Abstract
It is shown that also in a rank deficient Gauss-Markov model higher weights of the observations automatically improve the precision of the estimated parameters as long as they are computed in thesame datum. However, the amount of improvement in terms of the trace of the dispersion matrix isminimum for the so-called “free datum” which corresponds to the pseudo-inverse normal equations matrix. This behaviour together with its consequences is discussed by an example with special emphasis on geodetic networks for deformation analysis.
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References
W. BAARDA (1973), S-transformations and criterion matrices. Neth. Geod. Comm, Publ. on Geodesy, Vol.5, No. 1, Delft 1973.
Y. BOCK/B. SCHAFFRIN (1988): Deformation analysis based on robust inverse theory.Part 1: Theoretical background, Paper pres. to the 17th. Conf. on Math. Geophysics, Blanes/Spain 1988.
F. CROSILLA/T. RUSSO (1986): A software tool for the interactive improved design of a geodetic network. Boll. di Geod. e Sci. Affini45 (1986), pp. 1–32.
D. FRITSCH/B. SCHAFFRIN (1982). The “Choice-of-Norm” problem for the free net adjustment with orientation parameters. Boll. di Geod. e Sci. Affini41 (1982), pp. 259–282.
E. GRAFAREND (1974): Optimization of geodetic networks. Boll. di Geod. e Sci. Affini33 (1974), pp. 351–406.
E. GRAFAREND/E. KNICKMEYER/B. SCHAFFRIN (1982): Geodätische Datum-Transformationen” ZfV107 (1982), pp. 15–25.
K.R. KOCH (1980): Parameterschätzung und Hypothesentests in linearen Modellen. Dümmler: Bonn 1980.
K.R. KOCH (1982). S-transformations and projections for obtaining estimable parameters,in: “Forty Years of Thought” (Festschrift W. Baarda), Vol.1, Delft 1982, pp. 136–144.
W. MARSHALL/I. OLKIN (1979): Inequalities: Theory of majorization and its applications. Academic Press, New York.
G.A. MILLIKEN/F. AKDENIZ (1977) A theorem on the difference of the generalized inverses of two nonnegative matrices, Commun. Statist. A-6 (1977), pp. 73–79.
W.H. PRESCOTT (1981) The determination of displacement fields from geodetic data along a strike-slip fault, J. Geophys. Res. B-86 (1981), pp. 6067–6072.
T. RUSSO (1988). Negative weights as output from a SOD algorithm: Are they really a problem? Boll. di Geod. e Sci. Affini, 47, (1988), pp. 313–321.
B. SCHAFFRIN (1975). Zur Verzerrtheit von Ausgleichungsergebnissen. Mitt. des Inst fur Theoret Geodäsie der Univ. Bonn, No.39, Bonn 1975.
B. SCHAFFRIN (1983). Varianz-Kovarianz-Komponenten-Schätzung bei der Ausgleichung heterogener Wiederholungsmessungen. Deutsche Geodät. Komm. C-282, München 1983.
B. SCHAFFRIN (1985): Network Design,in: E. Grafarend and F. Sansò (eds.), Optimization and Design of Geodetic Networks, Springer: Berlin etc. 1985, pp. 548–597.
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Crosilla, F., Russo, T. & Schaffrin, B. Improved second order design and the datum choice. Bull. Geodesique 63, 191–202 (1989). https://doi.org/10.1007/BF02519150
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DOI: https://doi.org/10.1007/BF02519150