ZOD - Zero Order Design of Geodetic Networks - free networks, - - PowerPoint PPT Presentation

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ZOD - Zero Order Design of Geodetic Networks - free networks, - - PowerPoint PPT Presentation

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ZOD - Zero Order Design of Geodetic Networks - free networks, G-inverses, S-transformation - Fakultt Bau-, Geo-, Umwelt -Geodtisches Institut- Fakultt Bau-, Geo-, Umwelt -Geodtisches Institut- KIT Universitt des Landes

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Fakultät Bau-, Geo-, Umwelt -Geodätisches Institut-

ZOD - Zero Order Design of Geodetic Networks

  • free networks, G-inverses, S-transformation -

KIT – Universität des Landes Baden-Württemberg und nationales Großforschungszentrum in der Helmholtz-Gemeinschaft

Fakultät Bau-, Geo-, Umwelt -Geodätisches Institut-

www.kit.edu

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Zero Order Design - Free Network -

  • 1/2/3-dimensional geodetic networks
  • Observations: usually of geometrical nature
  • distances,directions, angles, zenith distances, height differences…
  • Parameters: coordinates 1D/2D resp. 3D
  • funktional relationship between observations ↔ parameters:

GMM - adjustment by observation equations

Geodätisches Institut

2

⇒

  • observations are of relative nature
  • they fix only the relative situation, that means the inner geometry
  • the position of the point field in plane/space is free

⇒

datum is free !

ZOD - Zero Order Design of Geodetic Networks

  • Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt
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SLIDE 3

Zero Order Design - Free Network -

visualising datum defects

Geodätisches Institut

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(Example: Reines Richtungsnetz; Niemeier 2008)

datum fixing as a central component in network adjustment

ZOD - Zero Order Design of Geodetic Networks

  • Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt

datum fixing

l

  • bserations

x

parameters

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Zero Order Design - Free Network -

Geodätisches Institut

4 ZOD - Zero Order Design of Geodetic Networks

  • Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt
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Zero Order Design - Free Network -

Geodätisches Institut

5 Analyse und Planung Geodätischer Netze Dr.-Ing. M. Illner

H1 H2 H3 H4

  • 1

+1

  • 1

+1

  • 1

+1 +1

  • 1
  • 1

+1

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Zero Order Design - Free Network -

Geodätisches Institut

6 ZOD - Zero Order Design of Geodetic Networks

  • Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt
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SLIDE 7

Zero Order Design - Free Network -

Geodätisches Institut

7 ZOD - Zero Order Design of Geodetic Networks

  • Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt
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Zero Order Design - Free Network -

Geodätisches Institut

8 ZOD - Zero Order Design of Geodetic Networks

  • Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt
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Zero Order Design - G - Inverses

  • Geodätisches Institut

9 ZOD - Zero Order Design of Geodetic Networks

  • Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt
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Zero Order Design - G - Inverses

  • Geodätisches Institut

10 ZOD - Zero Order Design of Geodetic Networks

  • Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt
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SLIDE 11

Zero Order Design - G - Inverses

  • Geodätisches Institut

11 ZOD - Zero Order Design of Geodetic Networks

  • Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt
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SLIDE 12

Zero Order Design - G - Inverses

  • Geodätisches Institut

12 ZOD - Zero Order Design of Geodetic Networks

  • Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt
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SLIDE 13

Zero Order Design - G - Inverses

  • Geodätisches Institut

13 ZOD - Zero Order Design of Geodetic Networks

  • Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt
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SLIDE 14

Zero Order Design - G - Inverses

  • Geodätisches Institut

14 ZOD - Zero Order Design of Geodetic Networks

  • Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt
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Zero Order Design - G - Inverses

  • Geodätisches Institut

15 ZOD - Zero Order Design of Geodetic Networks

  • Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt
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Zero Order Design - G - Inverses

  • Geodätisches Institut

16 ZOD - Zero Order Design of Geodetic Networks

  • Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt
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SLIDE 17

Zero Order Design - inner solution -

Geodätisches Institut

17 ZOD - Zero Order Design of Geodetic Networks

  • Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt
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SLIDE 18

