Skip to main content
SpringerLink
Log in

A new relationship between the quality criteria for geodetic networks

  • Original Article
  • Published:
Journal of Geodesy Aims and scope Submit manuscript

Abstract

The goal of this paper is to present a new relationship between the quality criteria for geodetic networks. The quality criteria described here are fourfold: positional uncertainty of network points, considering both bias and precision (at a given confidence level); the maximum allowable number of undetected outliers; the level of reliability and its homogeneity for the observations; and the minimum power of the data snooping test procedure for multiple alternative hypotheses. The highlights consist of the use of advanced concepts, such as reliability measures for multiple outliers and the power of the test for multiple alternative hypotheses (instead of the single outlier and/or the single alternative hypothesis case); and a sequential computational procedure, wherein the quality criteria are mathematically related, instead of being treated as separate criteria. Its practical application is demonstrated numerically in the design of a real horizontal network. A satisfactory performance was achieved by means of simulations. Furthermore, Monte Carlo experiments were conducted to verify the power of the test and the positional uncertainty following the approach proposed. Results provide empirical evidence that the quality criteria present realistic outputs.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2

Adapted from Vanícek et al. (1996)

Fig. 3
Fig. 4
Fig. 5
Fig. 6

Adapted from Google Earth

Fig. 7

Adapted from Google Earth

Fig. 8

Adapted from Google Earth

Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Alizadeh-Khameneh MA, Eshagh M, Sjöberg LE (2015) Optimisation of lilla edet landslide GPS monitoring network. J Geodetic Sci 5:57–66. https://doi.org/10.1515/jogs-2015-0005

    Article  Google Scholar 

  • Alizadeh-Khameneh MA, Sjöberg LE, Jensen ABO (2017) Optimisation of GNSS networks—considering baseline correlations. Surv Rev. https://doi.org/10.1080/00396265.2017.1342896

  • Aydin C, Demirel H (2004) Computation of Baarda’s lower bound of the non-centrality parameter. J Geodesy 78:437–441

    Article  Google Scholar 

  • Baarda W (1968) A testing procedure for use in geodetic networks. Publications on Geodesy, Netherlands Geodetic Commission, Delft

    Google Scholar 

  • Baarda W (1973) S-transformation and criterion matrices. Publications on Geodesy, Netherlands Geodetic Commission, Delft

    Google Scholar 

  • Baarda W (1977) Measures for the accuracy of geodetic networks. In: Symposium on optimization of design and computation of control networks, pp 419–436

  • Bagherbandi M, Eshagh M, Sjoberg LE (2009) Multi-objective versus single-objective models in geodetic network optimization. Nordic J Surv Real Estate Res 6(1):7–20. https://journal.fi/njs/article/view/2703

  • Baselga S (2011) Second order design of geodetic networks by the simulated annealing method. J Surv Eng 137:167–173

    Article  Google Scholar 

  • Berber M (2006) Robustness analysis of geodetic networks. Ph.D. thesis, Department of Surveying Engineering, University of New Brunswick, Fredericton

  • Berber M, Hekimoglu S (2003) What is the reliability of conventional outlier detection and robust estimation in trilateration networks? Surv Rev 37(290):308–318. https://doi.org/10.1179/sre.2003.37.290.308

    Article  Google Scholar 

  • Berné JL, Baselga S (2004) First-order design of geodetic networks using the simulated annealing method. J Geodesy 78:47–54

    Article  Google Scholar 

  • BIPM I, IFCC I, IUPAC I, ISO O (2008) The international vocabulary of metrology: basic and general concepts and associated terms (VIM), 3rd edn. JCGM (Joint Committee for Guides in Metrology)

  • Coulot D, Pollet A, Collilieux X, Berio P (2010) Global optimization of core station networks for space geodesy: application to the referencing of the SLR EOP with respect to ITRF. J Geodesy 84(1):31–50

    Article  Google Scholar 

  • Dare P, Saleh H (2000) GPS network design: logistics solution using optimal and near-optimal methods. J Geodesy 74:467–478

