The geodesic inverse problem

Bowring, B. R.

doi:10.1007/bf02520917

Cited by 12 publications

(9 citation statements)

References 5 publications

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“…Data alignment is done because a series (two at a time) of sequential measurement is required to calculate the direction of travel. The initial (α1) and final bearing (α2) as calculated from two measurements is done with the Vincenty formula [3] as follows:…”

Section: Online Methods Implementationmentioning

confidence: 99%

Making applications more intelligent: A case study of optimizing route selection for emergency vehicles

Pohorec

Verlic

Zorman

2009

2009 22nd IEEE International Symposium on Computer-Based Medical Systems

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We present the results of a data mining research on the use of GPS positions and speed of travel of vehicles in urban areas to determine optimal travel routes for emergency vehicles. A new approach using predictive programming is presented. The approach focuses on using data mining of existing data as the key factor in the application logic where various decisions are to be made. The main appeal of such an approach is that the application logic evolves over time according to the application data. As the data changes the decisions soon follow. This gives the impression of intelligent behavior of the application.

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Section: Online Methods Implementationmentioning

confidence: 99%

Making applications more intelligent: A case study of optimizing route selection for emergency vehicles

Pohorec

Verlic

Zorman

2009

2009 22nd IEEE International Symposium on Computer-Based Medical Systems

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“…Given that all trajectories are defined with reference to the earth's surface, which is an oblate ellipsoid, 20,22,23,[34][35][36] a direct trajectory corresponds to the orthodrome between the two delimiting points. [20][21][22][23][24][25][26][27] Third, given that an excessive increase in the total ground distance may eliminate and even reverse any gains due to favorable wind conditions, the selected area must ensure a specified maximal total ground distance. Fourth, the selection method must provide sufficient space around the departure and arrival airports for any and all take-off and landing procedure maneuverings.…”

Section: Geographical Area Selectionmentioning

confidence: 99%

“…He addressed this inefficiency by selecting a hexagonal-shaped geographical area. A third type of routing grid was considered in the optimization methods investigated at LARCASE, [9][10][11][12] constructed using a set of tracks: the orthodrome (also known as the geodesic) corresponding to the shortest distance between the initial and final waypoints, [20][21][22][23][24][25][26][27] and a number of 4-11 equally spaced, parallel tracks situated on both sides of the orthodrome. The grid points were uniformly distributed along the set of tracks.…”

Section: Introductionmentioning

confidence: 99%

Geographical area selection and construction of a corresponding routing grid used for in-flight management system flight trajectory optimization

Dancila

Botez

2016

Proceedings of the Institution of Mechanical Engineers, Part G:

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This paper proposes a new method for selecting an ellipse-shaped geographical area and constructing a routing grid that circumscribes the contour of the designated area. The resulting grid describes the set of points used by the flight trajectory optimization algorithms to determine an aircraft's optimal flight trajectory as a function of given particular atmospheric conditions. This method was developed with the intent of its employment in the context of Flight Management System trajectory optimization algorithms, but can be used in Air Traffic Management environments as well. The routing grid limits the trajectory's maximal total ground distance (between the departure and destination airports), maximizes the geographical area (for a better consideration of the wind conditions) and minimizes the number of grid nodes. The novelty of the proposed method resides in the fact that it allows a distinct and independent parameterization and control of the ellipse's total surface, and the required size of the take-off/landing procedure maneuvering areas at the departure/destination airports. The ellipse contour constructed using this method is, therefore, well adapted to the particular configuration of the trajectory for which the optimization is performed. Each design variables' influence is presented, as well as a set of routing grids generated for trajectories corresponding to different total flight distances, and were further compared with real flight trajectory data retrieved using the website Flight Aware.

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“…The methods of solving the above problems can be divided into two general categories: (i) using an auxiliary sphere, e.g., Bessel (1826), Rainsford (1955), Robbins (1962), Sodano (1965), Saito (1970), Vincenty (1975), Saito (1979), Bowring (1983), Karney (2013) and (ii) without using an auxiliary sphere, e.g., Kivioja (1971), Holmstrom (1976), Jank and Kivioja (1980), Thomas and Featherstone (2005), Panou (2013), Panou et al (2013), Tseng (2014). The methods which use an auxiliary sphere are based on the classical work of Bessel (1826) and its modifications.…”

Section: Introductionmentioning

confidence: 99%

Research Article. Geodesic equations and their numerical solutions in geodetic and Cartesian coordinates on an oblate spheroid

Πάνου

Korakitis

2017

Journal of Geodetic Science

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Abstract:The direct geodesic problem on an oblate spheroid is described as an initial value problem and is solved numerically using both geodetic and Cartesian coordinates. The geodesic equations are formulated by means of the theory of differential geometry. The initial value problem under consideration is reduced to a system of first-order ordinary differential equations, which is solved using a numerical method. The solution provides the coordinates and the azimuths at any point along the geodesic. The Clairaut constant is not used for the solution but it is computed, allowing to check the precision of the method. An extensive data set of geodesics is used, in order to evaluate the performance of the method in each coordinate system. The results for the direct geodesic problem are validated by comparison to Karney's method. We conclude that a complete, stable, precise, accurate and fast solution of the problem in Cartesian coordinates is accomplished.

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The geodesic inverse problem

Cited by 12 publications

References 5 publications

Making applications more intelligent: A case study of optimizing route selection for emergency vehicles

Making applications more intelligent: A case study of optimizing route selection for emergency vehicles

Geographical area selection and construction of a corresponding routing grid used for in-flight management system flight trajectory optimization

Research Article. Geodesic equations and their numerical solutions in geodetic and Cartesian coordinates on an oblate spheroid

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