A PRIORI RESEARCH RELATED TO THE CALCULATION OF THE REGIONAL ELLIPSOID FOR UKRAINE AND ITS EFFECTIVENESS
Authors:   Lviv Polytechnic National University, Ukraine, Sohor Andrii 
Published: September 2022

Despite the high accuracy of global geodetic reference systems and their widespread use in GPS measurements, regional (local) geodetic systems are becoming more widely used. For example, the World Geodetic System 1984 (WGS84) has 83 such local systems. The emergence of the latter is caused by the emergence of new problems of physical geodesy. These are the so-called regional problems, which make it possible to study in more detail both the geometric and gravimetric (physical) properties of the studied region (territory). For example, the tasks of constructing a high-precision regional geoid (quasi-geoid), regional ellipsoid, determining the regional normal formula of gravity, and others are becoming increasingly important. That is why at present both national and regional reference ellipsoids are accepted for processing geodetic data on a regional scale (for example, for a specific country), and for global research – a general terrestrial reference ellipsoid GRS80 or, when processing GPS data – a general terrestrial reference ellipsoid WGS84.In principle, any reference ellipsoid that represents a generalized figure of the Earth with appropriate accuracy can be used to process geodetic information. The deviations of the geoid from such an ellipsoid can determine the corrections that must be made in the results of geodetic measurements to bring the latter to the surface of this ellipsoid. However, with large deviations of the geoid from the reference ellipsoid, there are large corresponding reductions of geodetic measurements, which are burdened with significant errors due to the linearization of the main problem of geodesy and, consequently, the problem of bringing geodetic measurements to the ellipsoid. Therefore, from a practical point of view, to reduce the impact of these linearization errors and obtain methodologically optimal results of geodetic data processing, it is expedient and even necessary to use a reference ellipsoid that best describes the generalized geoid surface in the region of specific geodetic works.Given the above, the question arose about the national reference coordinate system, as such a system has some advantages over the national system in the process of practical processing of mass geodetic measurements, especially linear. In this regard, the issues of building a national reference system, namely, the definition of a regional ellipsoid, are very important and relevant. Therefore, the scope of our research is the construction of a national reference system based on data on the regional gravitational field of Ukraine. The methodology of such research is that the task of determining the regional ellipsoid is practically reduced to finding some corrections to the known, accepted by us, the general terrestrial ellipsoid GRS80. The regional ellipsoid for the territory of Ukraine should be the one that would best represent the geoid (quasi-geoid) of the region. That is, the heights of the geoid relative to the regional ellipsoid within the territory of Ukraine should be as small as possible. These questions are reflected in this monograph, the purpose of which is to investigate a priori calculations to determine the parameters of the internal orientation of the regional ellipsoid according to its gravitational field in Ukraine. Thus, based on the results of the above a priori studies, the following can be noted. Determining all five parameters of a regional ellipsoid leads to a strong functional dependence of the parameters. This dependence (correlation) is quite well demonstrated on the values of root mean square errors, which are proportional to the obtained parameters and even exceed the latter. Taking into account these remarks, we can conclude that the joint calculation of all five parameters by the method of least squares on the territory of Ukraine does not give us the expected good results. This is well seen from a priori calculations based on the heights of the geoid, presented in the form of a spheroidal trapezoid, which describes the territory of Ukraine. In contrast to this solution, studies to determine only the parameters of the internal orientation of the ellipsoid at a given major half-axis and compression of this ellipsoid, make it possible to choose a terrestrial regional ellipsoid that would best represent a geoid (quasi-geoid) built in Ukraine.