Changing Reference Frame

Frank Gielsdorf

technet GmbH Berlin

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

Adjustment Approach

Functional Model

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