Boundary Austria-Switzerland

EuroBoundaries Workshop Vienna June 6-8, 2005

Helmut Meissner: Boundary Austria-Switzerland in ETRS

Boundary Austria-Switzerland

Pilot Project

Austria - Switzerland

Boundary in ETRS89

Swisstopo BEV



Project

• The project was started by the Austrian – Swiss boundary commission in the year 2003

• The purpose is to compute the coordinates of

the boundary from the national systems to ETRS89

• Only by mathematical transformations without outdoor GPS-measurements



Advantage of ETRS

• International reference system• One reference system for the whole European Union• Technical developement GPS-measurement • Easier way to exchange geografic data• To facilitate co-operation for economy and

administration



The Boundary of Austria

Number of points on the boundary

27.000 marked points

40.000 not marked points

123.000 photogrammetric / digitised points

8 neighbouring countries

Total length : 2708km

Germany: 817 kmCzech Republic: 466 kmSlovakia:

107 kmHungary: 356 kmSlovenia: 330 kmItaly: 430 kmSwitzerland: 166 kmLiechtenstein: 35 km



The Boundary of Austria

0 25 Km 50 Km

Germany 817km

Italy

430kmSlovenia

330km

Hungary

356km

Slovakia

107km

Czech Republic

466km

Switzerland

166km

FL

35km

ETRS project with Switzerland

GPS-campaign with Italy

GPS-campaign with Germany



Boundary Austria - Switzerland

Some data of the boundary Austria-Switzerland

• 166km length of boundary (divided in 3 sections)• 355 marks on the boundary• 220 marked points beside to the boundary• 276 not marked points• About 6000 photogrammetric digitized points (mountain

ridge)



Boundary Austria - Switzerland

• Treaty Austria-Switzerland from 1972• Geodetic documentation of the boundary:

as part of the treaty

– Maps 1:25.000– Description– List of Coordinates

» The marks of the boundary were measured in the years 1951 to 1955 (in the mountains) and 1966 to 1968 at the Rhine



Map 1:25.000 of the Boundary Austria-Switzerland



Description of the Boundary Austria-Switzerland



List of Coordinates of the Boundary Austria-Switzerland



Austrian Projektion „Gauß-Krüger“

elliptischer Zylinder

M28

xy

M31

xy

M34

yx

Ellipsoid Bessel

Ferro

source BEV/V1E.Imrek



Projection of Switzerland

Some data about

the Swiss projection:

•Isogonal transversal

•Cylinder projection

•Bessel Ellispoid

•Contact circle in the direction

West-East

•Fundamental point in Bern



Projection UTM

M9

xy

M15

yx

Grw

Ellipsoid GRS80

source BEV/V1E.Imrek



Reference Systems

MGI Austrian traditional network MGI_hom homogenized Austrian network

LV03 Swiss traditional network (1903) LV95 homogenized Swiss network

ITRS International Terrestrial Reference SystemETRS European Terrestrial Reference System (ETRS89=ITRS89)UTM Universal Mercator Projection



PROCESS: Transformation National Systems to ETRS

MGI

LV03/LV95



Methods of calculation

National Reference System ETRS

With GPS-measurements:

• GPS-Measurement of all points• GPS-Measurement of some points and computation of

all the other points with a mathematical transformation

without GPS-Measurements:

• Transformation / interpolation with a mathematical model (prediction) in an optimal and consistent way



Problem:

Inhomogeneity of the Traditional Netpoints

Because of:

• The national networks were computed regionally not in one • Partially in some areas the design of the nets are not good

because of topographic characteristics• Methods of measurements - only few distances • Partially not including the influence of deflection vertical

between geoid and ellipsoid …..…………………..

• The regional accuracy is mostly good (cataster) but not so the absolutely (global) position, so you have to add a correction to the coordinates; the homogenous vector; in Austria the value could be up to 1 or 2m.



