Optimization and Design of Geodetic Networks

1. Front Matter

   Pages I-XVII

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2. Introduction

   • E. W. Grafarend

   Pages 1-5

3. Review of Network Designs: Criteria, Risk Functions, Design Ordering

   • G. Schmitt

   Pages 6-10

4. Zero Order Design: Generalized Inverses, Adjustment, the Datum Problem and S-Transformations

   • P. Teunissen

   Pages 11-55

5. First Order Design: Optimization of the Configuration of a Network by Introducing Small Position Changes

   • K. R. Koch

   Pages 56-73

6. Second Order Design

   • G. Schmitt

   Pages 74-121

7. Third Order Design

   • G. Schmitt

   Pages 122-131

8. Numerical Methods in Network Design

   • P. A. Cross

   Pages 132-168

9. Some Additional Informations on the Capacity of the Linear Complementarity Algorithm

   • D. Fritsch

   Pages 169-184

10. Quick Computation of Geodetic Networks Using Special Properties of the Eigenvalues

    • W. D. Schuh

    Pages 185-195

11. Estimability Analyses of the Free Networks of Differential Range Observations to GPS Satellites

    • D. Delikaraoglou

    Pages 196-220

12. Optimization Problems in Geodetic Networks with Signals

    • A. Dermanis

    Pages 221-256

13. Fourier Analysis of Geodetic Networks

    • H. Sünkel

    Pages 257-300

14. Continuous Networks I

    • E. W. Grafarend, F. W. Krumm

    Pages 301-341

15. Continuous Networks II

    • B. Benciolini

    Pages 342-362

16. Criterion Matrices for Deforming Networks

    • E. W. Grafarend

    Pages 363-428

17. A Criterion Matrix for Deforming Networks by Multifactorial Analysis Techniques

    • F. Crosilla

    Pages 429-435

18. The Analysis of Time Series with Applications to Geodetic Control Problems

    • F. Sansò

    Pages 436-525

19. Quality Control in Geodetic Networks

    • P. J. G. Teunissen

    Pages 526-547

20. Aspects of Network Design

    • B. Schaffrin

    Pages 548-597

During the period April 25th to May 10th, 1984 the 3rd Course of the International School of Advanced Geodesy entitled "Optimization and Design of Geodetic Networks" took place in Erice. The main subject of the course is clear from the title and consisted mainly of that particular branch of network analysis, which results from applying general concepts of mathematical optimization to the design of geodetic networks. As al­ ways when dealing with optimization problems, there is an a-priori choice of the risk (or gain) function which should be minimized (or maximized) according to the specific interest of the "designer", which might be either of a scientific or of an economic nature or even of both. These aspects have been reviewed in an intro­ ductory lecture in which the particular needs arising in a geodetic context and their analytical representations are examined. Subsequently the main body of the optimization problem, which has been conven­ tionally divided into zero, first, second and third order design problems, is presented. The zero order design deals with the estimability problem, in other words with the definition of which parameters are estimable from a given set of observa­ tions. The problem results from the fact that coordinates of points are not univocally determined from the observations of relative quantities such as angles and distances, whence a problem of the optimal choice of a reference system, the so-called "datum problem" arises.

• Design
• Optimization
• geodesy
• network analysis
• networks

• Geodätisches Institut, Universität Stuttgart, Stuttgart 1, Germany

  Erik W. Grafarend

• Fotogrammetria e Geofisica, Istituto di Topografia, Milano, Italy

  Fernando Sansò

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