Determination of the geodetic latitude and height by spatial 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.

GPS elevation fitting study based on ternary polynomial regression

For the traditional GPS elevation fitting method, the accuracy has not been significantly improved in recent years, and the method has become increasingly complicated. This paper proposes to insert the geodetic height ‘H’ into the calculation system and use a ternary polynomial regression function to fit the GPS elevation anomaly. The feasibility of the ternary polynomial regression method in GPS elevation fitting was verified by an example, and compared with the results of the traditional plane fitting and quadric surface fitting method, it was proved that the proposed method is suitable for terrain with large terrain fluctuations. The fitting residual error and the standard deviation are smaller, and through example calculations, it is concluded that the ternary polynomial regression method under the seven parameters has the highest fitting accuracy.

Implementation of CORS GNSS and local geoid for precise orthometric height determination in land subsidence region (a case study in Semarang City)

Geoid has an important role in converting geodetic heights to physical heights, both in orthometric height system and normal height systems. At present, Semarang City already has gravimetric geoid with centimeter-level precision. This gravimetric was validated by geometric geoid measured by static method. GNSS (Global Navigation Satellite System) measurement using static method needs long observation time and costly because it requires network that connect baselines and points. This study aims to implement CORS (Continous Operating Reference Station) GNSS in measuring geodetic height and to apply gravimetric geoid in orthometric height calculations. In this research, the gravimetric geoid recalculation process was carried out using gravity disturbance data of 2016. The geoid fitting process was carried out iteratively based on gravity data and modification of the integral of Hotine. Geodetic height measurements were carried out at 40 points distributed olong 50 km leveling network. Geodetic height measurements were refered to CORS GNSS of BIG (Geospatial Information Agency) and UNDIP (Diponegoro University) to produce standard deviation ranged from ±0.003 m to ±0.055. Geometric geoid checking with previous gravimetric geoid before fitting produced standard deviation of ±0.037 m and datum offset of -0.690 m. Geometric geoid checking for recent gravimetric geoid after fitting produces standard deviation of ±0.043 m and datum offset of -0.010 m. This study concluded that the refering geodetic coordinates to CORS stations by 1 hour observation of rapid static method and processing baselines in commercial software are sufficient for the determination of orthometric height in centimeter-level precision. This study also concluded that gravimetric geoid fitting based on gravity data shifting can minimize datum offset and shrinkage in geoid map.

The accurate calculation of the geodetic heights of the celestial body’s surface points relative to the triaxial ellipsoid

A sphere or ellipsoid of revolution are usually used for approximation of the physical surface of the Earth. In some cases, a triaxial ellipsoid is used. The calculation of the geodetic height of points on the Earth’s surface is carried out mainly by approximate methods using the formulas for the dependence of spatial rectangular coordinates x, y, z on geodesics B, L, H. However, there are small bodies of the Solar system, for example, Eros 433 asteroid, for which such variants of the first approximation are incorrect, since in this case both first approximations are not small quantities. This article proposes a fundamentally new approach to calculating the geodesic height relative to the triaxial ellipsoid, based on the joint use of the normal equation for a surface passing through a given point and the equations of the surface itself. The method is reduced to solving the sixth-degree equation by the Sturm method and the fourth-degree equation by the Ferrari method.

Method of transferring marks to the installation horizons using satellite measurement technology

Today, during the construction of especially high-rise buildings and structures GNSS technologies have found wide application. The authors proposed the method of transmission marks on mounting horizons. It is very promising to investigate the matter concerning with the rapid applying of satellite technologies coordinates into life. It is known that satellite definitions are not very accurate, especially in identifying normal heights. However, the geodetic height is determined sufficiently. In this investigation, the algorithm of using satellite definitions is shown, taking into account the results of geometric leveling and accordingly, anomalies of heights that allows you to go to the surface of the quasigeoid and ultimately to calculate normal heights according to satellite technology. The Specific calculation results and the obtained graphs reflecting the advantages of using the proposed approach in comparison with using the traditional techniques. It is shown numerically that the accuracy of determining marks using GNSS technology almost does not depend on the height of the building, which is important in the construction of high-rise buildings.

