Determination of the geodetic latitude and height by spatial geocentric coordinates

2021 ◽  
Vol 977 (11) ◽  
pp. 2-7
Author(s):  
P.D. Penev ◽  
E.P. Peneva
Keyword(s):  
Geodetic Height ◽  
Rectangular Coordinates ◽  
Geocentric Coordinates

The authors propose to derive the formulas given in [1, 2] for determining the height and latitude based on the Cartesian rectangular coordinates X, Y, Z, giving an accuracy for the geodetic height H of 1 mm for heights up to 50 km and for geodetic latitude B of 0,0001 arc seconds for H < 10 km. The formulas proposed in [1, 2] apply to all values of latitude and longitude (B and L). In [3], we propose two new formulas for H and B. In this paper, it is shown that the formulas proposed in [3] apply to points of ellipsoid surface and points with geodetic latitude of 0° and 90°. For the same formulas proposed in [3], the corrections are derived to ensure an accuracy of H of 1 mm at H ≤ 10 km, which apply to all values of B and L. Basing on the presented geometric conclusions, calculations and analyzes, a new solution for H and B respectively is proposed for given X, Y, Z, which provides an accuracy for H less than 1 mm for H ≤ 100 km and for B of 0,0001 arc seconds for H ≤ 50 km.

scholarly journals Methods for Transformation of Rectangular Spatial Coordinates to Geodetic Coordinates

2018 ◽  
Vol 7 (4.38) ◽  
pp. 1179
Author(s):  
Pavel Aleksandrovich Medvedev ◽  
Leonid Vasilevich Bykov ◽  
Vasiliy Leonidovich Bykov ◽  
Marina Vladimirovna Novorodskaya ◽  
Svetlana Ivanovna Sherstneva
Keyword(s):  
Transcendental Equation ◽  
Curvilinear Coordinates ◽  
Quartic Equation ◽  
Iterative Processes ◽  
Geodetic Height ◽  
Rectangular Coordinates ◽  
Spatial Coordinates ◽  
Root Isolation ◽  
Chord Method

The article gives a brief analysis of methods and algorithms for the transformation of spatial rectangular coordinates to curvilinear coordinates - geodetic latitude, geodetic longitude, geodetic height. Two algorithms for solving the equation for determining longitude are considered. Three formulas used to calculate the height are analyzed, with an estimate of their errors due to the approximate latitude. The shortcomings of mathematical solutions to these problems are revealed. A study of different approaches and methods for solving the transcendental equation for determining the latitude, based on the theory of separation of the root of the equation, is performed. Using this technique, iterative processes were performed to calculate the reduced latitude , using trigonometric identities, by introducing an auxiliary angle and transforming it to an algebraic quartic equation, which Borkowski solves by the Ferrari's method. The determination of the root isolation interval allowed using the chord method (proportional parts) to determine the latitude. In all cases, estimates of the convergence of the iterative processes that facilitate the comparative analysis of the proposed solutions are obtained. By further decreasing the separation interval of the root, the accuracy of the non-iterative determination of the latitude is improved by the Newton method.  

scholarly journals Determination of the Precise Coordinates of the GPS Reference Station in of a GBAS System in the Air Transport

2020 ◽  
Vol 22 (3) ◽  
pp. 11-18
Author(s):  
Kamil Krasuski ◽  
Stepan Savchuk
Keyword(s):  
Mathematical Model ◽  
Measurement Technique ◽  
Air Transport ◽  
Reference Station ◽  
The Real ◽  
Station Coordinates ◽  
Geocentric Coordinates

This paper presents results of research concerning determination of the GPS reference station coordinates located on the grounds of an EPDE airport in Deblin. The study uses a mathematical model of the PPP measurement technique in order to determine the coordinates of the reference station using the real GPS code-phase observations. The computations of the coordinates of the GPS reference station were carried out in numerical applications CSRS-PPP, APPS and GAPS. In this research was found that the accuracy of finding solutions to the XYZ geocentric coordinates of the reference station REF1 between solutions CSRS-PPP, APPS and GAPS ranges from 0.01m to 0.13m. In addition, the accuracy of determining the XYZ geocentric coordinates from the PPP method related to the GPS differential solution ranged from 0.01m to 0.11m.

