Accuracy Assessment of the Network Real-Time Kinematic Techniques for Geodetic and Plane Coordinates

Virtual Reference Station (VRS), Master-Auxiliary Corrections (MAX) and Individualised Master-Auxiliary Corrections (IMAX) are among the Network Real-Time Kinematic (NRTK) techniques supported by Malaysia Real-Time Kinematic GNSS Network (MyRTKnet) in rendering network-based solution to users. However, different network corrections have different limitations due to different manufacturers hence offering varieties output. Therefore, this study was conducted to assess the accuracy of VRS, MAX and IMAX for geodetic and plane coordinates. Three (3) techniques were implemented to observe points at Universiti Teknologi Malaysia (UTM) and cadastral lot in Johor Bahru. The results were analysed based on assessment with known values and baseline lengths. The findings showed that the accuracy of all techniques ranged from 0.16 to 3.61 cm (horizontal) and 2.86 to 6.20 cm (vertical) for geodetic coordinates. For plane coordinates, the values varied from 0.3 to 4.22 cm (horizontal) and 2.1 to 8.26 cm (vertical). IMAX provided the worst accuracy compared to others due to incompatibility of Radio Technical Commission for Maritime Services (RTCM) format. Moreover, the accuracy decreases as the baseline length between rover and reference station increases. In conclusion, VRS and MAX yielded acceptable accuracy and can be safely chosen rather than IMAX. Furthermore, the baseline length for applications involving high accuracy measurement should also be considered.

Results of comparing astronomical-geodetic and navigational-geodetic methods of determining the components of the deflection of vertical

The authors present the results of comparing the components of deflection of vertical obtained through astronomical-geodetic and navigational-geodetic methods. The first one is based on comparing astronomical and geodetic coordinates of a location. This method has recently been widely implemented in a digital zenith camera systems using a small-sized digital telescope with an astronomical camera based on CCD or CMOS technologies, a high-precision inclinometer and satellite navigation system receiver. In this case, the combination of a telescope, an astronomical camera and an inclinometer enables determining the local direction of the plumb line, expressed by astronomical coordinates, from observations of stars at the zenith and using high-precision star catalogs. The navigational-geodetic method is based on comparing the results of the normal heights’ increments, defined through geometric leveling, and geodetic heights, computed with the relative method of satellite coordinate determinations. For each method, random and systematic components of the error and its confidence bounds were calculated; the absolute values of the deflection of vertical components at two geographically separated points were compared.

GEODESY, CARTOGRAPHY, AND AERIAL PHOTOGRAPHY

Aim. The aim of the proposed research is to substantiate the scientific and practical significance of calculating centers of states and regions territories , to conduct a historical review of centrographic research in Ukraine and in the world in the context of evolution of their methodology, to establish geodetic coordinates of the set of points lying on the line of the land state border and coastlines along the seas, and to determine the center of dead weight of the territory of Ukraine as the center of gravity of the broken polygon formed by state territory contours (geodesic center of Ukraine). Methods. In calculating the geodesic center of Ukraine, the authors used a method (in their own interpretation) of determining the center of gravity of the territory, proposed by Jean-Georges Affholder and tested by him in establishing the center of Europe. Results. The history of centrographic research is more than 250 years old, but only in the last-half century they have acquired a proper scientific character, becoming a solid geodesic base. The main milestones in the formation of the centrographic dimension in context of determining the centers of a number of leading world countries and the evolution of research methods are presented. It is established that it is necessary to distinguish the geometric, geographical and geodesic centers of territories, which differ in method of definition and level of accuracy stipulated by calculations requirements. Each of the recognized centers of the territory of Ukraine has its own significance and justification. Scientific novelty. A historical review of definition of the territories centers in the world and in Ukraine has been made. A method of calculating the center of territory gravity of Ukraine as the center of a broken landfill formed by its contours, including the land state border and coastline, is proposed. The concept of "geodesic center" has been introduced to denote the center of territory gravity, which describes a polygonal, including irregular, figure. The location and exact coordinates of the geodesic center of Ukraine, located in the Novoukrayinsky district of Kirovohrad region, has been established. Practical significance . Specifying the location of territories centers is important in terms of optimizing location of manufacturing facilities and infrastructure, as well as potential tourism facilities. The methods used in calculating territories centers of Ukraine can be used not only in conducting similar studies for administrative regions, but also in newly created districts, united territorial communities, etc.