    Article  Google Scholar 

  • Eshagh M, Alizadeh-Khameneh MA (2015) The effect of constraints on bi-objective optimisation of geodetic networks. Acta Geodaetica et Geophysica 50:449–459

    Article  Google Scholar 

  • Eshagh M, Kiamehr R (2007) A strategy for optimum designing of the geodetic networks from the cost, reliability and precision views. Acta Geodaetica et Geophysica Hungarica 42(3):297–308

    Article  Google Scholar 

  • Even-Tzur G (2002) GPS vector configuration design for monitoring deformation networks. J Geodesy 76:455–461

    Article  Google Scholar 

  • Förstner W (1983) Reliability and discernability of extended gauss-markov models. In: Deut. Geodact. Komm. Seminar on Math. Models of Geodetic Photogrammetric Point Determination with Regard to Outliers and Systematic Errors, pp 79–104

  • Förstner W (1987) Reliability analysis of parameter estimation in linear models with applications to mensuration problems in computer vision. Comput Vis Graph Image Process 40(3):273–310

    Article  Google Scholar 

  • Ghilani CD (2010) Adjustment computations: spatial data analysis, 5th edn. Wiley, Hoboken

    Google Scholar 

  • Grafarend EW (1974) Optimization of geodetic networks. Bollettino di geodesia e scienze affini 33:351–406

    Google Scholar 

  • Grafarend EW, Sanso F (1985) Optimization and design of geodetic networks. Springer, Berlin

    Book  Google Scholar 

  • Guzatto MP (2017) Design of horizontal networks by means of numerical simulations (in Portuguese). Master’s thesis, Universidade Federal do Rio Grande do Sul, Porto Alegre

  • Hekimoglu S (1997) Finite sample breakdown points of outlier detection procedures. J Surv Eng 123(1):15–31. https://doi.org/10.1061/(ASCE)0733-9453(1997)123:1(15)

    Article  Google Scholar 

  • Helmert FB (1868) Studien uber rationelle vermessungen im gebiete der hoheren geodasie... Leipzig, Druck von BG Teubner 1

  • Huber PJ (1964) Robust estimation of a location parameter. Ann Math Stat 35:73–101

    Article  Google Scholar 

  • Kargoll B (2007) On the theory and application of model misspecification tests in geodesy. Ph.D. thesis, Universitäts-und Landesbibliothek, Bonn

  • Kavouras M (1982) On the detection of outliers and the determination of reliability in geodetic networks. Ph.D. thesis, Department of Surveying Engineering, University of New Brunswick, Fredericton

  • Klein I (2014) Proposal of a new method for geodetic networks design (in Portuguese). Ph.D. thesis, Universidade Federal do Rio Grande do Sul, Porto Alegre

  • Klein I, Matsuoka MT, Souza SF, Collischonn C (2012) Design of geodetic networks reliable against multiple outliers (in Portuguese). Boletim de Ciências Geodésicas 18:480–507

    Article  Google Scholar 

  • Klein I, Matsuoka MT, Guzatto MP (2015) How to estimate the minimum power of the test and bound values for the confidence interval of data snooping procedure (in Portuguese). Boletim de Ciências Geodésicas 21:26–42

    Article  Google Scholar 

  • Klein I, Matsuoka M, Guzatto M, Nievinski F (2017) An approach to identify multiple outliers based on sequential likelihood ratio tests. Surv Rev 49(357):449–457

    Article  Google Scholar 

  • Knight NL, Wang J, Rizos C (2010) Generalised measures of reliability for multiple outliers. J Geodesy 84:625–635

    Article  Google Scholar 

  • Koch KR (2015) Minimal detectable outliers as measures of reliability. J Geodesy 89(5):483–490

    Article  Google Scholar 

  • Kotsakis C (2013) Generalized inner constraints for geodetic network densification problems. J Geodesy 87(7):661–673

    Article  Google Scholar 

  • Kuang S (1991) Optimization and design of deformation monitoring schemes. Ph.D. thesis, Department of Surveying Engineering, University of New Brunswick, Fredericton

  • Kuang S (1993) Second-order design: shooting for maximum reliability. J Surv Eng 119(3):102–110

