Skip to main content

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

  • Conference paper
Book cover Optimization and Design of Geodetic Networks

Abstract

Free networks only, i.e. networks for which the datum has to be defined, will be considered in the following. Thus, the property of these networks, especially the dependency of the covariance matrix of the estimated coordinates on the choice of the datum will be reviewed first. Estimable coordinates for the free nets will be obtained by means of projected parameters and it will be shown that these projections also give the transformations between different datums.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Alberda, J.E.: Planning and optimization of networks: some general considerations.Bollettino di Geodesia e Science Affini, 33, 209–240, 1974

    Google Scholar 

  • Baarda, W.: S-transformations and criterion matrices. Netherlands Geodetic Commission, Publ. on Geodesy, 5, No.1, Delft 1973

    Google Scholar 

  • Bazaara, M.S. and C.M. Shetty: Nonlinear Programming. J.Wiley, New York 1979

    Google Scholar 

  • Fritsch, D.: Entwurf digitaler zweidimensionaler nichtrekursiver Filter Deutsche Geodätische Kommission, C, 275, München 1982

    Google Scholar 

  • Grafarend, E., H. Heister, R. Kelm, H. Kropff and B. Schaffrin: Optimierung geodätischer Meßoperationen. Wichmann, Karlsruhe 1979

    Google Scholar 

  • Koch, K.R.: Parameterschätzung und Hypothesentests in linearen Modellen Dümmler, Bonn 1980

    Google Scholar 

  • Koch, K.R.: O Deutsche Geodätische Kommission, B ptimization of the configuration of geodetic networks., 258/III, 82–89, München 1982 a

    Google Scholar 

  • Koch, K.R.: S-transformationsand projections for obtaining estimable parameters. In “Forty Years of Thought”, Anniversary Volume on the Occasion of Prof. Baarda’s 65th Birthday, 1, 136–144, Delft 1982 b

    Google Scholar 

  • Koch, K.R.: Die Wahl des Datums eines trigonometrischen Netzes bei Punkteinschaltungen. Zeitschrift für Vermessungswesen, 108, 104–111, 1983

    Google Scholar 

  • Lemke, C.E.: On complementary pivot theory. In “Mathematics of the Deci sion Sciences, Part 1]’, edited by G.B. Dantzig and A. F. Veinott, 95–114, American Mathematical Society, Providence 1968

    Google Scholar 

  • Liew, C.K. and J.K. Shim: A computer program for inequality constrained least-squares estimation. Econometrica, 46, 237, 1978

    Article  Google Scholar 

  • Pope, A.J.: Transformation of covariance matrices due to changes in minimal control (abstract). EOS, Transactions, American Geophysical Union, 52, 820, 1971

    Google Scholar 

  • Schaffrin, B.: Some proposals concerning the diagonal second order design of geodetic networks. Manuscripta Geodaetica, 6, 303–326, 1981

    Google Scholar 

  • Schaffrin, B., F. Krumm and D. Fritsch: Positivdiagonale Genauigkeitsoptimierung von Realnetzen über den Komplementaritäts-Algorithmus. In Ingenieurvermessung 80” edited by R. Conzett, H.J. Matthias, H. Schmid, 1, A 15/1 - A 15/19, Dümmler, Bonn 1981

    Google Scholar 

  • Schaffrin, B. and E.W. Grafarend: Kriterion-Matrizen II. Zweidimensionale homogene und isotrope geodätische Netze. Zeitschrift für Vermessungswesen, 107, 183–194, 1982

    Google Scholar 

  • Shapiro, J.F.: Mathematical Programming: Structures and Algorithms. J.Wiley, New York 1979

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1985 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Koch, K.R. (1985). First Order Design: Optimization of the Configuration of a Network by Introducing Small Position Changes. In: Grafarend, E.W., Sansò, F. (eds) Optimization and Design of Geodetic Networks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-70659-2_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-70659-2_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-70661-5

  • Online ISBN: 978-3-642-70659-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics