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Two variants of M split estimation – similarities and differences

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Języki publikacji
EN
Abstrakty
EN
M split estimation is a novel method developed to process observation sets that include two (or more) observation aggregations. The main objective of the method is to estimate the location parameters of each aggregation without any preliminary assumption concerning the division of the observation set into respective subsets. Up to now, two different variants of M split estimation have been derived. The first and basic variant is the squared M split estimation, which can be derived from the assumption about the normal distribution of observations. The second variant is the absolute M split estimation, which generally refers to the least absolute deviation method. The main objective of the paper is to compare both variants of M split estimation by showing similarities and differences between the methods. The main dissimilarity stems from the different influence functions, making the absolute M split estimation less sensitive to gross errors of moderate magnitude. The empirical analyses presented confirm that conclusion and show that the accuracy of the methods is similar, in general. The absolute M split estimation is more accurate than the squared M split estimation for less accurate observations. In contrast, the squared M split estimation is more accurate when the number of observations in aggregations differs much. Concerning all advantages and disadvantages of M split estimation variants, we recommend using the absolute M split estimation in most geodetic applications.
Rocznik
Strony
art. no. e22, 2022
Opis fizyczny
Bibliogr. 19 poz., tab., wykr.
Twórcy
Bibliografia
  • [1] Baselga, S., Klein, I., Suraci, S.S. et al. (2021). Global optimization of redescending robust estimators. Math. Probl. Eng., 1–13. DOI: 10.1155/2021/9929892.
  • [2] Czaplewski, K., Waz, M., and Zienkiewicz, M.H. (2019). A novel approach of using selected unconventional geodesic methods of estimation on VTS areas. Mar. Geodesy, 42, 447–468. DOI: 10.1080/01490419.2019.1645769.
  • [3] Duchnowski, R. (2021). Vertical displacement analysis based on application of univariate model for several chosen estimation methods. In: Proceedings of FIG e-Working Week 2021, 20-25 June 2021 (pp. 1–13), Netherlands.
  • [4] Duchnowski, R., and Wyszkowska, P. (2018). Empirical influence functions of Hodges-Lehmann weighted estimates applied in deformation analysis. In: Proceedings of 2018 Baltic Geodetic Congress (BGC Geomatics), 21-23 June 2018 (pp. 169–173). Olsztyn, Poland. DOI: 10.1109/BGC Geomatics.2018.00038.
  • [5] Duchnowski, R., and Wisniewski, Z. (2020). Robustness of squared Msplit(𝑞) estimation: Empirical analyses. Studia Geophys. et Geod., 64, 153–171. DOI: 10.1007/s11200-019-0356-y.
  • [6] Duchnowski, R., and Wyszkowska, P. (2022). Empirical influence functions and their non-standard applications. J.Appl. Geod., 16, 9–23. DOI: 10.1515/jag-2021-0012.
  • [7] Guo, Y., Li, Z., He, H. et al. (2020). A squared Msplit similarity transformation method for stable points selection of deformation monitoring network. Acta Geod. et Cartogr. Sin., 49, 1419–1429. DOI: 10.11947/j.AGCS.2020.20200023.
  • [8] Janicka, J., and Rapinski, J. (2013). Msplit transformation of coordinates. Surv. Rev., 45, 269–274. DOI: 10.1179/003962613X13726661625708.
  • [9] Janicka, J., Rapinski, J., Blaszczak-Baąk, W. et al. (2020). Application of the Msplit estimation method in the detection and dimensioning of the displacement of adjacent planes. Remote Sens., 12, 3203. DOI: 10.3390/rs12193203.
  • [10] Li, J., Wang, A., and Xinyuan, W. (2013). Msplit estimate the relationship between LS and its application in gross error detection. Mine Surv., 2, 57–59. DOI: 10.3969/j.issn.1001-358X.2013.02.20.
  • [11] Nowel, K. (2019). Squared Msplit(𝑞) S-transformation of control network deformations. J. Geod., 93, 1025–1044. DOI: 10.1007/s00190-018-1221-4.
  • [12] Rousseeuw, P.J., and Verboven, S. (2002). Robust estimation in very small samples. Comput. Stat. Data Anal., 40, 741–758. DOI: 10.1016/S0167-9473(02)00078-6.
  • [13] Wisniewski, Z. (2009). Estimation of parameters in a split functional model of geodetic observations (Msplit estimation). J. Geod., 83, 105–120. DOI: 10.1007/s00190-008-0241-x.
  • [14] Wisniewski, Z. (2010). Msplit(𝑞) estimation: estimation of parameters in a multi split functional model of geodetic observations. J. Geod., 84, 355–372. DOI: 10.1007/s00190-010-0373-7.
  • [15] Wyszkowska, P., and Duchnowski, R. (2019). Msplit estimation based on L1 norm condition. J. Surv. Eng., 145, 04019006. DOI: 10.1061/(ASCE)SU.1943-5428.0000286.
  • [16] Wyszkowska, P., and Duchnowski, R. (2020). Iterative process of Msplit(𝑞) estimation. J. Surv. Eng., 146, 06020002. DOI: 10.1061/(ASCE)SU.1943-5428.0000318.
  • [17] Wyszkowska, P., Duchnowski, R., and Dumalski, A. (2021). Determination of terrain profile from TLS data by applying Msplit estimation. Remote Sens., 13, 31. DOI: 10.1061/(ASCE)SU.1943-5428.0000318.
  • [18] Zienkiewicz, M.H. (2022). Identification of unstable reference points and estimation of displacements using squared Msplit estimation. Measurement, 195, 111029. DOI: 10.1016/j.measurement.2022.111029.
  • [19] Zienkiewicz, M.H., and Baryla, R. (2020). Determination of an adequate number of competitive functional models in the square Msplit(𝑞) estimation with the use of a modified Baarda’s approach. Surv. Rev., 52, 13–23. DOI: 10.1080/00396265.2018.1507361.
Uwagi
PL
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-4a050419-5bc4-4f44-9680-77476e46f427
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