Tracking of geodetic height of sea level in the west of Java Sea, Indonesia: A preliminary assessment

This paper assesses the agreement between observed heights of sea level from Global Navigation Satellite System (GNSS) and a global model of Mean Sea Surface (MSS). The assessment of the agreement is carried out according to the direct comparison between the height of MSS model and the geodetic height of actual sea level. Here, MSS is generated according to Gravity Recovery And Climate Experiment (GRACE) Gravity Model (GGM) and Mean Dynamic Ocean Topography (MDOT). The tracking of geodetic heights of actual sea level are done by Wide Area Differential (WA D) and Real Time Precise Point Positioning (RTPPP) Global Navigation Satellite System (GNSS) along an approximately 180 Nm SW-NE transect of away-return ship track in the west of the Java Sea, Indonesia. It is found that the overall agreement between geodetic height of sea level and MSS observed by WA DGNSS is 7.5 cm (away tracking), while those observed by RTPPP GNSS is 39.5 cm (away tracking) and 36.0 cm (return tracking). This work recommends selection of the best-fit tide model and careful examination on the dynamics of antenna offset due to vessel attitude.

Methods for Transformation of Rectangular Spatial Coordinates to Geodetic Coordinates

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.

Subsidence in the Dutch Wadden Sea

Ground surface dynamics is one of the processes influencing the future of the Wadden Sea area. Vertical land movement, both subsidence and heave, is a direct contributor to changes in the relative sea level. It is defined as the change of height of the Earth's surface with respect to a vertical datum. In the Netherlands, the Normaal Amsterdams Peil (NAP) is the official height datum, but its realisation via reference benchmarks is not time-dependent. Consequently, NAP benchmarks are not optimal for monitoring physical processes such as land subsidence. However, surface subsidence can be regarded as a differential signal: the vertical motion of one location relative to the vertical motion of another location. In this case, the actual geodetic height datum is superfluous.In the present paper, we highlight the processes that cause subsidence, with specific focus on the Wadden Sea area. The focus will be toward anthropogenic causes of subsidence, and how to understand them; how to measure and monitor and use these measurements for better characterisation and forecasting; with some details on the activities in the Wadden Sea that are relevant in this respect. This naturally leads to the identification of knowledge gaps and to the formulation of notions for future research.

Definition of geodetic height namely by measured 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.

COORDINATE TRANSFORMATION USING FEATHERSTONE AND VANÍČEK PROPOSED APPROACH - A CASE STUDY OF GHANA GEODETIC REFERENCE NETWORK

Most developing countries like Ghana are yet to adopt the geocentric datum for its surveying and mapping purposes. It is well known and documented that non-geocentric datums based on its establishment have more distortions in height compared with satellite datums. Most authors have argued that combining such height with horizontal positions (latitude and longitude) in the transformation process could introduce unwanted distortions to the network. This is because the local geodetic height in most cases is assumed to be determined to a lower accuracy compared with the horizontal positions. In the light of this, a transformation model was proposed by Featherstone and Vaníček (1999) which avoids the use of height in both global and local datums in coordinate transformation. It was confirmed that adopting such a method reduces the effect of distortions caused by geodetic height on the transformation parameters estimated. Therefore, this paper applied Featherstone and Vaníček (FV) model for the first time to a set of common points coordinates in Ghana geodetic reference network. The FV model was used to transform coordinates from global datum (WGS84) to local datum (Accra datum). The results obtained based on the Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) in both Eastings and Northings were satisfactory. Thus, a RMSE value of 0.66 m and 0.96 m were obtained for the Eastings and Northings while 0.76 m and 0.73 m were the MAE values achieved. Also, the FV model attained a transformation accuracy of 0.49 m. Hence, this study will serve as a preliminary investigation in avoiding the use of height in coordinate transformation within Ghana’s geodetic reference network.