Gauss-Markov model with random parameters to adjust results of surveys of geodetic control networks

• Autorzy: Banaś Marek , Czaja Józef , Dąbrowski Janusz

Identyfikatory

DOI

10.2478/rgg-2021-0001

• Języki publikacji: EN

Abstrakty

EN

Alignment of an engineering object project in the field is always conducted at the points of the geodetic control network, the coordinates of which are determined on the basis of the results of its elements survey and with connection to the national spatial reference system. The points of the national spatial reference system determined on the basis of previous surveys have specified coordinates with adequate accuracy, which is included in their covariance matrix. The coordinates of the geodetic control network points are determined more accurately than the points of the national spatial reference system and this means that the results of surveys of the geodetic control network have to be adequately incorporated into the coordinates of the reference points. In order to perform this incorporation, it may be assumed that the coordinates of the reference points are random, that is, they have acovariance matrix, which should be used in the process of adjusting the results of the geodetic control network observation. This research paper presents the principles for the estimation of the Gauss-Markov model parameters applied in case of those geodetic control networks in which the coordinates of the reference points have random character. On the basis of the observation equations δ+AX=L for the geodetic control network and using the weighting matrix Pand the matrix of conditional covariances [wzór] for the observation vector L, the parameter vector X is estimated in the form of the derived formula [wzór]. The verification of these estimation principles has been illustrated by the example of a fragment of a levelling geodetic control network consisting of three geodetic control points and two reference points of the national spatial reference system. The novel feature of the proposed solution is the application of covariance matrices of the reference point coordinates to adjust the results of the survey of geodetic control networks and to determine limit standard deviations for the estimated coordinates ofgeodetic control network points.

Słowa kluczowe

EN

model estimation; random parameters; geodetic control network

PL

estymacja modelu; parametry losowe; osnowa geodezyjna

• Wydawca: Wydział Geodezji i Kartografii Politechniki Warszawskiej
• Czasopismo: Reports on Geodesy and Geoinformatics
• Rocznik: 2021
• Tom: Vol. 111
• Strony: 1--6
• Opis fizyczny: Bibliogr. 14 poz., tab., wykr.

Twórcy

autor

Banaś Marek

• Institute of Technical Engineering, PWSTE in Jarosław, 16 Czarnieckiego Street, 37-500, Jarosław, Poland

autor

Czaja Józef

• Institute of Technical Engineering, PWSTE in Jarosław, 16 Czarnieckiego Street, 37-500, Jarosław, Poland

autor

Dąbrowski Janusz

• Institute of Technical Engineering, PWSTE in Jarosław, 16 Czarnieckiego Street, 37-500, Jarosław, Poland

Bibliografia

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• 4. Caspary, W. (1998). Anmerkungen zur balancierten Ausgleichung (Comments on the balanced adjustment). Zeitschrift für Vermessungswesen, 123(8):271-273.
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• 6. Dąbrowski, J. (2014). Zagadnienia geodezji inżynieryjnej dotyczące inwestycji drogowych [Geodesy engineering issues for road investments]. Wydawnictwa Naukowe / Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie, Cracow.
• 7. Hekimoglu, S. (1998). Change of the diagonal elements of the hatmatrix under changing weight and changing position of an observation. Zeitschrift für Vermessungswesen, 123(8):266-271.
• 8. Kampmann, G. (1994). Robuste Deformations analyse mittels balancierter Ausgleichung (Robust deformation analysis by means of balanced adjustment). Allgemeine Vermessungs-Nachrichten, 101(1):8-17.
• 9. Kampmann, G. and Krause, B. (1996). Balanced observations with a straight line fit. Bollettino di geodesia e scienze affini, 55(2):133-141.
• 10. Pope, A. J. (1976). The statistics of residuals and the detection of outliers. US Department of Commerce, National Oceanic and Atmospheric Administration, National Ocean Survey, National Geodetic Survey, Geodetic Research and Development Laboratory.
• 11. Prószyński, W. (1997). Measuring the robustness potential of the least-squares estimation: geodetic illustration. Journal of Geodesy, 71(10):652-659.
• 12. Prószyński, W. (2000). On outlier-hiding effects in specific Gauss-Markov models: geodetic examples. Journal of geodesy,74(7):581-589, doi:10.1007/s001900000121.
• 13. Rao, C. (1982). Linear models in mathematical statistics. PWN, Warsaw, Poland.
• 14. Teunissen, P. J. (2000). Adjustment theory. VSSD, Delft, The Netherlands

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).