scholarly journals About the decision regularized equations of perturbed motion body

2019 ◽  
Vol 110 ◽  
pp. 01031
Author(s):  
Vera Petelina
Keyword(s):  
Higher Order ◽  
The Body ◽  
Body Motion ◽  
Motion Velocity ◽  
Intermediate Point ◽  
Rectangular Coordinates ◽  
The Right ◽  
Approximating Polynomials ◽  
Disturbed Motion

The article deals with determination of the second- and higher-order perturbations in Cartesian coordinates and body motion velocity constituents. A special perturbed motion differential equations system is constructed. The right-hand sides of this system are finite polynomials relative to an independent regularizing variable. This allows constructing a single algorithm to determine the second and higher order perturbations in the form of finite polynomials relative to some regularizing variables that are chosen at each approximation step. Following the calculations results with the use of the developed method, the coefficients of approximating polynomials representing rectangular coordinates and components of the regularized body speed were obtained. Comparison with the results of numerical integration of the equations of disturbed motion shows close agreement of the results. The developed methods make it possible to calculate, by the approximating polynomials, any intermediate point of the motion trajectory of the body.

Definition of geodetic height namely by measured geocentric coordinates

2017 ◽  
Vol 921 (3) ◽  
pp. 20-23
Author(s):  
Y.P. Kureniov ◽  
T.N. Malik
Keyword(s):  
Calculation Method ◽  
Moving Target ◽  
Iterative Calculation ◽  
Geodetic Height ◽  
Definition Of ◽  
Geocentric Coordinates

The article describes one of the methods for determining the geodetic height by using the satellite as a moving target points. It is shown that the chronology of the development of the satellite method for determining the geodetic height of the iterative calculation method for the open-closed formulas for the dependence of the geodetic latitude and, finally, to closed formulas determining the geodetic height in function exclusively from geocentric coordinates. This article describes the geometrical (volumetric and flat) models to perform the derivation of the formulas for determining the geodetic height as a function of the geocentric coordinates of the point. Two variants of the formulas obtained by the authors to determine the geodetic height.

scholarly journals DETERMINATION OF GEODESIC LATITUDE BY SPATIAL RIGHT-MUGAL COORDINATES BY USING A DIFFERENTIAL AMENDMENT

2019 ◽  
Vol 1 (2) ◽  
pp. 3-8
Author(s):  
Konstantin Afonin ◽  
Yulia Trifonova
Keyword(s):  
Iterative Methods ◽  
Practical Application ◽  
Third Way ◽  
Differential Correction ◽  
Numerical Example ◽  
The Third ◽  
Rectangular Coordinates

GNSS technologies are currently essential for coordinate support of territories. However, theymakeit possible to obtain spatial rectangular coordinates of the points being determined. While most users need the flat rectangular coordinates of Gauss – Kruger. And these coordinates can be calculated only by geodetic latitudes and longitudes. The special literature describes more than a dozen methods for calculating the geodetic latitude in spatial rectangular coordinates. To solve this problem, usually use any iterative or non-iterative methods. Both those and others have their ad-vantages and disadvantages. In the work applied the third way to solve the problem. It is proposed to calculate and use the differential correction to the initial (approximate) value of the geodesic lati-tude. Received working formulas that implement this idea. A numerical example is given showing the possibility of practical application oftheproposedmethod.

scholarly journals Design procedure of first-order perturbations for collisions trajectories with a perturbing body

