Adjustment and Gross Errors Detection of Free Triangulation Geodetic Network Using Minimum-Norm Least-Squares Inverses and Data Snooping
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Keywords

Minimum-norm least-squares
triangulation network
iterative procedure
free-network
data snooping procedure
T-Test criterion
critical value

How to Cite

1.
Ahmed Abdalla, Awadelgeed Mohamed, Abdelrhman Khabeer. Adjustment and Gross Errors Detection of Free Triangulation Geodetic Network Using Minimum-Norm Least-Squares Inverses and Data Snooping. Glob. J. Earth Sci. Eng. [Internet]. 2015Dec.31 [cited 2022Jan.16];2(2):31-40. Available from: https://www.avantipublishers.com/jms/index.php/gjese/article/view/368
Received 2016-02-03
Accepted 2016-02-03
Published 2015-12-31

Abstract

We utilise minimum-norm least-squares based on the indirect observations methods to adjust our 2-dimensional triangulation network. The main objective of this paper is to optimally adjust the approximate coordinates of the nodes (points) of the given network. The network observations (11 measured distances and 17 angles) have been adjusted by being combined in linear system of equations in terms of free-network adjustment procedure to rigorously adjust the approximate coordinates over the network points. We obtained better converged values by applying an iterative procedure, the minimum corrections for the free-network coordinates are obtained after a number of five iterations. The data snooping procedure has been used to test the reliability and precision of the network observations. The T-Test criterion is then applied for gross error detection, five angles and two lines are suspected to include gross errors at a critical value of 1.98.

https://doi.org/10.15377/2409-5710.2015.02.02.2
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References

Allan AL, Hollwey JR and Maynes JHB. Practical Field Surveying and Computations. London: Butterworth- Heinemann Ltd; 1973.

Anderson JM, Anderson JM and Mikhail EM. Surveying, theory and practice. 7th ed WCB/McGraw-Hill; 1998.

De A. Plane Surveying. S Chand 2000.

Ghilani CD. Adjustment Computations: Spatial Data Analysis. 5th ed. Hoboken. NJ Wiley; 2010.

Kuang S. Geodetic Network Analysis and Optimal Design: Concepts and Applications. Ann Arbor Press 1996.

Schmitt G. Review of Network Designs: Criteria, Risk Functions. Design Ordering In: Grafarend EW, Sansó F, editors. Optimization and Design of Geodetic Networks. Springer Berlin Heidelberg 1985; 6-10.

Schmitt G. Second Order Design. In: Grafarend EW, Sansó F, editors. Optimization and Design of Geodetic Networks. Springer Berlin Heidelberg 1985; 74-121.

Schmitt G. Third Order Design. In: Grafarend EW, Sansó F, editors. Optimization and Design of Geodetic Networks. Springer Berlin Heidelberg 1985; 122-131.

Teunissen P. Zero Order Design: Generalized Inverses, Adjustment, the Datum Problem and S-Transformations. In: Grafarend EW, Sansó F, editors. Optimization and Design of Geodetic Networks. Springer Berlin Heidelberg 1985; 11-55.

Grafarend EW and Sansó F. Optimization and Design of Geodetic Networks. Springer Berlin Heidelberg 1985.

Mittermayer E. A generalisation of the least-squares method for the adjustment of free networks. Bulletin Géodésique 1972; 104(1): 139-157.

Welsch W. A review of the adjustment of free networks. Survey Review 1979; 25(194): 167-180.

Perelmuter A. Adjustment of free networks. Bulletin Géodésique 1979; 53(4): 291-295.

Blaha G. A note on adjustment of free networks. Bulletin Géodésique 1982; 56(4): 281-299.

Eshagh M and Kiamehr R. A strategy for optimum designing of the geodetic networks from the cost, reliability and precision views. Acta Geodaetica et Geophysica Hungarica 2013; 42(3): 297-308.

Bjerhammar A. Theory of errors and generalized matrix inverses. Elsevier 1973.

Fan H. Theory of Errors and Least Squares Adjustment. Stockholm, Sweden: Royal Institute of Technology (KTH) 1997.

Abdalla A. Adjustment of 2-dimensional geodetic networks. Royal Institute of Technology (KTH) 2008.

Chan T and Hansen P. Some Applications of the Rank Revealing QR Factorization. SIAM Journal on Scientific and Statistical Computing 1992; 13(3): 727-741.

Hong YP and Pan CT. Rank-Revealing QR Factorizations and the Singular Value Decomposition. Mathematics of Computation 1992; 58(197): 213-232.

Gu M and Eisenstat SC. Efficient algorithms for computing a strong rank-revealing QR factorization. Siam Journal on Scientific Computing 1996; 17(4): 848-869.

Baarda W. Some Remarks on the Computation and Adjustment of Large Systems of Geodetic Triangulation: Report Pres. at the Tenth General Assembly of the Int Ass of Geodesy at Rome 1954; 1957.

Baarda W. Statistical concepts in geodesy. Netherlands: Waltman 1967.

Baarda W. S-transformations and criterion matrices. Netherlands: Rijkscommissie voor Geodesie 1981.

Baarda W. Precision, Accuracy and Reliability of Observations. Delft, Netherlands: Technische Hogeschool Delft Afdeling der Geodesie 1983.

Teunissen P. Network quality control. VSSD 2006.