Land surveyors, photogrammetrists, remote sensing engineers and professionals in the Earth sciences are often faced with the task of transferring coordinates from one geodetic datum into another to ...serve their desired purpose. The essence is to create compatibility between data related to different geodetic reference frames for geospatial applications. Strictly speaking, conventional techniques of conformal, affine and projective transformation models are mostly used to accomplish such task. With developing countries like Ghana where there is no immediate plans to establish geocentric datum and still rely on the astro-geodetic datums as it national mapping reference surface, there is the urgent need to explore the suitability of other transformation methods. In this study, an effort has been made to explore the proficiency of the Extreme Learning Machine (ELM) as a novel alternative coordinate transformation method. The proposed ELM approach was applied to data found in the Ghana geodetic reference network. The ELM transformation result has been analysed and compared with benchmark methods of backpropagation neural network (BPNN), radial basis function neural network (RBFNN), two-dimensional (2D) affine and 2D conformal. The overall study results indicate that the ELM can produce comparable transformation results to the widely used BPNN and RBFNN, but better than the 2D affine and 2D conformal. The results produced by ELM has demonstrated it as a promising tool for coordinate transformation in Ghana.
Cartesian coordinate transformation between two erroneous coordinate systems is considered within the Errors-In-Variables (EIV) model. The adjustment of this model is usually called the total ...Least-Squares (LS). There are many iterative algorithms given in geodetic literature for this adjustment. They give equivalent results for the same example and for the same user-defined convergence error tolerance. However, their convergence speed and stability are affected adversely if the coefficient matrix of the normal equations in the iterative solution is ill-conditioned. The well-known numerical techniques, such as regularization, shifting-scaling of the variables in the model, etc., for fixing this problem are not applied easily to the complicated equations of these algorithms. The EIV model for coordinate transformations can be considered as the nonlinear Gauss-Helmert (GH) model. The (weighted) standard LS adjustment of the iteratively linearized GH model yields the (weighted) total LS solution. It is uncomplicated to use the above-mentioned numerical techniques in this LS adjustment procedure. In this contribution, it is shown how properly diminished coordinate systems can be used in the iterative solution of this adjustment. Although its equations are mainly studied herein for 3D similarity transformation with differential rotations, they can be derived for other kinds of coordinate transformations as shown in the study. The convergence properties of the algorithms established based on the LS adjustment of the GH model are studied considering numerical examples. These examples show that using the diminished coordinates for both systems increases the numerical efficiency of the iterative solution for total LS in geodetic datum transformation: the corresponding algorithm working with the diminished coordinates converges much faster with an error of at least 10
-5
times smaller than the one working with the original coordinates.
A novel RANSAC robust estimation technique is presented as an effiecient method for solving the seven-parameter datum transformation problem in the presence of outliers. RANSAC method, which is ...frequently employed in geodesy, has two sensitive features: (i) the user adjusts some parameters of the algorithm, making it subjective and a rather difficult procedure, and (ii) in its shell, a nonlinear system of equation should be solved repeatedly. In this contribution, we suggest an automatic adjustment strategy for the most important parameter, 'the threshold value', based on the 'early stopping' principle of the machine-learning technology. Instead of using iterative numerical methods, we propose the use of an algebraic polynomial system developed via a dual-quaternion technique and solved by a non-iterative homotophy method, thereby reducing the computation time considerably. The novelty of the proposed approach lies in three major contributions: (i) the provision for automatically finding the proper error limit parameter for RANSAC method, which has until now been a trial-and-error technique; (ii) employing the algebraic polynomial form of the dual-quaternion solution in the RANSAC shell, thereby accelerating the repeatedly requested solution process; and (iii) avoiding iterations via a heuristic approach of the scaling parameter. To illustrate the proposed method, the transformation parameters of the Western Australian Geodetic Datum (AGD 84) to Geocentric Datum Australia (GDA 94) are computed.
Machine learning algorithms have emerged as a new paradigm shift in geoscience computations and applications. The present study aims to assess the suitability of Group Method of Data Handling (GMDH) ...in coordinate transformation. The data used for the coordinate transformation constitute the Ghana national triangulation network which is based on the two-horizontal geodetic datums (Accra 1929 and Leigon 1977) utilised for geospatial applications in Ghana. The GMDH result was compared with other standard methods such as Backpropagation Neural Network (BPNN), Radial Basis Function Neural Network (RBFNN), 2D conformal, and 2D affine. It was observed that the proposed GMDH approach is very efficient in transforming coordinates from the Leigon 1977 datum to the official mapping datum of Ghana, i.e. Accra 1929 datum. It was also found that GMDH could produce comparable and satisfactory results just like the widely used BPNN and RBFNN. However, the classical transformation methods (2D affine and 2D conformal) performed poorly when compared with the machine learning models (GMDH, BPNN and RBFNN). The computational strength of the machine learning models’ is attributed to its self-adaptive capability to detect patterns in data set without considering the existence of functional relationships between the input and output variables. To this end, the proposed GMDH model could be used as a supplementary computational tool to the existing transformation procedures used in the Ghana geodetic reference network.
