Influence of Systematic Effects in Stochastic and Functional Models

des Instituts für Geodäsie

Heft 7/1982

Influence of Systematic Effects
in Stochastic and Functional Models

Hannover, Federal Republic of Germany


In: BORRE, Kai / WELSCH, Walter M. (Eds.) [1982]:
International Federation of Surveyors - FIG -
Proceedings Survey Control Networks
Meeting of Study Group 5B, 7th-9th July, 1982, Aalborg University Centre, Denmark

Schriftenreihe Wissenschaftlicher Studiengang Vermessungswesen, Hochschule der Bundeswehr München, Heft 7, Neubiberg, S. 309-320.



Systematic errors in the observations my be interpreted as errors in the mathematical adjustment model, which can be eliminated by insertion of additional parameters in the model. A general solution of this problem can be found if these additional parameters are considered as random variables. In this solution, all information about these parameters is concentrated in the covariance matrix of .

With any matrix norm    we get

  .                                  (6.1)

In the first (left hand) extreme case    we have no further information about the systematic effects and have to detect them from the network adjustment alone (s. Ch. 3). In the right hand extrem case, however, we known exactly the true values of the systematic errors and can reduce our observations l before carying out the network adjustment.

In most practical cases the covariance matrix is neither the zero nor an infinite matrix and therefore one of the solutions given in Ch. 4 and 5 heve to be used. Because the results of both solutions are identical, we can use one of these solutions with respect to the practical computation. From this point of view, normally the solution in Ch. 4 may be more suitable.

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