Analyzing the Impact of Climate Factors on GNSS-Derived Displacements by Combining the Extended Helmert Transformation and XGboost Machine Learning Algorithm

A variety of climate factors influence the precision of the long-term Global Navigation Satellite System (GNSS) monitoring data. To precisely analyze the effect of different climate factors on long-term GNSS monitoring records, this study combines the extended seven-parameter Helmert transformation and a machine learning algorithm named Extreme Gradient boosting (XGboost) to establish a hybrid model. We established a local-scale reference frame called stable Puerto Rico and Virgin Islands reference frame of 2019 (PRVI19) using ten continuously operating long-term GNSS sites located in the rigid portion of the Puerto Rico and Virgin Islands (PRVI) microplate. The stability of PRVI19 is approximately 0.4 mm/year and 0.5 mm/year in the horizontal and vertical directions, respectively. The stable reference frame PRVI19 can avoid the risk of bias due to long-term plate motions when studying localized ground deformation. Furthermore, we applied the XGBoost algorithm to the postprocessed long-term GNSS records and daily climate data to train the model. We quantitatively evaluated the importance of various daily climate factors on the GNSS time series. The results show that wind is the most influential factor with a unit-less index of 0.013. Notably, we used the model with climate and GNSS records to predict the GNSS-derived displacements. The results show that the predicted displacements have a slightly lower root mean square error compared to the fitted results using spline method (prediction: 0.22 versus fitted: 0.31). It indicates that the proposed model considering the climate records has the appropriate predict results for long-term GNSS monitoring.

Realizing ITRF-Consistent Continental-Scale Geodetic Reference Frames

<p>To achieve a regional or continental-scale reference frame that is a densification of the International Terrestrial Reference Frame (ITRF), one can use a set of fiducial GPS / GNSS stations in the ITRF and regional frames.  Predicting coordinates in the realization epoch using the fiducial stations’ trajectory parameters in the ITRF and applying a Helmert transformation aligns the regional solution’s polyhedron onto the ITRF.  This paper shows inconsistencies in the regional realization of ITRF when the fiducial stations’ trajectory model ignores the periodic terms, resulting in a periodic coordinate bias in the regional frame.  We describe a generalized procedure to minimize this inconsistency when realizing any regional frame aligned to ITRF or any other ‘primary’ frame. We show the method used to realize the Argentine Geodetic Positions (Posiciones Geodésicas Argentinas, POSGAR) reference frame and discuss its results. Inconsistencies in the vertical were reduced from 4 mm to less than 1 mm for multiple stations after applying our technique.  We also propose adopting object-oriented programming terminology to describe the relationship between different reference frames, such as a regional and a global frame. This terminology assists in describing and understanding the hierarchy in geodetic reference frames.</p>

Helmert Transformation Problem. From Euler Angles Method to Quaternion Algebra

The three-dimensional coordinate’s transformation from one system to another, and more specifically, the Helmert transformation problem, is one of the most well-known transformations in the field of engineering. In this paper, its solution, in reverse problem, was investigated for specific data using three different methods. It is presented by solving it with the method of Euler angles as well as with the use of quaternion and dual-quaternion algebra, after first giving some basic mathematical theory. After research, not only were three artificial sets of data used, which were structured in a specific way and forced into specific transformations to be solved, but also a real geodesy problem was tested, in order to identify the sensitivity and problems of each method. Statistical analysis of the results was performed by each method, while it was found that there were significant deviations in rotations and translations in the method of Euler angles and dual quaternions, respectively.

Helmert transformation strategies in analysis of GPS position time-series

SUMMARY Global positioning system (GPS) position time-series generated using inconsistent satellite products should be aligned to a secular Terrestrial Reference Frame by Helmert transformation. However, unmodelled non-linear variations in station positions can alias into transformation parameters. Based on 17 yr of position time-series of 112 stations produced by precise point positioning (PPP), we investigated the impact of network configuration and scale factor on long-term time-series processing. Relative to the uniform network, the uneven network can introduce a discrepancy of 0.7–1.1 mm, 21.3–27.5 μas and 1.3 mm in terms of root mean square (RMS) for the translation, rotation and scale factor (if estimated), respectively, no matter whether the scale factor is estimated. The RMS of vertical annual amplitude differences caused by such network effect reaches 0.5–0.6 mm. Whether estimating the scale factor mostly affects the Z-translation and vertical annual amplitude, leading to a difference of 1.3 mm when the uneven network is used. Meanwhile, the annual amplitude differences caused by the scale factor present different geographic location dependences over the north, east and up components. The seasonal signals derived from the transformation using the uniform network and without estimating scale factor have better consistency with surface mass loadings with more than 41 per cent of the vertical annual variations explained. Simulation studies show that 40–50 per cent of the annual signals in the scale factor can be explained by the aliasing of surface mass loadings. Another finding is that GPS draconitic errors in station positions can also alias into transformation parameters, while different transformation strategies have limited influence on identifying the draconitic errors. We suggest that the uniform network should be used and the scale factor should not be estimated in Helmert transformation. It is also suggested to perform frame alignment on PPP time-series, even though the used satellite products belong to a consistent reference frame, as the origin of PPP positions inherited from satellite orbits and clocks is not so stable during a long period. With Helmert transformation, the seasonal variations would better agree with surface mass loadings, and noise level of time-series is reduced.

Different Approaches to Coordinate Transformation Parameters Determination of Nonhomogeneous Coordinate Systems

During reconstruction and restoration of city geodetic networks, there is quite a common problem that is related to the nonhomogeneity of existing geodetic networks. In any city, local authorities operate with their coordinate systems. Such conditions lead to inconsistency between data of different services. There is only one way how to overcome the problem that lies in the creation and deployment of the new common coordinate system for the whole city. But such an approach has a lack connected with the necessity of transformation parameters acquisition for the latest and old coordinate systems. Insofar as old coordinate systems had been created with different accuracy, using various equipment, and measuring technologies, it is not possible to consider them as homogeneous. It means that we cannot use a classical conformal Helmert transformation to link different coordinate systems. In the presented paper were studied the different approaches for transformation parameters acquisition. A case study of the Almaty city coordinate system was researched and compared the following methods: Helmert transformation, bilinear transformation, the second and third-order regression transformation, and the fourth-order conformal polynomial transformation. It was found out that neither of the considered methods maintains the necessary transformation accuracy (>5 cm). That is why the creation of the transformation field using the finite element method (FEM) was suggested. The whole city was divided into triangles using Delaunay triangulation. For each triangle, the transformation parameters were found using affine transformation with the necessary accuracy.

HELMERT TRANSFORMATION ON THE CASE OF GAUSS-KRÜGER AND UTM

Globally, maps are our primary source of comprehensive information about the shape, size and arrangement of Earth features. Maps are the only way we can get a unique and comprehensive view of the world. Unfortunately, globally, all maps are somehow deformed, affecting our perception and understanding of the various geometrical properties of the world. Cartographic projection is a way of mapping points from an ellipsoid to a plane and as such is the basis for making a mathematical map basis. The two projections most used in our geospatial are the Gauss-Krüger projection and the UTM (Universal Transverse Mercator) projection. The paper deals with Helmert's transformation of these two projections.