DOI: https://doi.org/10.14710/geoplanning.6.1.21-30

Monte Carlo Simulation for Outlier Identification Studies in Geodetic Network: An Example in A Levelling Network Using Iterative Data Snooping

*Marcelo Tomio Matsuoka scopus  -  Federal University of Uberlândia, Brazil
Vinícius Francisco Rofatto  -  Federal University of Uberlândia (UFU), Brazil
Ivandro Klein  -  Federal Institute of Santa Catarina (IFSC), Brazil
Alexandre Gomes  -  Federal University of Uberlândia (UFU), Brazil
Matheus Guzatto  -  Federal Institute of Santa Catarina (IFSC), Brazil

Citation Format:
Abstract
Today with the fast and powerful computers, large data storage systems and modern softwares, the probabilities distribution and efficiency of statistical testing algorithms can be estimated using computerized simulation. Here, we use Monte Carlo simulation (MCS) to investigate the power of the test and error probabilities of the Baarda’s iterative data snooping procedure as test statistic for outlier identification in the Gauss-Markov model. The MCS discards the use of the observation vector of Gauss-Markov model. In fact, to perform the analysis, the only needs are the Jacobian matrix; the uncertainty of the observations; and the magnitude intervals of the outliers. The random errors (or residuals) are generated artificially from the normal statistical distribution, while the size of outliers is randomly selected using standard uniform distribution. Results for simulated closed leveling network reveal that data snooping can locate an outlier in the order of magnitude 5σ with high success rate. The lower the magnitude of the outliers, the lower is the efficiency of data snooping in the simulated network. In general, considering the network simulated, the data snooping procedure was more efficient for α=0.01 (1%) with 82.8% success rate.
Fulltext View|Download
Keywords: Geodetic Network; Outlier; Monte Carlo Simulation

Article Metrics:

