1. Changing Reference Frame Frank Gielsdorf technet GmbH Berlin

2. Definition of Reference Frames Horizontal Control Network Vertical Control Network Datum/ Gauge Rauenberg Potsdam ETRS89 Amsterdam Kronstadt Genua Reference Surface Bessel Ellipsoid Krassovski Ellipsoid GRS80 Ellipsoid Geoid Quasigeoid Projection Gauss-Krueger Soldner UTM

3. Situation in 1990 West GermanyEast Germany Horizontal Control Network Potsdam Datum Bessel Ellipsoid Gauss-Krueger (different resurveys) Pulkovo Datum Krassovski Ellipsoid Gauss-Krueger Vertical Control Network Amsterdam Gauge Geoid Kronstadt Gauge Quasigeiod

4. Were is the Problem? Example: German Railways Positioning System for Trains Required Positional Accuracy: 50cm Necessary: Data base of the rail geometry with a unique spatial reference frame! Train with GPS Antenna Surveying and Navigation with GPS!

5. Reference Frames Old: German Main Triangle Network (DHDN) datum point:TP Rauenberg reference ellipsoid:Bessel ( a = 6 377 397.155m, f = 1:299.1528 ) New: European Terrestrial Reference System 1989 (ETRS89) datum points:23 laser- und VLBI positions in Europe reference ellipsoid:Geodetic Reference System 1980 (GRS80) ( a = 6 378 137m, f = 1:298.2572 )

6. Projection m = cosh(y/R)m = cosh(y/R)*0,9996 Gauss-Krueger UTM (Universal Transversal Mercator)

7. 3D Datum Transformation (X, Y, h) DHDN / Gauss-Krueger (X, Y, Z) DHDN / geocentric (X, Y, Z) ETRS89 / geocentric (X, Y, h) ETRS89 / UTM Conversion Datum Transformation (adjustment problem) Prerequisite: identical points

8. Adjustment Approach Functional Model

9. Transformation Parameter NRW Teilnetztx [m]ty [m]tz [m] dm [ppm] ex [‘‘]ey [‘‘]ez [‘‘]σp [cm] BRD+ 582.+ 105.+ 414.+ 8.3+ 1.04+ 0.35- 3.08± 113 NRW+ 566.1+ 116.3+ 390.1+ 12.6+ 1.11+ 0.24- 3.76± 34 I+ 580.6+ 107.4+ 403.4+ 9.7+ 0.27+ 0.05- 4.28± 13 II+ 564.8+ 101.9+ 396.2+ 12.2+ 0.31+ 0.34- 4.01± 42 III+ 567.5+ 108.7+ 406.8+ 10.5+ 0.91+ 0.54- 3.56±37 IV+ 566.9+ 105.4+ 388.3+ 12.9+ 1.03+ 0.21- 3.31±10 V+ 565.0+ 92.5+ 372.9+ 15.1+ 0.84- 0.05- 2.93± 5 VI+ 570.4+ 96.4+ 398.4+ 11.5+ 0.93+ 0.34- 2.92± 10 VII+ 573.6+ 108.0+ 394.2+ 11.5+ 1.31+ 0.19- 3.05± 8 VIII+ 567.3+ 89.4+ 370.0+ 15.2+ 0.98- 0.14- 2.60± 7 Quelle: Landesvermessungsamt NRW

10. 2D Datum Transformation The analytical function of an complex number impart a conformal mapping. Special case: Helmert-Transformation

11. Example North Rhine-Westphalia two meridional zones 155 TP 1. order degree 3 resp. 4 n =310 u =18 r =300 σ p =0,097 m V max =0,201 m

12. Problem: Remaining Discrepancies Remaining Discrepancies : –Residuals of coordinate observations Causes: –Random deviations  adjustment calculation –Systematic influences  model extension Solution: –Extension of the mapping rule

13. Extension of the Mapping Rule 1.Step Transformation 2. Step Neighborhood Fitting Identical Points DHDN Identical Points ETRS89 Calculation of Transformation Parameters Transformation of New Points New Points DHDN Artificial Observations, Geometrical Constraints Adjustment Transformation Parameters + Residuals All Points in ETRS89 + Residuals All Points in ETRS89

14. Subproject from Hamburg Points:6973 Reference Points:36 Point Identities:38 Triangle Sides:20883