Getchell’s method for conversion of Cartesian-geocentric to geodetic coordinates – Its properties and Newtonian alternative

The paper concentrates on the iterative Getchell’s method (formulated in 1972) and its alternative Newtonian implementation for conversion of Cartesian geocentric coordinates into geodetic coordinates. The same basic equation formulated in the Getchell’s method is used in both cases. The equation has a stable form in the whole range of argument (latitude) variation \langle -\pi /2,\pi /2\rangle . The original Getchell’s method (somehow “forgotten”) has a simple geometric interpretation and its applications turn out to be particularly effective. Many studies on iterative algorithms usually omit theoretical proofs of convergence replacing them with conclusions based on numerical examples. This paper presents theoretical proofs of algorithms convergence both for the Getchell’s method and the Newton procedure. The convergence parameter and numerical error of results were estimated in each case. Numerical tests were carried out for a set of points distributed on the Earth’s space, also for extreme h values. For typical practical applications of the Getchell’s method, sufficiently accurate results are obtained after 1–3 iterations, while in the Newton procedure already after one iteration, assuming the same numerical error and initial conditions. The accuracy of the geodetic coordinates determinations meets all practical requirements with some margin. For example an absolute numerical error for latitude is approx. 0.4\cdot {10^{-13}} [rad] i. e. about 0.00026 mm in the length of the meridian arc. The proposed methods were compared with other methods (algorithms), including in terms of stability and non-singularity in the entire usable space of the Earth, but excluding the near geocenter, which has no practical significance. Both the modification of the Getchell method and its Newtonian alternative are very good determined in this area (in the Earth’s poles, the final solution is directly the starting value of iterative algorithms). The discussed algorithms were implemented in the form of procedures in DELPHI language.

ALGORITHMS FOR CALCULATING GEODETIC HEIGHTS AND LATITUDES BY RECTANGULAR COORDINATES IN THE MERIDIAN ELLIPSE PLANE

Owing to the widespread use of GNSS technologies in geodetic practice, the problem arises of transition from rectangular spatial coordinates of points to spatial geodetic coordinates, which are necessary for the transition to flat rectangular coordinates in the Gauss-Kruger projection. The authors proposed five algorithms for converting rectangular coordinates of points in the plane of the meridian ellipse into geodetic heights and latitudes. The first two algorithms are geometrically related to the intersection point of the ellipse with the normal passing through the point at which the rectangular spatial coordinates were obtained. The formulas of the other three algorithms are based on the geometric relationships of the point of intersection of the meridian ellipse with the straight line connecting the point with the center of curvature of the meridian. As a result of the experiments, deviations of the calculated latitudes and heights from the reference values of the given grid of geodetic coordinates were obtained. The formulas were tested not only for points under and on the earth's surface, but also outside the earth at different heights up to an altitude of 20,000 km.

THE IMPROVING OF THE ACCURACY OF ENGINEERING AND GEODETIC WORKS IN THE CONSTRUCTION AND CONTROL OF THE GEOMETRIC PARAMETERS OF HIGH-RISE BUILDINGS

. In the article, the authors had done a brief analysis of existing modern, traditional methods and tools that allow to determine the planned coordinates of geodetic signs, located on the last tier of super-high engineering structures, paid special attention to the disadvantages and concluded that it’s necessary to develop a method and device for determining the geodetic coordinates on ultra-high engineering structures with high accuracy to provide engineering and geodetic works during the construction and operation of high-rise structures. In the article, the authors propose their method and device for determining the planar coordinates of the upper geodetic sign of the line of vertical design on ultra-high engineering structures with high accuracy, which is based on the method of the straight linear resection by the light distance meter. The result of the proposed method is the enhancing of the accuracy of engineering and geodetic works during the construction and control of geometric parameters of high-rise structures. This method of distance measurements allows getting the enhancing of the accuracy of the engineering and geodetic measurements by fixing the moment of occurrence of the double frequency with root mean square error (RMSE) above 0.5 mm, thus eliminating the need to measure the phase difference between direct and reflected pulses. A particular advantage of the proposed method is that the accuracy of the measurements depends on the comparison of the radiated f and double fg frequencies, which makes the measurement precision.