ORIGINAL ARTICLE
A crossvalidation-based comparison of kriging and IDW in local GNSS/levelling quasigeoid modelling
1
Department of Integrated Geodesy and Cartography, Faculty of Geo-Data Science, Geodesy and Environmental Engineering, AGH University of Science and Technology, al. Mickiewicza 30, 30-059, Kraków, Poland
Submission date: 2022-08-06
Acceptance date: 2022-09-21
Online publication date: 2022-10-28
Publication date: 2022-12-01
Reports on Geodesy and Geoinformatics 2022;114:1-7
KEYWORDS
ABSTRACT
This study compares two interpolation methods in the problem of a local GNSS/levelling (quasi) geoid modelling. It uses raw data, no global geopotential model is involved. The methods differ as to the complexity of modelling procedure and theoretical background, they are ordinary kriging/least-squares collocation with constant trend and inverse distance weighting (IDW). The comparison itself was done through leave-one-out and random (Monte Carlo) cross-validation. Ordinary kriging and IDW performance was tested with a local (using limited number of data) and global (using all available data) neighbourhoods using various planar covariance function models in case of kriging and various exponents (power parameter) in case of IDW. For the study area both methods assure an overall accuracy level, measured by mean absolute error, root mean square error and median absolute error, of less than 1 cm. Although the method of IDW is much simpler, a suitably selected parameters (also trend removal) may contribute to differences between methods that are virtually negligible (fraction of a millimetre).
REFERENCES (25)
1.
Akyilmaz, O., Özlüdemir, M., Ayan, T., and Çelik, R. (2009). Soft computing methods for geoidal height transformation. Earth, planets and space, 61(7):825–833, doi:10.1186/BF03353193.
2.
Babak, O. and Deutsch, C. V. (2009). Statistical approach to inverse distance interpolation. Stochastic Environmental Research and Risk Assessment, 23(5):543–553.
3.
Banasik, P., Bujakowski, K., Kudrys, J., and Ligas, M. (2020). Development of a precise local quasigeoid model for the city of Krakow – QuasigeoidKR2019. Reports on Geodesy and Geoinformatics, 109(1):25–31, doi:10.2478/rgg-2020-0004.
4.
Borowski, Ł. and Banaś, M. (2019). The best robust estimation method to determine local surface. Baltic Journal of Modern Computing, 7(4):525–540, doi:10.22364/bjmc.2019.7.4.06.
5.
Borowski, Ł. and Banasik, P. (2020). The conversion of heights of the benchmarks of the detailed vertical reference network into the PL-EVRF2007-NH frame. Reports on geodesy and geoinformatics, 109(1):1–7, doi:10.2478/rgg-2020-0001.
6.
Chiles, J.-P. and Delfiner, P. (1999). Geostatistics: modeling spatial uncertainty. John Wiley & Sons.
8.
Dawod, G. M. and Abdel-Aziz, T. M. (2020). Utilization of geographically weighted regression for geoid modelling in Egypt. Journal of Applied Geodesy, 14(1):1–12, doi:10.1515/jag-2019-0009.
9.
Elshambaky, H. T. (2018). Application of neural network technique to determine a corrector surface for global geopotential model using GPS/levelling measurements in Egypt. Journal of Applied Geodesy, 12(1):29–43, doi:10.1515/jag-2017-0017.
10.
Gucek, M. and Bašić, T. (2009). Height transformation models from ellipsoidal into the normal orthometric height system for the territory of the city of Zagreb. Studia Geophysica et Geodaetica, 53(1):17–38, doi:10.1007/s11200-009-0002-1.
11.
Hofmann-Wellenhof, B. and Moritz, H. (2006). Physical geodesy. Springer Science & Business Media.
12.
Jordan, S. K. (1972). Self-consistent statistical models for the gravity anomaly, vertical deflections, and undulation of the geoid. Journal of Geophysical Research, 77(20):3660–3670, doi:10.1029/JB077i020p03660.
13.
Kaloop, M. R., Pijush, S., Rabah, M., Al-Ajami, H., Hu, J. W., and Zaki, A. (2021). Improving accuracy of local geoid model using machine learning approaches and residuals of GPS/levelling geoid height. Survey Review, pages 1–14, doi:10.1080/00396265.2021.1970918.
14.
Kim, S.-K., Park, J., Gillins, D., and Dennis, M. (2018). On determining orthometric heights from a corrector surface model based on leveling observations, GNSS, and a geoid model. Journal of Applied Geodesy, 12(4):323–333, doi:10.1515/jag-2018-0014.
15.
Ligas, M. (2022). Comparison of kriging and least-squares collocation–revisited. Journal of Applied Geodesy, 16(3):217–227, doi:10.1515/jag-2021-0032.
16.
Ligas, M. and Szombara, S. (2018). Geostatistical prediction of a local geometric geoid-kriging and cokriging with the use of EGM2008 geopotential model. Studia Geophysica et Geodaetica, 62(2):187–205, doi:10.1007/s11200-017-0713-7.
17.
Meier, S. (1981). Planar geodetic covariance functions. Reviews of geophysics, 19(4):673–686, doi:10.1029/RG019i004p00673.
18.
Moritz, H. (1972). Advanced least-squares methods, volume 175. Ohio State University Research Foundation Columbus, OH, USA.
19.
Orejuela, I. P., González, C. L., Guerra, X. B., Mora, E. C., and Toulkeridis, T. (2021). Geoid undulation modeling through the Cokriging method–A case study of Guayaquil, Ecuador. Geodesy and Geodynamics, 12(5):356–367, doi:10.1016/j.geog.2021.04.004.
20.
Radanović, M. and Bašić, T. (2018). Accuracy assessment and comparison of interpolation methods on geoid models. Geodetski Vestnik, 62(1):68–78, doi:10.15292/geodetskivestnik.2018.01.68-78.
21.
Schaffrin, B. (2001). Equivalent systems for various forms of kriging, including least-squares collocation. Zeitschrift für Vermessungswesen, 126(2):87–93.
22.
Tusat, E. and Mikailsoy, F. (2018). An investigation of the criteria used to select the polynomial models employed in local GNSS/leveling geoid determination studies. Arabian journal of geosciences, 11(24):1–15, doi:10.1007/s12517-018-4176-0.
23.
Wackernagel, H. (2003). Multivariate geostatistics: an introduction with applications. Springer Science & Business Media, doi:10.1007/978-3-662-05294-5.
24.
You, R.-J. (2006). Local geoid improvement using GPS and leveling data: case study. Journal of Surveying Engineering, 132(3):101–107, doi:10.1061/(ASCE)0733-9453(2006)132:3(101).
25.
Zhong, D. (1997). Robust estimation and optimal selection of polynomial parameters for the interpolation of GPS geoid heights. Journal of Geodesy, 71(9):552–561, doi:10.1007/s001900050123.
Share
RELATED ARTICLE
| eISSN: | 2391-8152 |
| ISSN: | 2391-8365 |
© 2006-2024 Journal hosting platform by Bentus
We process personal data collected when visiting the website. The function of obtaining information about users and their behavior is carried out by voluntarily entered information in forms and saving cookies in end devices. Data, including cookies, are used to provide services, improve the user experience and to analyze the traffic in accordance with the Privacy policy. Data are also collected and processed by Google Analytics tool (more).
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
