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
ProjectionGauss-Krueger
Soldner
UTM
Situation in 1990
West Germany East Germany
Horizontal
Control Network
Potsdam Datum
Bessel Ellipsoid
Gauss-Krueger
(different resurveys)
Pulkovo Datum
Krassovski Ellipsoid
Gauss-Krueger
Vertical
Control NetworkAmsterdam Gauge
Geoid
Kronstadt Gauge
Quasigeiod
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!
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 )
Projection
4 3 2 1
0° 3° 6° 9° Y
X
Equator
32
6° 9° 12° 15° Y
X
Equator
33
18°
m = cosh(y/R) m = cosh(y/R)*0,9996
Gauss-Krueger UTM(Universal Transversal Mercator)
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
Conversion
Datum Transformation
(adjustment problem)
Prerequisite:identical points
Transformation Parameter NRW
Teilnetz tx [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
2D Datum Transformation
The analytical function of an complex number impart a conformal mapping.
Special case: Helmert-Transformation
Example North Rhine-Westphalia
two meridional zones
155 TP 1. order
degree 3 resp. 4
n = 310
u = 18
r = 300
σp = 0,097 m
Vmax = 0,201 m
Problem: Remaining Discrepancies
• Remaining Discrepancies :– Residuals of coordinate observations
• Causes:– Random deviations adjustment calculation– Systematic influences model extension
• Solution:– Extension of the mapping rule
Extension of the Mapping Rule
1. StepTransformation
2. StepNeighborhood Fitting
IdenticalPoints DHDN
IdenticalPoints
ETRS89
Calculation of Transformation
Parameters
Transformation of New Points
New PointsDHDN
Artificial Observations, Geometrical Constraints
Adjustment
Transformation Parameters +
Residuals
All Points in ETRS89 + Residuals
All Points in ETRS89
Subproject from Hamburg
Points: 6973Reference Points:36Point Identities: 38Triangle Sides: 20883