The correct determination of geodetic datum is an obligatory condition for the proper determination of the point displacements. There are various methods of deformation analysis focused on the right ...identification of stable points, which may define an appropriate coordinate basis for calculating the displacements of other points. These methods are largely based on the statistical testing and represent a comprehensive and complex analysis of change of geometry of geodetic network and allow definition of statistically significant displacements. Knowing the characteristics of the transformation between the solutions of displacements that are based on different definitions of geodetic datums, the problem of defining an appropriate geodetic datum can be solved in a slightly different way.In this article we have focused on the problem of determining the appropriate weighting matrix E in the model of S-transformation. We used the generally known methods of robust statistics. The robustness of the three selected methods were tested on two different situations of preselected displacements in the considered geodetic network and the results on selected case of geodetic network with results of conventional methods of deformation analysis were compared.
To accommodate the effects of crustal deformation in the current national static geodetic datum (Taiwan Geodetic Datum 1997 (TWD97)) in SW Taiwan, 221 campaign-mode global positioning system (GPS) ...stations from 2002 to 2010 were used in this study to generate a surface horizontal velocity model for establishing a semi-dynamic datum in SW Taiwan. An interpolation method, Kriging, and a tectonic block model, DEFNODE, were used to construct the surface horizontal velocity model. Forty-four continuous GPS stations were used to examine the performance of the semi-dynamic datum through exterior validation. The average values of the residual errors obtained using the Kriging method for the north and east components are ±1.9 and ±2.2 mm/year, respectively, whereas those obtained using the block model are ±2.0 and ±2.9 mm/year, respectively. The distribution of residuals greater than 5 mm/year for both models generally corresponds to a high strain rate area derived using the horizontal velocity field. In addition, these residuals may result from deep-seated landslide and active folding or mud diapir in a mudstone area. Similar exterior checking results obtained using the Kriging interpolation method and block model for SW Taiwan indicate a high station density and a relatively satisfactory station spatial coverage. However, the block model is superior to the Kriging method due to the consideration of characteristics of the geological structure in the block model. In addition, result from traditional coordinate transformation was used to compare with the semi-dynamic datum. The results indicate that a semi-dynamic datum is a feasible solution for maintaining the accuracy of TWD97 at an appropriate level over time in Taiwan.
Two national horizontal geodetic datums, namely, the Accra and Leigon datum, have been the only available datum used in Ghana. These two datums are non-geocentric and were established based on ...astro-geodetic observations. Relating these different geodetic datums mostly involves the use of conformal transformation techniques which could produce results that are not very often satisfactory for certain geodetic, surveying and mapping purposes. This has been ascribed to the incapability of the conformal models to absorb more of the heterogeneous and local character of deformations existing within the local geodetic networks. Presently, application of new approaches such as artificial neural network (ANN) is highly recommended. Whereas the ANN has been gaining much popularity to solving coordinate transformation-related problems in recent times, the existing researches carried out in Ghana have shown that only three-dimensional conformal transformation methods have been utilized. To the best of our knowledge, plane coordinate transformation between the two local geodetic datums in Ghana has not been investigated. In this paper, an attempt has been made to explore the plane coordinate transformation performance of two different ANN approaches (backpropagation neural network (BPNN) and radial basis function neural network (RBFNN)) compared with two different traditional techniques (six- and four-parameter models) in the Ghana national geodetic reference network. The results revealed that transforming plane coordinates from Leigon to Accra datum, the RBFNN was better than the BPNN and traditional techniques. Transforming from Accra to Leigon datum, both the BPNN and RBFNN produced closely related results and were better than the traditional methods. Therefore, this study will create the opportunity for Ghana to recognize the significance and strength of the ANN technology in solving coordinate transformation problems.
According to Minister of Internal Affair regulation which is Permendagri No.1 Tahun 2006, Peta Lingkungan
Laut Indonesia (LLN) must be utilized to define boundaries of province sea jurisdiction. ...Unfortunately, Peta
Lingkunan Laut Indonesia still applies Indonesia Datum 1974 instead of Datum Geodesi Nasional 1995. It is
contrary with Permendagri No 76 Tahun 2012 and UU No.4 Tahun 2011 which declare the urgency of single
reference datum for Indonesia region. To fit the requirement, Peta Lingkungan Laut Indonesia must be
transformed into official datum. This research applied two transformation formulae. There was Lauf
Transformations to accomodate 2 Dimension Transformation. Computation of transformation parameters and
application of those parameters were tested at North Coast of Java from Kendal regency to Brebes regency. As
calculated in MatLab software, this research concluded that Lauf transformation was good for transforming
Lingkungan Laut Indonesia from ID74 to DGN95.
At each point of the geodetic network, kinematic quantities are considered: normal strain, shear strain and rotation. This differs from the treatment of deformations on the basis of point movements ...as the traditional geodetic approach. Strain and rotation depend on the changes of geodetic datum. In the case of two different coordinate systems in each epoch, we cannot calculate the real value of movements, strains and rotations. Despite the empirical studies of the datum invariance, we derived analytical mathematical expressions of functional dependency of strains and rotations from the relative change of datum parameters between two measurement epochs. Practical demonstration of functional dependencies has been shown in the case of the selected planar geodetic network.
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