Inhomogeneity of the Austrian MGI

Inhomogeneity of the controlpoints (TP) of the network1. - 3. order (long wave trend)

ca. 2000 TP 1. - 3. order

source BEV / V1



Homogenisation of the Traditional Systems

Requirement for the project are homogenious basic data of the controlpoints:

In both countries in process: • GPS-measurement of selected

controlpoints (TP)

• computation of all GPS + terrestrial measurements:– Austria: controlpoints 1. to 5. order- Switzerland 1. to 2. order

Result homogeneous coordinates of the controlpoints



Steps to transform coordinates to ETRS

Points of boundary:

1. step: Homogenisation - Interpolation

MGI MGI_hom (A) LV03 LV95 (CH)

2. step: Transformation

from Bessel Ellipsoid to

GRS80-Ellipsoid MGI_hom ETRS89 (A)

LV95 ETRS89 (CH)

MGI MGI_hom ETRS89 (A)

LV03 LV95 ETRS89 (CH)



Austrian Solution

Connection between UTM and GK

system MGI

GK

Bessel

GRS80

system ITRS

UTM

X, Y, Z

X, Y, Z

x, y, h‘

orthometric height

„Traditional Austrian System“

x, y, h

GK‘ x‘, y‘, h‘

homogenious coordinate and orthometric height

7 Par

GG Geoid

Source: E.Imrek / V1)

Hom

vector for homogenizing dy, dx, dh



Results

Table of ETRS89 coordinates: Swiss – Austrian

• Section Vorarlberg-Graubünden (mountain)• Section Vorarlberg-St. Gallen (Rhine)



Comparison of the Results

Austria – SwitzerlandSection „Vorarlberg-Graubünden“ (mountains)

Interpolation

116 marks • 66% <= 10cm• 33% <= 11-20cm• 1 % > 20cm• arithmetical mean

ds= 9cm• variance +/-4cm• maximum 24cm

0

2

4

6

8

10

12

14

1 3 5 7 9 11 13 15 17 19 21 23

Number

of

points

Delta s in cm




Austria – SwitzerlandSection „Vorarlberg-St. Gallen“ (Rhine)

Interpolation

434 points• 95% <= 10cm• 5% <= 11-17cm• arithmetical mean • ds= 6cm• variance +/-2cm• maximum 17cm

0

10

20

30

40

50

60

70

1 3 5 7 9 11 13 15 17

Number

of

points

Delta s in cm




Austria – SwitzerlandSection „Vorarlberg-St. Gallen“ (Rhine)

and Section „Vorarlberg-Graubünden“ (mountains)Interpolation

550 points• 89% <= 10cm• 11% 11-20cm• 0,4% > 20cm arithmetical mean ds= 7cm variance +/-3cm maximum 24cm

0

10

20

30

40

50

60

70

80

1 3 5 7 9 11 13 15 17 19 21 23

number

of

points

Delta s in cm



Conclusio 1

Average accuracy values of the pointsin MGI and LV03 (surveyed by terrestrial methods)

controlpoints 1. - 3. order better than +/- 5cm

controlpoints 4.- 6. order better than +/- 7cm

Points of the the borderline and cadastre about +/- 10 – 20cm

The quality of the ETRS89-coordinates of the points can not be better than the quality of the coordinates in the documents, except there is a new measurement with GPS



Conclusio 2

Question: How to get one common value for the coordinates of the

boundary points in ETRS89

• Because the differences of the result between the Austrian and the Swiss solution are mostly less than 10cm, it should be a possible way to get one homogenous coordinate in ETRS for every point of the borderline to calculate the arithmetical mean. Every country has to accept an average deviation of about 3 to 5 cm; this would be within the accuracy of the controlpoints.

• If the difference is more than 20cm a measurement with GPS will be necessary.



Conclusio 3

So if• the traditional networks have a good quality at the

time of surveying the points of the boundary

and

• a new dataset for a homogenised system exists,

the transformation without GPS- measurements seems to be a good method to get a homogenised dataset for the boundary.



Next Steps

• The coordinates of the boundary points of the last section „Tirol-Graubünden“ will be calculated soon, as well as all photogrammetric / digitised points (mountain ridge).

• The ellipsoid heights of the marked points will be computed soon from Austria

• Check of the results by measurement a few points with GPS

• In the near future the land registers will be transformed in the new homogenised system - in Switzerland in LV95 and in Austria in MGI_hom and probably also in UTM (project UTMK).

• The borderline should be determined in the ETRS89 system if possible before the land register (cadaster).



Thank you for your interest

Helmut Meissner

email: [email protected]

Boundary Austria-Switzerland

Documents

boundary of austriagermany

marked points

swiss projection

national networks

traditional netpointsbecause

mathematical transformations

mathematical model prediction

transformation interpolation