Case Studies
May 17, 2021

Geodetic Network Geometry versus Reliability Measures in Examples of the Trilateration Network

Publication: Journal of Surveying Engineering
Volume 147, Issue 3

Abstract

The article describes selected case studies of the trilateration network design. The analyzed case studies may be of interest to the geodetic community but may also be potentially interesting for educational purposes. The reference system of the trilateration network in all analyzed variants defined two fixed points. The aim of this article is to assess the impact of network geometry on reliability measures. To investigate this impact, seven criteria for assessing network geometry were defined. Four criteria relate to the shape of the network, whereas the other three describe the location of two fixed points (reference system) relative to the other network points. The subject of the research were correlations between the values of the adopted criteria for assessing the network geometry and the values of reliability measures that were obtained in individual analyzed variants of the network. Based on these studies, appropriate conclusions were formulated regarding the impact of the network geometry on the values of reliability measures in relation to the tested network examples.

Get full access to this article

View all available purchase options and get full access to this article.

Data Availability Statement

All data, models, or code generated or used during the study are available from the corresponding author by request.

Acknowledgments

The research was carried out as part of the work WZ/WBiIŚ/6/2019 financed from the funds of the Ministry of Science and Higher Education.

References

Baarda, W. 1968. A testing procedure for use in geodetic networks. Delft, Netherlands: Netherlands Geodetic Commission.
Baarda, W. 1973. S-transformation and criterion matrices. Delft, Netherlands: Netherlands Geodetic Commission.
Berné, J. L., and S. Baselga. 2004. “First-order design of geodetic networks using the simulated annealing method.” J. Geod. 78 (1–2): 47–54. https://doi.org/10.1007/s00190-003-0365-y.
Cross, P. A. 1985. “Numerical methods in network design.” In Optimization and design of geodetic networks, edited by E. W. Grafarend and F. Sansò, 429–435. Berlin: Springer.
Cross, P. A., and B. M. Whiting. 1982. “On the design of vertical control networks using iterative methods.” In Vol. 111 of Proc., 6th Symp. on Geodetic Networks and Computations, 35–46. Munich, Germany: Deutsche Geodätische Kommision.
Evans, J. D. 1996. Straightforward for the behavioral sciences. Pacific Grove, CA: Brooks/Cole.
Even-Tzur, G. 2006. “Datum definition and its influence on the reliability of geodetic networks.” Z. Vermessungswesen 131 (2): 87–95.
Even-Tzur, G., and H. B. Papo. 1996. “Optimization of GPS networks by linear programming.” Surv. Rev. 33 (262): 537–545. https://doi.org/10.1179/sre.1996.33.262.537.
Grafarend, E. W. 1974. “Optimization of geodetic networks.” Can. Surveyor 28 (5): 716–723. https://doi.org/10.1139/tcs-1974-0120.
Grafarend, E. W., and F. Sansò. 1985. Optimization and design of geodetic networks. 1st ed. Berlin: Springer.
Hsu, R., H. C. Lee, and S. P. Kao. 2008. “Three-dimensional networks are horizontally superior in robustness: A mathematical reasoning.” J. Surv. Eng. 134 (2): 61–65. https://doi.org/10.1061/(ASCE)0733-9453(2008)134:2(61).
Kobryń, A. 2020. “Multicriteria decision making in geodetic network design.” J. Surv. Eng. 146 (1): 1–10. https://doi.org/10.1061/(ASCE)SU.1943-5428.0000301.
Koch, K. R. 1982. Optimization of the configuration of geodetic networks, 82–89. Munich, Germany: Deutsche Geodaetische Kommission.
