4 Final combination
The Bernese ADDNEQ2 program was used for the final combination based on stacking daily normal equations (NEQ). Although the network spread over a stable part of Europe, coordinates and velocities were introduced as unknown parameters for this campaign covering the period of 4 years. The combination step consists in the identification of outliers and jumps, selection of fiducial stations and in setting pre-defined intervals for coordinate and velocity estimation. More different combination variants have been computed in order to achieve the best results. Because we introduced 24 EPN stations of Class A (6 in the Czech Republic and 18 external) in daily solutions, we didn’t need to combine NEQs with EPN weekly solutions. This was confirmed by a stable realization of the IGS05 reference frame on a daily basis, which was visualized in the preliminary time-series of coordinate differences with respect to a simple mean from independent days, see http://www.pecny.cz/EUREF-Czech-2009/DAILY-TIMESERIES.
4.1 Fiducial stations
Sufficient number of EPN Class A station candidates was available for the campaign and the selection of the most reliable set resulted in these different variants (full station lists are given in Table 3):
- A) 11 EPN (Class A) stations used as fiducial in the EPN cumulative solution
- B) 10 IGS/EUREF (Class A) stations used in IGS05 realization (applied in daily solutions)
- C) All EPN (Class A) stations with GOPE excluded before GPS week 1400 (24 stations)
- D) All EPN (Class A) stations with excluded intervals with larger residuals (23 stations)
4.2 Reference coordinates and velocities
The coordinates and velocities from the EPN cumulative solution EPN_A_ITRF2005_C1570 were used as a reference for all fiducial stations. During the campaign period, several sets of coordinates were published for most of the stations included in the campaign. These are usually related to the change of antenna or receiver. However, there are many coordinate changes at GPS week 1400, which are related to the changes in the EPN processing strategy – the most important was a switch from the relative to absolute phase centre model. For many stations, this caused a station-specific change in coordinates at a level of millimetres for horizontal position and centimetres in height.
The campaign covered the period both before and after GPS week 1400, while the absolute phase centre variation model was applied for the whole campaign processing period. Since the coordinates in the EPN cumulative solution before GPS week 1400 are based only on the processing that use relative phase centre variation model, we clearly identified jumps in our preliminary coordinates induced by this model change. These artificial jumps were eliminated in our campaign by omitting those sets of EPN coordinates with a time span limited only to a period before GPS week 1400. Instead, the coordinates starting at GPS week 1400 were used also for such station for the period without any instrumentation change. A consistency of the coordinates was thus guaranteed as long as possible also before GPS week 1400 and reference coordinates from the old model were used only in a few short periods at the beginning for these stations – DRES, GOPE, PENC, RIGA, TUBO and WROC.
A priori coordinates of all non-EUREF campaign stations could be set up at a decimetre level. Since the campaign covered 4-year period and the processing has been done in a global reference frame, velocities should be estimated as well. For a few stations we tightly constrained these velocities to their a priori values (because of short-time observed period), therefore we set their a priori velocities consistently with the rotation of ETRF2000 with respect to ITRF2005.
4.3 Outlier rejection
The final combination was done in an iterative way in order to eliminate outliers. The following criteria were used for the outlier detection:
- 8, 8 and 25 mm in North, East and Up for all EPN sites
- 15, 15 and 40 mm in North, East and Up for all other stations
The number of excluded days in final combination due to these criteria was 182 and 62 on fiducial and other stations, respectively.
|2005 12 01
|2006 02 28
|2005 11 20
|2006 03 10
|2007 12 12
|2007 12 23
|series of Up outliers
|2005 10 15
|2005 10 25
|winter 2005/6, part 1
|2005 11 01
|2006 04 15
|winter 2005/6, part 2
|2006 10 15
|2007 03 20
|2007 10 10
|2008 02 20
|all winter periods excluded in daily solutions
|2006 01 01
|2006 03 07
4.4 Coordinate and velocity estimation
The coordinates of all stations were estimated in pre-defined intervals according to the jumps identified from residual time-series. Sets of fiducial stations were used for the datum definition using the minimum constrained solution (no-net translation). The velocities were estimated only for all non-EUREF stations observed over 3 years. Since a priori velocities for such stations originated from a common ETRF2000 trend, we estimated corrections only and whenever more intervals for station coordinates were pre-defined, these corrections were estimated uniquely over the whole interval (there was no reason for splitting velocities during the campaign period).
In variants A, B and C, we have estimated only horizontal velocities in all variants, while vertical velocities were tightly constrained to their a priori values. In variant D, vertical velocities were also estimated for all stations observed over more than 3 years. The reference velocities of all EPN stations were always tightly constrained since we assumed that they could not be estimated with a higher quality than in the EPN cumulative solution.