Bulletin géodésique

, Volume 57, Issue 1–4, pp 226–239 | Cite as

A criterion matrix for the second order design of control networks

  • Fabio Crosilla
Article
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Accepted:

Abstract

This paper proposes an original method of constructing a criterion matrix for the optimal design of control networks by means of the contraction of the eigenvalues and the rotation of the eigenvectors of a covariance matrix. The rotation of the eigenvectors is carried out by two different methods, that is through independent rotations of the pairs of the eigenvector matrix components and through a procrustean transfomation of the same matrix. The required criterion is that the “essential eigenvector components” must be as orthogonal as possible to the predicted direction of deformation. A Second Order Design problem is then resolved, that is the optimization of the precision of the observations of a local free distance network to be constructed for the study of recent crustal movements in the seismogenetic area of Friuli (Italy). The results obtained show a high degree of correspondence for the two proposed methods of rotation if limited rotations of the eigenvectors are considered.

Keywords

Covariance Matrix Control Network Geodetic Network Error Ellipse Limited Rotation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References

  1. W. BAARDA, 1973: S-transformations and criterion matrices. Neth. Geod. Comm., Pubbl. on Geod., New Series, 4, no 1, Delft (1973).Google Scholar
  2. J. BOSSLER, E. GRAFAREND, R. KELM, 1973: Optimal design of geodetic nets II. Journal Geophysical Research, 78 (1973), pp. 5887–5897.CrossRefGoogle Scholar
  3. F. CROSILLA, C. MARCHESINI, 1982: Geodetic network optimization for the detection of crustal movements using a mekometer. Bollettino di Geodesia e Sc. Affini, to appear.Google Scholar
  4. H. DUPRAZ, W. NIEMEIER, 1979: Un critère pour l'analyse des réseaux géodésiques de contrôle, Mensuration, Photogrammétrie, Génie rural. 4 (1979), pp. 70–76.Google Scholar
  5. E. GRAFAREND, 1972: Genauigkeitsmasse geodätischer Netze. Deutsche Geodätische Kommission, Reihe A, no 73 (1972).Google Scholar
  6. E. GRAFAREND, B. SCHAFFRIN, 1979: Kriterion Matrizen I. Zeitschrift für Vermessungswesen, 104 (1979), pp. 133–149.Google Scholar
  7. R.M. JOHNSON, 1963: On a theorem stated by Eckart and Young. Psychometrika, 28 (1963), pp. 259–263.CrossRefGoogle Scholar
  8. H. PELZER, 1976: Genauigkeit und Zuverlässigkeit geodätischer Netze Tagung, Mathematische Probleme der Geodäsie. Oberwolfach (1976).Google Scholar
  9. H. PELZER, 1980: Some criteria for the accuracy and the reliability of networks. Deutsche Geodatische Kommission, Reihe B, no 252 (1980).Google Scholar
  10. C.R. RAO, S.K., MITRA, 1971: Generalized inverse of matrices and its applications. New York/London/Sydney/Toronto, (1971).Google Scholar
  11. P.H. SCHONEMANN, 1965: On the formal differentiation of traces and determinants. Research Memorandum no 27, chapel Hill, N.C.: The Psychometric Laboratory, (1965).Google Scholar
  12. P.H. SCHONEMANN, 1966: The generalized solution of the orthogonal procrustes problem. Psychometrika no 31, (1966), pp. 1–16.CrossRefGoogle Scholar
  13. P.H. SHONEMANN, R.D. BOCK, L.R. TUCKER, 1965: Some notes on a theorem by Eckart and Young. Research Memorandum no 25, Chapel Hill, N.C.: The Psychometric Laboratory, (1965).Google Scholar
  14. W.H. SPRINSKY, 1978: Improvement of parameter accuracy by choice and quality of observation. Bulletin géodésique, 52, (1978), pp. 269–279.CrossRefGoogle Scholar
  15. H. WIMMER, 1987: Eine Bemerkung zur günstigsten Gewichtsverteilung bei vergegebener Dispersionsmatrix der Unbekannten. Allgemeine Vermessungs-Nachrichten, 95, (1978). pp. 375–377.Google Scholar
  16. H. WIMMER, 1981: Second Order Design of geodetic networks by an iterative approximation of a given criterion matrix. Paper presented at the Symposium on Geodetic Networks and Computations, Munich, August 31–September 5, (1981).Google Scholar

Copyright information

© Bureau Central de L'Association Internationale de Géodésie 1983

Authors and Affiliations

  • Fabio Crosilla
    • 1
  1. 1.Facoltà di IngegneriaUniversità di TriesteTrieste(Italia)

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