Article Info
Section: Original Research
Language : EN
Recent articles
Spatial Distribution of Potential Area for Community Forest Development in Grindulu Watershed Assessing Landscape Pattern Relationship with Dengue Incidence in Peninsular Malaysia Geometric Accuracy Assessment for Shoreline Derived from NDWI, MNDWI, and AWEI Transformation on Various Coastal Physical Typology in Jepara Regency using Landsat 8 OLI Imagery in 2018 More recent articles
Most cited articles
SATELLITE-DERIVED BATHYMETRY USING RANDOM FOREST ALGORITHM AND WORLDVIEW-2 IMAGERY Geometric Accuracy Assessment for Shoreline Derived from NDWI, MNDWI, and AWEI Transformation on Various Coastal Physical Typology in Jepara Regency using Landsat 8 OLI Imagery in 2018 QUALITY ANALYSIS OF SINGLE TREE OBJECT WITH OBIA AND VEGETATION INDEX FROM LAPAN SURVEILLANCE AIRCRAFT MULTISPECTRAL DATA IN URBAN AREA MODEL OF CLIMATE AND LAND-USE CHANGES IMPACT ON WATER SECURITY IN AMBON CITY, INDONESIA SPATIAL EXPLICIT MODELING TO UNDERSTAND THE DYNAMICS OF LANDUSE SWITCH USING OPEN SOURCE SATELLITE DATA More cited articles
  1. Aydin, C. and Demirel, H. (2004). Computation of Baarda's lower bound of the non-centrality parameter. Journal of Geodesy,78(4), pp. 437-411. DOI: http://dx.doi.org/10.1007/s00190-004-0406-1
  2. Baarda, W. (1968). A testing procedure for use in geodetic networks. [pdf] Delft: Publications on Geodesy, Netherlands Geodetic Commission. Available at: < https://pdfs.semanticscholar.org/71ae/0ba924157ba4b64a5e80fab2abba8401444b.pdf > [Accessed 02 april 2018]
  3. Berber, M. and Hekimoglu, S. (2003). What is the reliability of conventional outlier detection and robust estimation in trilateration networks? Survey Review,37(290), pp.308-318. DOI: https://doi.org/10.1179/sre.2003.37.290.308
  4. Erdogan, B. (2014). An outlier detection method in geodetic networks based on the original observations. Boletim de Ciências Geodésicas. 20(3), pp.578-589. DOI: http://dx.doi.org/10.1590/S1982-21702014000300033
  5. 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
  6. Ghilani, C. D. (2010). Adjustment computations: spatial data analysis, 5th edn. John Wiley & Sons, New Jersey
  7. Guzatto, M.P. (2017). Design of horizontal networks by numerical simulations (in Portuguese). Masters Dissertation, Programa de Pós-Graduação em Sensoriamento Remoto, Porto Alegre: Universidade Federal do Rio Grande do Sul
  8. Hekimoglu, S. and Koch, K. R. (1999). How Can Reliability of the Robust Methods be Measured?, in Third Turkish German Joint Geodetic Days, Altan and Gründing (Eds), 1-4June, Istanbul, Turkey, pp. 179-196
  9. Huber, P. J. (1964). Robust estimation of a location parameter. Annals of Mathematical Statistics. 35(1), pp.73-101
  10. Kavouras, M. (1982). On the detection of outliers and the determination of reliability in geodetic networks. PhD thesis, Fredericton: Department of Surveying Engineering, University of New Brunswick
  11. Klein, I. Matsuoka, M.T. Souza, S.F. and Veronez, M.R. (2011). Adjustment of observations: a geometric interpretation for the least squares method (in Portuguese). Boletim de Ciências Geodésicas, 17(2), pp.272-294. DOI: http://dx.doi.org/10.1590/S1982-21702011000200007
  12. Klein, I. Matsuoka, M. T. Souza, S. F. and Collischonn, C. (2012). Design of geodetic networks reliable against multiple outliers (in Portuguese). Boletim de Ciências Geodésicas, 18(3), pp.480-507. DOI: http://dx.doi.org/10.1590/S1982-21702012000300008
  13. Klein, I. Matsuoka, M. T. Guzatto, M. P. Souza, S. F. and Veronez, M. R. (2015a). On evaluation of different methods for quality control of correlated observations. Survey Review. 47(340), pp.28-35. DOI: https://doi.org/10.1179/1752270614Y.0000000089
  14. Klein, I. Matsuoka, M. T. and Guzatto, M. P. (2015b). 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(1), pp.26-42. DOI: http://dx.doi.org/10.1590/S1982-21702015000100003
  15. Klein, I. Matsuoka, M. T. Guzatto, M. P. and Nievinski, F. G. (2017). An approach to identify multiple outliers based on sequential likelihood ratio tests. Survey Review. 49(357), pp. 449-457. DOI: https://doi.org/10.1080/00396265.2016.1212970
  16. Koch, K. R. (1999). Parameter Estimation and Hypothesis Testing in Linear Models. Berlin Heidelberg New York, Springer Verlag
  17. Lehmann, R. (2012). Improved critical values for extreme normalized and studentized residuals in gauss-markov models. Journal of Geodesy. 86(12), pp.1137-1146. DOI: https://link.springer.com/article/10.1007/s00190-012-0569-0
  18. Lehmann, R. (2013). On the formulation of the alternative hypothesis for geodetic outlier detection. Journal of Geodesy, 87(4), pp.373-386. DOI: https://link.springer.com/article/10.1007%2Fs00190-012-0607-y
  19. Lehmann, R. and Scheffler, T. (2011). Monte Carlo-based data snooping with application to a geodetic network. Journal of Applied Geodesy. 5(3-4), pp.123-134. DOI: https://doi.org/10.1515/JAG.2011.014
  20. Lehmann, R. and Lösler, M. (2016). Multiple outlier detection: hypothesis tests versus model selection by information criteria. Journal of Surveying Engineering, 142(4), DOI: https://doi.org/10.1061/(ASCE)SU.1943-5428.0000189
  21. Lehmann, R. and Voß-Böhme, A. (2017). On the statistical power of Baarda’s outlier test and some alternative. Journal of Geodetic Science, 7(1), pp.68-78. DOI: https://doi.org/10.1515/jogs-2017-0008
  22. Niemeier, W. and Tengen, D. (2017). Uncertainty assessment in geodetic network adjustment by combining GUM and Monte-Carlo-simulations. Journal of Applied Geodesy., 11(2), pp.67-76. DOI: 10.1515/jag-2016-0017
  23. Rofatto, V.F. Matsuoka, M,T. and Klein, I. (2017). An attempt to analyse Baarda’s Iterative Data Snooping procedure based on Monte Carlo Simulation. South African Journal of Geomatics, 6(3), pp.416-435. DOI: http://dx.doi.org/10.4314/sajg.v6i3.11
  24. Rousseeuw, P. J. and Leroy, A. M. (1987). Robust regression and outlier detection. John Wiley & Sons, New Jersey
  25. Teunissen, P. J. G. (2003). Adjustment Theory: An Introduction. Delft University Press, Delft
  26. Teunissen, P. J. G. (2006). Testing theory: An Introduction. 2nd ed. VSSD, Delft
  27. Wilcox, R.R. (2012). Introduction to robust estimation and hypothesis testing. Academic Press, Waltham, MA
  28. Yang, L. Wang, J. Knight, N. L. Shen, Y. (2013). Outlier separability analysis with a multiple alternative hypotheses test. Journal of Geodesy, 87(6), pp.591-604. DOI: 10.1007/s00190-013-0629-0

Last update:

No citation recorded.

Last update: 2024-11-20 22:14:04

No citation recorded.