm (including effects such as daily datum realization, antenna changes etc). All time-series are available at http://www.pecny.cz/EUREF-Czech-2009/DAILY-TIMESERIES.