2019 ◽  
Vol 138 ◽  
pp. 01034
Author(s):  
Vera Petelina
Keyword(s):  
Design Procedure ◽  
Equation System ◽  
Body Motion ◽  
Differential Equation System ◽  
Motion Equations ◽  
Rectangular Coordinates ◽  
The Right ◽  
Approximating Polynomials ◽  
Disturbed Motion

The article is devoted to the determination of firstand secondorder perturbations in rectangular coordinates and velocity components of body motion. Special differential equation system of perturbed motion is constructed. The right-hand sides of this system are finitesimal polynomials in powers of an independent regularizing variate. This allows constructing a single algorithm to determine firstand second-order perturbations in the form of finitesimal polynomials in powers of regularizing variates that are chosen at each approximation step. Following the calculations results with the developed method use, the coefficients of approximating polynomials representing rectangular coordinates and components of the regularized body speed were obtained. Comparison with the numerical results of the disturbed motion equations shows their close agreement. The developed method make it possible to calculate any visa point of body motion by the approximating polynomials.

scholarly journals New Strategy for Improving the Accuracy of Aircraft Positioning Based on GPS SPP Solution

Sensors ◽  
2020 ◽  
Vol 20 (17) ◽  
pp. 4921 ◽  
Author(s):  
Kamil Krasuski ◽  
Adam Ciećko ◽  
Mieczysław Bakuła ◽  
Damian Wierzbicki
Keyword(s):  
Single Point ◽  
Weighted Average ◽  
Navigation Data ◽  
Gps Satellites ◽  
New Strategy ◽  
Weighted Average Model ◽  
Geocentric Coordinates ◽  
Better Than

The paper describes and presents a new calculation strategy for the determination of the aircraft’s resultant position using the GPS (Global Positioning System) SPP (Single Point Positioning) code method. The paper developed a concept of using the weighted average model with the use of measuring weights to improve the quality of determination of the coordinates and accuracy of GPS SPP positioning. In this research, measurement weights were used as a function of the number of GPS satellites being tracked, and geometric PDOP (Position Dilution of Precision) coefficient. The calculations were made using navigation data recorded by two independent GPS receivers: Thales Mobile Mapper and Topcon HiPerPro. On the basis of the obtained results, it was found that the RMS (Root Mean Square) accuracy of positioning for XYZ geocentric coordinates was better than 1.2% to 33.7% for the weighted average method compared to a single GPS SPP solution. The proposed approach is therefore of practical application in air navigation to improve the quality of aircraft positioning.

scholarly journals Accuracy Assessment of Aircraft Positioning Using the Dual-Frequency GPS Code Observations in Aviation

2020 ◽  
Vol 22 (2) ◽  
pp. 23-30
Author(s):  
Kamil Krasuski ◽  
Stepan Savchuk
Keyword(s):  
Linear Combination ◽  
Accuracy Assessment ◽  
Dual Frequency ◽  
Positioning Accuracy ◽  
Gps Navigation ◽  
The Mathematical Model ◽  
Geocentric Coordinates ◽  
Error Parameter ◽  
Made In

This study publishes results of tests with regard to determination of the aircraft positioning accuracy by means of the GPS navigation in aviation. The research exploits the mathematical model of the linear combination "IonosphereFree" in order to designate the coordinates of an aircraft. The research uses the actual GPS code observations, recorded by a satellite receiver mounted in the Cessna 172, at the time of the experiment for the EPDE military aerodrome in Dęblin. The computations of the position of the Cessna 172 aircraft for the linear combination "Ionosphere-Free" were made in the APS Toolbox v.1.0.0. programme. Within evaluation of accuracy of the GPS positioning in aviation, the determined coordinates of the aircraft Cessna 172 from the APS programme were compared to an accurate reference position from the solution derived by the PPP measurement technique. In the research, the authors obtained an average positioning accuracy of approximately 5 m in the geocentric XYZ coordinates and approximately 4 m in the ellipsoidal BLh coordinates. In addition, the 3D-error parameter is lower than 7 m for the XYZ geocentric coordinates.

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