Koch, K. R. 1985. “First order design: Optimization of the configuration of a network by introducing small position changes.” In Proc., Optimization and Design of Geodetic Networks. Berlin: Springer.
Kuang, S. L. 1993. “Second-order design. Shooting for maximum reliability.” J. Surv. Eng. 119 (3): 102–110. https://doi.org/10.1061/(ASCE)0733-9453(1993)119:3(102).
Kuang, S. L. 1996. Geodetic network analysis and optimal design: Concepts and application. Ann Arbor, MI: Ann Arbor Press.
Prószyński, W., and M. Kwaśniak. 2018. “Analytic tools for investigating the structure of network reliability measures with regard to observation correlations.” J. Geod. 92 (3): 321–332. https://doi.org/10.1007/s00190-017-1064-4.
Schaffrin, B. 1985. “Aspects of network design.” In Optimization and design of geodetic networks, edited by E. W. Grafarend and F. Sansò, 548–597. Berlin: Springer.
Schmitt, G. 1980. “Second order design of free distance networks considering different types of criterion matrices.” Bull. Géodésique 54 (4): 531–542. https://doi.org/10.1007/BF02530711.
Schmitt, G. 1982. “Optimization of geodetic networks.” Rev. Geophys. 20 (4): 877–884. https://doi.org/10.1029/RG020i004p00877.
Schmitt, G. 1985. “Second order design.” In Optimization and design of geodetic networks, edited by E. W. Grafarend and F. Sansò, 74–121. Berlin: Springer.
Seemkooei, A. A. 2001a. “Comparison of reliability and geometrical strength criteria in geodetic networks.” J. Geod. 75 (4): 227–233. https://doi.org/10.1007/s001900100170.
Seemkooei, A. A. 2001b. “Strategy for designing geodetic network with high reliability and geometrical strength.” J. Surv. Eng. 127 (3): 104–117. https://doi.org/10.1061/(ASCE)0733-9453(2001)127:3(104).
Simkooei, A. A. 2004. “A new method for second order design of geodetic network: Aiming of high reliability.” Surv. Rev. 37 (293): 552–560. https://doi.org/10.1179/sre.2004.37.293.552.
Simkooei, A. A., J. Asgari, F. Zangeneh-Nejad, and S. Zaminpardaz. 2012. “Basic concepts of optimization and design of geodetic networks.” J. Surv. Eng. 138 (4): 172–183. https://doi.org/10.1061/(ASCE)SU.1943-5428.0000081.
Singh, V., R. Dwivedi, O. Dikshit, and A. K. Singh. 2016. “First-order design of GPS networks using particle swarm optimization.” J. Surv. Eng. 142 (3): 04016002. https://doi.org/10.1061/(ASCE)SU.1943-5428.0000176.
Vaniček, P., M. R. Craymer, and E. J. Krakiwsky. 2001. “Robustness analysis of geodetic horizontal networks.” J. Geod. 75 (4): 199–209. https://doi.org/10.1007/s001900100162.
Vaniček, P., M. R. Craymer, E. J. Krakiwsky, Y. Gao, and P. Ong. 1991. Robustness analysis. Ottawa, Canada: Geodetic Survey Division.
Xu, P. L. 1980. “Multi-objective optimal second order design of networks.” Bull. Gédésique 63 (3): 297–308. https://doi.org/10.1007/BF02520478.
Xu, P. L., and E. W. Grafarend. 1995. “A multi-objective second order optimal design of deforming networks.” Geophys. J. Int. 120 (3): 577–589. https://doi.org/10.1111/j.1365-246X.1995.tb01840.x.

Information & Authors

Information

Published In

Go to Journal of Surveying Engineering
Journal of Surveying Engineering
Volume 147Issue 3August 2021

History

Received: Sep 5, 2020
Accepted: Mar 25, 2021
Published online: May 17, 2021
Published in print: Aug 1, 2021
Discussion open until: Oct 17, 2021

Permissions

Request permissions for this article.

Authors

Affiliations

Professor, Faculty of Civil Engineering and Environmental Sciences, Bialystok Univ. of Technology, Wiejska St. 45E, Białystok 15-351, Poland. ORCID: https://orcid.org/0000-0002-4775-8164. Email: [email protected]

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

  • Horizontal Reference Network Densification by Multiple Free Stations, Journal of Surveying Engineering, 10.1061/JSUED2.SUENG-1461, 149, 4, (2023).

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share