    Article  Google Scholar 

  • Kuang S (1996) Geodetic network analysis and optimal design: concepts and applications. Ann Arbor Press Inc., Ann Arbor

    Google Scholar 

  • Kusche J (2002) A monte-carlo technique for weight estimation in satellite geodesy. J Geodesy 76:641–652

    Article  Google Scholar 

  • Lehmann R (2012) Improved critical values for extreme normalized and studentized residuals in Gauss–Markov models. J Geodesy 86:1137–1146

    Article  Google Scholar 

  • Lehmann R (2013) On the formulation of the alternative hypothesis for geodetic outlier detection. J Geodesy 87:373–386

    Article  Google Scholar 

  • Lehmann R, Lösler M (2016) Multiple outlier detection: hypothesis tests versus model selection by information criteria. J Surv Eng 142(4):04016,017

    Article  Google Scholar 

  • Lehmann R, Voß-Böhme A (2017) On the statistical power of Baardas outlier test and some alternative. J Geodetic Sci 7(1):68–78

    Article  Google Scholar 

  • Leick A, Rapoport L, Tatarnikov D (2015) GPS satellite surveying. Wiley, Hoboken

    Book  Google Scholar 

  • Monico JFG, Dal Poz AP, Galo M, Dos Santos MC, Oliveira LC (2009) Accuracy and precision: reviewing the concepts by means of an accurate procedure (in Portuguese). Boletim de Ciências Geodésicas 15:469–483

    Google Scholar 

  • Ober P (1996) A new, generally applicable metrics for RAIM/AAIM integrity monitoring. Proc ION GPS Inst Navig 9:1677–1686

    Google Scholar 

  • Pelzer H (1980) Some criteria for the accuracy and the reliability of networks. Deutsche Geodätische Kommission, Reihe B, p 252

  • Prószyński W (2015) Revisiting Baardas concept of minimal detectable bias with regard to outlier identifiability. J Geodesy 89(10):993–1003

    Article  Google Scholar 

  • Rousseeuw PJ, Leroy AM (1987) Robust regression and outlier detection. Wiley, Hoboken

    Book  Google Scholar 

  • Schaffrin B (1981) Some proposals concerning the diagonal second order design of geodetic networks. Manuscripta Geodetica 6:303–326

    Google Scholar 

  • Schaffrin B (1997) Reliability measures for correlated observations. J Surv Eng 123:126–137

    Article  Google Scholar 

  • Seemkooei AA (2001a) Comparison of reliability and geometrical strength criteria in geodetic networks. J Geodesy 75:227–233

    Article  Google Scholar 

  • Seemkooei AA (2001b) Strategy for designing geodetic network with high reliability and geometrical strength. J Surv Eng 127:104–117

    Article  Google Scholar 

  • Seemkooei AA (2004) A new method for second order design of geodetic networks: aiming at high reliability. Surv Rev 37:552–560

    Article  Google Scholar 

  • Seemkooei AA, Sharifi MA (2004) Approach for equivalent accuracy design of different types of observations. J Surv Eng 130:1–5

    Article  Google Scholar 

  • Seemkooei AA, Asgari J, Zangeneh-Nejad F, Zaminpardaz S (2012) Basic concepts of optimization and design of geodetic networks. J Surv Eng 138:172–183

    Article  Google Scholar 

  • Singh V, Dwivedi R, Dikshi O (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

    Article  Google Scholar 

  • Song Z, Zhao C, Pu H, Li X (2016) Configuration analysis of two-dimensional resection networks. J Surv Eng 142(4):04016018. https://doi.org/10.1061/(ASCE)SU.1943-5428.0000193

    Article  Google Scholar 

  • Teunissen PJG (2018) Distributional theory for the dia method. J Geodesy 92(1):59–80. https://doi.org/10.1007/s00190-017-1045-7

    Article  Google Scholar 

  • Teunissen PJG (2003) Adjustment theory: an introduction. Delft University Press, Delft

    Google Scholar 

  • Teunissen PJG (2006) Testing theory: an introduction, 2nd edn. VSSD, Delft

    Google Scholar 

  • Vanícek P, Krakiwsky EJ (1986) Geodesy-the concepts, 2nd edn. Elsevier, Amsterdam

