Article Index


5 Campaign Results

Table 2. Translations and RMS errors with respect to the EPN cumulative solution
Variant

Translations [mm]

(all "Class A" sites)

Translations [mm]

(selected fiducal sites only)

RMS [mm] of Helmert transformation

(selected fiducal sites only)

NorthEastUpNorthEast UpNorthEastUpTotal
A-0.0-0.9-0.5+0.1-0.1-0.01.00.83.52.1
B-0.0-0.9-0.6+0.1-0.1-0.01.00.83.62.2
C+0.3-0.1-0.9+0.1-0.1-0.11.12.13.22.3
D+0.4-0.4-1.3+0.1-0.1-0.01.11.22.51.7

Coordinate residuals at fiducial EPN stations (red) for D variant (non-fiducial EPN stations are plotted with pink). Figure 5. Coordinate residuals at fiducial EPN stations (red) for D variant (non-fiducial EPN stations are plotted with pink).

3D Helmert transformation (translation estimates) was performed for all the combination variants in order to assess the closeness of resulting coordinates to the ETRS89 realization (EPN cumulative product). The estimated translations for each variant using all class ‘A’ stations are within 1.3 mm in East, North and Up component, see Table 2. This result proved that any selection of ten or more fiducial stations in the campaign is reliable for the realization of the ETRS89 reference system at a millimetre level.


Estimated corrections (variant D) for non-EUREF stations (pink points) to the common ETRF2000 velocity field.
For all EPN stations (red points) velocities were constrained to the EPN cumulative solution. Figure 6. Estimated corrections (variant D) for non-EUREF stations (pink points) to the common ETRF2000 velocity field. For all EPN stations (red points) velocities were constrained to the EPN cumulative solution.

The table further shows fulfilled NNT conditions and RMS from coordinate residuals of applied fiducial stations. The solution ‘D’ shows clearly a superior performance while total RMS of Helmert transformation decreased to 1.7 mm. The solution ‘D’ was selected as final also because it includes as many as fiducial stations and excluding only three stations (MATE, and partly GOPE, WROC) with residuals larger than 6 mm in any component. Besides the station selection, Table 3 summarizes residuals from the final solution D and Figure 6 plots their geographical distribution.


North, East and Up repeatabilities for all stations from the final combination (D variant). Figure 7. North, East and Up repeatabilities for all stations from the final combination (D variant).

Estimated coordinates and velocities in ITRF2005 and ETRF2000 reference frames are summarized in Appendix. Figure 5 visualizes velocity corrections from the final solution (D) with respect to a priori velocities. Velocity differences are very small (bellow 1mm/year) for all stations, but for SNEC and CPRA.


Repeatabilities for all stations were calculated for each variant, but they do not differ significantly – 2mm in horizontal component (only SNEC slightly more) and usually 4 mm in vertical (with a few stations up to 6 mm). Figure 7 shows repeatabilities for final solution (D).


The examples of coordinate time-series from the final combination are given in Figure 9 for three stations – one fiducial (POTS) and two CZEPOS stations (CPAR, CJIH). While CPAR is an example of an excellent performance, CJIH suffers from a seasonal effect probably due to steel mast monumentation. A similar but smaller effect was detected at some other CZEPOS stations with the same type. The time-series of all other stations can be found at http://www.pecny.cz/EUREF-Czech-2009/FINAL-TIMESERIES.


Table 3. Selection of fiducial stations for different variants. Residuals from Helmert transformation between final variant D and EPN cumulative solution. Stations with flag M were only compared in the transformation.
Station Fiducial set D - final solution
A B C D North [mm] East [mm] Up [mm] Flag
BISK 11520M001 x x 0.2 0.8 0.6
BOR1 12205M002B x x x x -0.3 -0.5 0.4
BRUS 13101M004B x x x x -0.7 1.7 -1.2
DRES 14108M001 x x -1.3 -2.1 -2.3
DRES 14108M001C x x -1.2 -1.7 -1.3
DRES 14108M001D x 2.2 0.0 6.7 M
GLSV 12356M001B x x x x 2.3 -0.3 2.5
GLSV 12356M001C x x x x 1.2 0.0 3.6
GOPE 11502M002 3.2 -1.4 -17.2 M
GOPE 11502M002B 2.7 -1.1 -20.3 M
GOPE 11502M002C x x 0.1 0.1 0.7
GRAS 10002M006B x x x x 0.2 1.3 -4.1
GRAZ 11001M002 x x 0.3 0.1 -1.1
GRAZ 11001M002B x x -0.7 -2.1 -2.5
GRAZ 11001M002D x x 0.0 1.0 -1.5
JOZE 12204M001B x x x x 0.0 -0.2 1.3
LINZ 11033S001B x x 0.1 1.0 -2.0
MARJ 11517M001B x x 0.2 1.0 0.4
MATE 12734M008B x x x 2.4 0.8 -6.5 M
MATE 12734M008C x x x 0.4 1.5 -7.1 M
MOPI 11507M001B x x 0.1 0.3 -1.9
ONSA 10402M004B x x x x -0.7 -0.1 2.8
PENC 11206M006 x x -3.6 -0.2 -0.2
PENC 11206M006B x x 0.2 0.4 1.7
PENC 11206M006C x x 3.0 -2.3 -1.9
POTS 14106M003 x x x x -0.3 0.3 2.3
POUS 11518M001 x x -0.1 1.2 0.1
RIGA 12302M002 x x -0.4 -1.0 1.9
RIGA 12302M002B x x -0.6 -1.0 2.5
RIGA 12302M002C x x 0.3 -0.6 4.6
SOFI 11101M002 x x x 0.4 0.3 -1.5
TUBO 11503M001 x x -0.8 -2.1 -2.7
TUBO 11503M001B x x 1.4 3.0 -5.7
TUBO 11503M001D x x -0.3 -1.0 4.6
VACO 11516M001B x x 0.7 0.4 1.5
WROC 12217M001 x 0.3 -0.5 -6.3 M
WROC 12217M001C -0.8 -10.9 -0.9 M
WROC 12217M001D x x -0.2 -0.4 0.7
WTZR 14201M010B x x x x 0.3 1.1 1.3
ZIMM 14001M004B x x x x 0.2 0.7 -3.8
RMS / comp. x 1.1 1.2 2.5
Translations x 0.1 -0.1 0.0