Generalized least-squares adjustment, a timely but much neglected tool

  • Heinrich Eichhorn
Session On Misellaneous Problems


A considerable amount of work has been done to make least-squares adjustment a more versatile tool, and it is the purpose of this article to give brief descriptions of all generalized leastsquares adjustment techniques that have been developed so far. Algorithms have been established which will allow one to work with problems in which any number of (possibly correlated) observations occurs explicitly in any of the nonlinear condition equations, and in which at least a subset of the adjustment parameters may be known to be samples from a multivariate normal distribution with known covariance matrix but unknown modes. Furthermore, “filtering” algorithms have been developed which allow one to take advantage of previous results in finding revised adjustments when either the set of observations, or the set of adjustment parameters or both have been augmented over the sets on which the previous adjustment was based. The most recent generalization, in which the condition equations are not available explicitly but only through the differential equations whose solutions they are, was presented during this Colloquium. (Kallrathet al., 1992)

Key words

Least-squares adjustment data analysis 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Branham, R.L.: 1990,Scientific data analysis. New York &c. (Springer)Google Scholar
  2. Brosche, P.: 1985,Naturwissenschaften,772, 668Google Scholar
  3. Brown, D.C.: 1955,Ballistic Research Laboratories Report No. 937, Aberdeen Proving Grounds, Md.Google Scholar
  4. Eichhorn, H.: 1978,Mon. Not. Roy. astron. Soc.,182, 335Google Scholar
  5. Eichhorn, H.: 1988,Astrophys. Journ.,334, 465Google Scholar
  6. Eichhorn, H.: 1989a,Anz. d. Oesterr. Ak. d. Wiss.,126, 89Google Scholar
  7. Eichhorn, H.: 1989b,Bull. Astr. Inst. Czechosl.,40, 394Google Scholar
  8. Eichhorn, H. & Clary, W.G.: 1974,Mon. Not. Roy. astron. Soc.,166, 425Google Scholar
  9. Jefferys, W. H. 1979,Astron. Journ.,84, 175Google Scholar
  10. Jefferys, W. H.: 1980,Astron. Journ.,85, 177Google Scholar
  11. Jefferys, W. H.: 1981,Astron. Journ.,86, 149Google Scholar
  12. Kallrath, J., Schlöder, J. & Bock, H. G.: 1992,Celest. Mech., this issueGoogle Scholar
  13. Lawson, C. L., & Hanson, R. J.: 1974.Solving Least Squares Problems, Englewood Cliffs, N.J. (Prentice Hall)Google Scholar

Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Heinrich Eichhorn
    • 1
  1. 1.University of FloridaGainesville

Personalised recommendations