Date Log
This work is licensed under a Creative Commons Attribution 4.0 International License.
Application of Advanced Statistical Procedures for Adjustment of Results in Measurements of Displacements
Corresponding Author(s) : Janusz Andrzej Dąbrowski
Geomatics and Environmental Engineering,
Vol. 13 No. 1 (2019): Geomatics and Environmental Engineering
Abstract
In this paper, the authors verified the formulated principles of the estimation of Gauss‑Markov models in which estimated parameters X were random. For this purpose, methods for the prior definition of covariance matrix CX for the estimated parameters were provided, which were used to determine the conditional covariance matrix of observation vector L and then estimate the most probable values of parameters X^. Covariance matrix Cov(X^) obtained as a result of this estimation was used to define the limit values of the variance of these parameters.
Practical application of the proposed method for the Gauss‑Markov model estimation for random parameters was illustrated on a fragment of a leveling network of points to determine the vertical displacements of a landslide surface.
Keywords
Download Citation
Endnote/Zotero/Mendeley (RIS)BibTeX
- Wiśniewski Z.: Rachunek wyrównawczy w geodezji: (z przykładami). Wydawnictwo Uniwersytetu Warmińsko-Mazurskiego, Olsztyn 2005.
- Baarda W.: Statistical concepts in geodesy. Netherlands Geodetic Commission, Publications on Geodesy, New Series 2, No. 4, Delft 1967.
- Teunissen P.J.G.: Adjustment theory – an introduction. VSSD, Delft 2000.
- Rao C.R.: Modele liniowe statystyki matematycznej. PWN, Warszawa 1982.
- Cross P.A.: Numerical methods in network design. [in:] Grafarend E.W., Sanso F. (eds.), Optimization and design of geodetic networks, Springer, Berlin – Heidelberg – New York 1985, pp. 132–168.
- Kampmann G.: Robuste Deformationsanalyse mittels balancierter Ausgleichung. Allgemeine Vermessungs-Nachrichten: AVN. Zeitschrift für alle Bereiche der Geodäsie und Geoinformation, vol. 101, 1994, 1, pp. 8–18.
- Caspary W.: Anmerkungen zur balancierten Ausgleichung. Zeitschrift für Vermessungswesen, vol. 123, no. 8, 1998, pp. 271–273.
- Kampmann G., Krause B.: Balanced observations with a straight line fit. Bollettino di Geodesia a Scienze Affini, vol. 55, no. 2, 1996, pp. 134–141.
- Hekimoglu S.: Change of the diagonal elements of the hat matrix under changing weight and changing position of an observation. Zeitschrift für Vermessungswesen, vol. 123, no. 8, 1998, pp. 266–271.
- Czaja J., Dąbrowski J.: Application of advanced statistical procedures for the adjustment of measurement results in engineering surveying. Geomatics and Environmental Engineering, vol. 12, no. 4, 2018, pp. 33–44.
References
Wiśniewski Z.: Rachunek wyrównawczy w geodezji: (z przykładami). Wydawnictwo Uniwersytetu Warmińsko-Mazurskiego, Olsztyn 2005.
Baarda W.: Statistical concepts in geodesy. Netherlands Geodetic Commission, Publications on Geodesy, New Series 2, No. 4, Delft 1967.
Teunissen P.J.G.: Adjustment theory – an introduction. VSSD, Delft 2000.
Rao C.R.: Modele liniowe statystyki matematycznej. PWN, Warszawa 1982.
Cross P.A.: Numerical methods in network design. [in:] Grafarend E.W., Sanso F. (eds.), Optimization and design of geodetic networks, Springer, Berlin – Heidelberg – New York 1985, pp. 132–168.
Kampmann G.: Robuste Deformationsanalyse mittels balancierter Ausgleichung. Allgemeine Vermessungs-Nachrichten: AVN. Zeitschrift für alle Bereiche der Geodäsie und Geoinformation, vol. 101, 1994, 1, pp. 8–18.
Caspary W.: Anmerkungen zur balancierten Ausgleichung. Zeitschrift für Vermessungswesen, vol. 123, no. 8, 1998, pp. 271–273.
Kampmann G., Krause B.: Balanced observations with a straight line fit. Bollettino di Geodesia a Scienze Affini, vol. 55, no. 2, 1996, pp. 134–141.
Hekimoglu S.: Change of the diagonal elements of the hat matrix under changing weight and changing position of an observation. Zeitschrift für Vermessungswesen, vol. 123, no. 8, 1998, pp. 266–271.
Czaja J., Dąbrowski J.: Application of advanced statistical procedures for the adjustment of measurement results in engineering surveying. Geomatics and Environmental Engineering, vol. 12, no. 4, 2018, pp. 33–44.