changing reference frame
DESCRIPTION
Changing Reference Frame. Frank Gielsdorf technet GmbH Berlin. Definition of Reference Frames. Situation in 1990. Were is the Problem?. Surveying and Navigation with GPS!. Example: German Railways. Positioning System for Trains. Required Positional Accuracy: 50cm. Necessary: - PowerPoint PPT PresentationTRANSCRIPT
Definition of Reference Frames
Horizontal Control Network
VerticalControl Network
Datum/Gauge
RauenbergPotsdamETRS89
AmsterdamKronstadt
Genua
Reference Surface
Bessel EllipsoidKrassovski Ellipsoid
GRS80 Ellipsoid
GeoidQuasigeoid
ProjectionGauss-Krueger
SoldnerUTM
Situation in 1990
West Germany East Germany
HorizontalControl Network
Potsdam DatumBessel EllipsoidGauss-Krueger
(different resurveys)
Pulkovo DatumKrassovski Ellipsoid
Gauss-Krueger
VerticalControl Network
Amsterdam GaugeGeoid
Kronstadt GaugeQuasigeiod
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 Rauenbergreference 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 TransformationThe 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 = 310u = 18r = 300σp = 0,097 mVmax = 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