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    Wyświetlanie 1-2 z 2
    Tytuł:
    A method for local approximation of a planar deformation field
    Autorzy:
    Ligas, Marcin
    Banaś, Marek
    Szafarczyk, Anna
    Powiązania:
    https://bibliotekanauki.pl/articles/106795.pdf
    Data publikacji:
    2019
    Wydawca:
    Politechnika Warszawska. Wydział Geodezji i Kartografii
    Tematy:
    deformation analysis
    polar decomposition
    affine transformation
    rotation matrix
    stretch tensor
    analiza deformacji
    rozkład biegunowy operatora
    transformacja afiniczna
    macierz obrotu
    Opis:
    We present a method of approximation of a deformation eld based on the local ane transformations constructed based on n nearest neighbors with respect to points of adopted grid. The local ane transformations are weighted by means of inverse distance squared between each grid point and observed points (nearest neighbors). This work uses a deformation gradient, although it is possible to use a displacement gradient instead – the two approaches are equivalent. To decompose the deformation gradient into components related to rigid motions (rotations, translations are excluded from the deformation gradient through dierentiation process) and deformations, we used a polar decomposition and decomposition into a sum of symmetric and an anti-symmetric matrices (tensors). We discuss the results from both decompositions. Calibration of a local ane transformations model (i.e., number of nearest neighbors) is performed on observed points and is carried out in a cross-validation procedure. Verication of the method was conducted on simulated data-grids subjected to known (functionally generated) deformations, hence, known in every point of a study area.
    Źródło:
    Reports on Geodesy and Geoinformatics; 2019, 108; 1-8
    2391-8365
    2391-8152
    Pojawia się w:
    Reports on Geodesy and Geoinformatics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Development of a precise local quasigeoid model for the city of Krakow – QuasigeoidKR2019
    Autorzy:
    Banasik, Piotr
    Bujakowski, Kazimierz
    Kudrys, Jacek
    Ligas, Marcin
    Powiązania:
    https://bibliotekanauki.pl/articles/1396889.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Warszawska. Wydział Geodezji i Kartografii
    Tematy:
    local quasi geoid
    GNSS
    levelling data
    height anomaly
    QuasigeoidKR2019
    cross-validation
    Opis:
    A geoid or quasigeoid model allows the integration of satellite measurements with ground levelling measurements in valid height systems. A precise quasigeoid model has been developed for the city of Krakow. One of the goals of the model construction was to provide a more detailed quasigeoid course than the one offered by the national model PL-geoid2011. Only four measurement points in the area of Kraków were used to build a national quasigeoid model. It can be assumed that due to the small number of points and their uneven distribution over the city area, the quasigeoid can be determined less accurately. It became the reason for developing a local quasigeoid model based on a larger number of evenly distributed points. The quasigeoid model was based on 66 evenly distributed points (from 2.5 km to 5.0 km apart) in the study area. The process of modelling the quasigeoid used height anomalies determined at these points on the basis of normal heights derived through levelling and ellipsoidal heights derived through GNSS surveys. Height anomalies coming from the global geopotential model EGM2008 served as a long-wavelength trend in those derived from surveys. Analyses showed that the developed height anomaly model fits the empirical data at the level of single millimetres – mean absolute difference 0.005 m. The developed local model QuasigeoidKR2019, similar to the national model PL-geoid2011, are models closely related to the reference and height systems in Poland. Such models are used to integrate GNSS and levelling observations. A comparison of the local QuasigeoidKR2019 and national PL-geoid2011 model was made for the reference frame PL-ETRF2000 and height datum PL-KRON86-NH. The comparison of the two models with respect to GNSS/levelling height anomalies shows a triple reduction in the values of individual quartiles and a mean absolute difference for the developed local model. These summary statistics clearly indicate that the accuracy of the local model for the city of Krakow is significantly higher than that of the national one.
    Źródło:
    Reports on Geodesy and Geoinformatics; 2020, 109; 25-31
    2391-8365
    2391-8152
    Pojawia się w:
    Reports on Geodesy and Geoinformatics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-2 z 2

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