Zero Order Design - inner solution -

Geodätisches Institut

18 ZOD - Zero Order Design of Geodetic Networks

  • Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt
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SLIDE 19

Zero Order Design - inner solution -

Geodätisches Institut

19 ZOD - Zero Order Design of Geodetic Networks

  • Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt
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SLIDE 20

Zero Order Design - inner solution -

Geodätisches Institut

20 ZOD - Zero Order Design of Geodetic Networks

  • Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt
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Zero Order Design - trace minimization -

Geodätisches Institut

21 ZOD - Zero Order Design of Geodetic Networks

  • Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt
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Zero Order Design - trace minimization -

Geodätisches Institut

22 Analyse und Planung Geodätischer Netze Dr.-Ing. M. Illner

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structure of the G-matrices for 1D- and 2D-networks

dimen- sion type of net- work kind of

  • bservations

defect free datum parameters eigenvector components gi

  • f the i-th point

translation rotation about X Y Z scale 1-D height net- work height differences d=1 1 translation (vertical shift) 1

Geodätisches Institut

23 ZOD - Zero Order Design of Geodetic Networks

  • Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt

work 2-D plane net- work distances and azimuths, GNSS d=2 translations in Y- and X- direction 1 0 1 distances or distances and directions d=3 2 translations, rotation about Z-axis 1 0 1 xi

  • yi

directions, dis- tance ratios or as for d=3 with scale d=4 2 translations, rotation about Z- axis, scale 1 0 1 xi

  • yi

yi xi

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structure of G-matrices for 3D-networks

Zero Order Design - nullspace G –

dimen- sion type of net- work kind of

  • bservations

defect free datum parameters eigenvector components gi

  • f the i-th point

translation rotation about X Y Z scale

GNSS d=3 translations in X-, Y- and Z- direction 1 0 0 0 1 0 0 0 1

Geodätisches Institut

24 ZOD - Zero Order Design of Geodetic Networks

  • Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt

3-D space network si and zi or si and ri and zi d=4 translations in X-, Y- and Z- direction, rotation about Z 1 0 0 0 1 0 0 0 1

  • yi

xi ri and zi or as in the case d=4 with scale d=5 3 translations, 1 rotation, 1 scale 1 0 0 0 1 0 0 0 1

  • yi

xi xi yi zi distances or dis- tances and directions d=6 3 translations, rotations about X-, Y- and Z-axis 1 0 0 0 1 0 0 0 1 0 zi

  • yi
  • zi

0 xi yi

  • xi

As in the case d=6 with scale d=7 3 translations, 3 rotations, 1 scale 1 0 0 0 1 0 0 0 1 0 zi

  • yi
  • zi

0 xi yi

  • xi

xi yi zi

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Zero Order Design - nullspace G -

Geodätisches Institut

25 ZOD - Zero Order Design of Geodetic Networks

  • Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt

3 translations 3 rotations scale

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Zero Order Design - S-transformation -

Geodätisches Institut

26 ZOD - Zero Order Design of Geodetic Networks

  • Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt
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Zero Order Design - S-transformation -

Geodätisches Institut

27 ZOD - Zero Order Design of Geodetic Networks

  • Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt
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Zero Order Design - S-transformation -

Geodätisches Institut

28 ZOD - Zero Order Design of Geodetic Networks

  • Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt
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Zero Order Design - 1D-network -

Geodätisches Institut

29 ZOD - Zero Order Design of Geodetic Networks

  • Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt
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Zero Order Design - 1D-network -

Geodätisches Institut

30 ZOD - Zero Order Design of Geodetic Networks

  • Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt
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Zero Order Design - 1D-network-

Geodätisches Institut

31 ZOD - Zero Order Design of Geodetic Networks

  • Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt
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Zero Order Design - elimination of

  • rientation unknowns -

2 1 3 t1,3 l1 l3 l2

Geodätisches Institut

32 ZOD - Zero Order Design of Geodetic Networks

  • Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt

4

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Zero Order Design - elimination of

  • rientation unknowns -

Geodätisches Institut

33 ZOD - Zero Order Design of Geodetic Networks

  • Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt