Conversion between Cartesian and geodetic coordinates on a rotational ellipsoid by solving a system of nonlinear equations

Ligas, Marcin; Banasik, Piotr

doi:10.2478/v10277-012-0013-x

Cited by 40 publications

(13 citation statements)

References 16 publications

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“…Geodesic slope: In 2017, ArcGIS added support for computing slope on a geodesic. Instead of computing the results in a Cartesian plane, the geodesic method computes directly on the ellipsoid [30]. It retains the use of a 3 × 3 neighborhood, but improves on the planar method by measuring the angle between the surface and the geodetic datum for each of the 8 adjacent cells, and is fitted with least squares described in Figure 1.…”

Section: Surface Gradientsmentioning

confidence: 99%

Unified Geomorphological Analysis Workflows with Benthic Terrain Modeler

et al. 2018

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High resolution remotely sensed bathymetric data is rapidly increasing in volume, but analyzing this data requires a mastery of a complex toolchain of disparate software, including computing derived measurements of the environment. Bathymetric gradients play a fundamental role in energy transport through the seascape. Benthic Terrain Modeler (BTM) uses bathymetric data to enable simple characterization of benthic biotic communities and geologic types, and produces a collection of key geomorphological variables known to affect marine ecosystems and processes. BTM has received continual improvements since its 2008 release; here we describe the tools and morphometrics BTM can produce, the research context which this enables, and we conclude with an example application using data from a protected reef in St. Croix, US Virgin Islands.Geosciences 2018, 8, 94 2 of 24 and better understanding of the algorithms in use, the field will lend itself more readily to expanding understanding of our oceans.Today, modern seafloor mapping technologies such as light detection and ranging (LiDAR) and multibeam bathymetry have done much to lower the costs, and provide consistent bathymetric products which incorporate in-sensor error models, provide high point density, and accurate georeferencing making them suitable for scientific analysis [10,11]. Bathymetric data are often captured, processed to remove artifacts and errors, and integrated into a consistent geomorphological model. Creation and interpretation of such a model has been aided by geomorphometry analysis tools in packages such as Benthic Terrain Modeler (BTM) [12,13]. BTM is built on top of the popular ArcGIS platform, is open source, has an intuitive interface, and has received continual development. When BTM was first introduced in 2006, transforming collected data to research results required mastery of many different pieces of software.Recent methodological developments have reduced the complexity of doing such analysis, but this has coincided with the emergence of even more sophisticated tools and the ability to collect much higher resolution data. Here, we describe the tools provided with the current release of BTM (v3.0), and highlight how it can be used in powerful analytical workflows for seafloor classification, by combining it with the capabilities of ArcGIS, the Python scientific stack, and the R statistical programming language. As the sphere of scientific software continues to grow, it will be important to provide easy-to-use tools to aid the broader community in performing rigorous analysis of marine geomorphometry.

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Section: Surface Gradientsmentioning

confidence: 99%

Unified Geomorphological Analysis Workflows with Benthic Terrain Modeler

et al. 2018

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“…There are few algorithms that can be used for this purpose. Ligas and Banasik (2011) proposed a new approach based on the solution of the system of nonlinear equations. The proposed algorithm consists of two steps.…”

Section: Diverse Algorithmsmentioning

confidence: 99%

Theoretical geodesy

Borkowski¹,

Kosek²

2015

Geodesy and Cartography

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The paper presents a summary of research activities concerning theoretical geodesy performed in Poland in the period of 2011-2014. It contains the results of research on new methods of the parameter estimation, a study on robustness properties of the M-estimation, control network and deformation analysis, and geodetic time series analysis. The main achievements in the geodetic parameter estimation involve a new model of the M-estimation with probabilistic models of geodetic observations, a new Shift-Msplit estimation, which allows to estimate a vector of parameter differences and the Shift-Msplit(+) that is a generalisation of Shift-Msplit estimation if the design matrix A of a functional model has not a full column rank. The new algorithms of the coordinates conversion between the Cartesian and geodetic coordinates, both on the rotational and triaxial ellipsoid can be mentioned as a highlights of the research of the last four years. New parameter estimation models developed have been adopted and successfully applied to the control network and deformation analysis. New algorithms based on the wavelet, Fourier and Hilbert transforms were applied to find time-frequency characteristics of geodetic and geophysical time series as well as time-frequency relations between them. Statistical properties of these time series are also presented using different statistical tests as well as 2nd, 3rd and 4th moments about the mean. The new forecasts methods are presented which enable prediction of the considered time series in different frequency bands.

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“…These satellite positioning technologies provide vast amounts of spatio-temporal datums in either curvilinear geodetic coordinates (ϕ, λ, h) or cartesian coordinate (X, Y, Z ) system. In the quest for solving most practical GPS navigation, geodetic, cartographical and astro-geodetic problems, it is important to convert geodetic coordinates into cartesian coordinates and vice versa (Civicioglu 2012;Ligas and Banasik 2011;Shu and Li 2010;Zhu 1994). The process of converting geodetic coordinates to cartesian coordinates is known as the forward conversion.…”

Section: Introductionmentioning

confidence: 99%

Capability of Artificial Neural Network for Forward Conversion of Geodetic Coordinates $$(\phi ,\lambda ,h)$$ ( ϕ , λ , h ) to Cartesian Coordinates (X, Y, Z)

Ziggah

et al. 2016

Math Geosci

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The standard forward transformation equation plays a major role in coordinate transformation between global and local datums. Thus, it is a prerequisite step in the forward conversion of geodetic coordinates into cartesian coordinates in coordinate transformation from global to local datum and vice versa. Numerous studies have been carried out on converting cartesian coordinates to geodetic coordinates (reverse procedure) through the application of iterative, approximate, closed form, vector-based and computational intelligence algorithms. However, based on literature covered pertaining to this study, it was realized that the existing researches do not fully address the issue of applying and testing alternative techniques in the case of the forward conversion. Hence, the purpose of this present study was to explore the coordinate conversion performance of two different artificial neural network approaches (backpropagation artificial neural network (BPANN) and radial basis function neural network (RBFNN)) and multiple linear regression (MLR). The statistical findings revealed that the BPANN, RBFNN and MLR offered satisfactory prediction of cartesian coordinates. However, the RBFNN compared to BPANN and MLR showed better stability and more accurate prediction results. Furthermore, in terms of maximum three-dimensional position error, the RBFNN attained 0.004 m while 0.011 and 0.627 m were achieved, respectively, by MLR and BPANN. By virtue of the success achieved in this study, the main conclusion drawn here is that RBFNN provides a promising alter-B Hu Youjian 123 Math Geosci native in the forward conversion of geodetic coordinates into cartesian coordinates. Therefore, the capability of artificial neural network as a powerful tool for solving majority of function approximation problems in geodesy has been demonstrated.

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Conversion between Cartesian and geodetic coordinates on a rotational ellipsoid by solving a system of nonlinear equations

Cited by 40 publications

References 16 publications

Unified Geomorphological Analysis Workflows with Benthic Terrain Modeler

Unified Geomorphological Analysis Workflows with Benthic Terrain Modeler

Theoretical geodesy

Capability of Artificial Neural Network for Forward Conversion of Geodetic Coordinates $$(\phi ,\lambda ,h)$$ ( ϕ , λ , h ) to Cartesian Coordinates (X, Y, Z)

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