    Google Scholar 

  • Vanícek P, Krakiwsky EJ, Craymer MR, Gao Y, Ong PJ (1990) Robustness analysis. Department of Surveying Engineering, University of New Brunswick, Frederiction

    Google Scholar 

  • Vanícek P, Ong PJ, Krakiwsky EJ, Craymer MR (1996) Application of robustness analysis to large geodetic networks. Department of Geodesy and Geomatics Engineering, University of New Brunswick, Frederiction

    Google Scholar 

  • Wang J, Chen Y (1994) On the reliability measure of observations. Acta Geodaet et Cartograph Sin 4:42–51

    Google Scholar 

  • Xu P (1989) Multi-objective optimal second order design of networks. Bulletin géodésique 63(3):297–308

    Article  Google Scholar 

  • Xue S, Yang Y, Dang Y, Chen W (2014) Dynamic positioning configuration and its first-order optimization. J Geodesy 88(2):127–143

    Article  Google Scholar 

  • Yang L, Wang J, Knight NL, Shen Y (2013) Outlier separability analysis with a multiple alternative hypotheses test. J Geodesy 87:591–604

    Article  Google Scholar 

  • Yang L, Li B, Shen Y, Rizos C (2017) Extension of internal reliability analysis regarding separability analysis. J Surv Eng 143(3):04017,002

    Article  Google Scholar 

  • Yetkin M (2013) Metaheuristic optimisation approach for designing reliable and robust geodetic networks. Surv Rev 45(329):136–140

    Google Scholar 

  • Yetkin M, Berber M (2012) GPS baseline configuration design based on robustness analysis. J Geodetic Sci 2(3):234–239

    Article  Google Scholar 

  • Yetkin M, Inal C, Yigit CO (2008) Optimal design of deformation monitoring networks using PSO algorithm. In: 13th FIG symposium on deformation measurement and analysis, 4th IAG symposium on geodesy and geotechnical and structural engineering, pp 12–15

Download references

Acknowledgements

The authors would like to thank the National Council for Scientific and Technological Development (CNPq) for financial support (Processes 303306/2012-2, 477914/2012-8, 305599/2015-1 and 309399/2014-9). We also like to thank the reviewers for their comments and suggestions which helped in the improvement of this paper. Finally, we dedicate this work to Professor Baarda (in memoriam) for the fifty years of Baarda (1968).

Author information

Authors and Affiliations

  1. Land Surveying Program, Federal Institute of Santa Catarina (IFSC), Florianópolis, Brazil

    Ivandro Klein & Matheus Pereira Guzatto

  2. Graduate Program in Geodetic Sciences Federal University of Paraná (UFPR), Curitiba, Brazil

    Ivandro Klein

  3. Laboratory of Surveying and Geodesy, Federal University of Uberlândia (UFU), Monte Carmelo, Brazil

    Marcelo Tomio Matsuoka & Vinicius Francisco Rofatto

  4. Graduate Program in Remote Sensing Federal University of Rio Grande do Sul (UFRGS), Porto Alegre, Brazil

    Marcelo Tomio Matsuoka & Vinicius Francisco Rofatto

  5. Department of Geodesy, Graduate Program in Remote Sensing, Federal University of Rio Grande do Sul (UFRGS), Porto Alegre, Brazil

    Felipe Geremia Nievinski

  6. Advanced Visualization Laboratory (Vizlab), Graduate Program in Applied Computing, Unisinos University, São Leopoldo, Brazil

    Mauricio Roberto Veronez

Authors
  1. Ivandro Klein
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marcelo Tomio Matsuoka
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Matheus Pereira Guzatto
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Felipe Geremia Nievinski
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Mauricio Roberto Veronez
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Vinicius Francisco Rofatto
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ivandro Klein.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Klein, I., Matsuoka, M.T., Guzatto, M.P. et al. A new relationship between the quality criteria for geodetic networks. J Geod 93, 529–544 (2019). https://doi.org/10.1007/s00190-018-1181-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00190-018-1181-8

Keywords

Search

Navigation