CALCULATION OF THE REGIONAL ELLIPSOID FOR UKRAINE AND ITS EFFICIENCY

The novelty and relevance of scientific solutions lies in the need to build a national reference system, namely, to determine the parameters of the regional ellipsoid. The methodology of such a scientific study consists of the fact that the task of determining the regional ellipsoid practically boils down to finding corrections to the general terrestrial ellipsoid GRS80 adopted by us. The regional ellipsoid for the territory of Ukraine should be the one that would best represent the geoid (quasi-geoid) of the given region. That is, the heights of the geoid relative to the regional ellipsoid within the territory of Ukraine should be as small as possible. The purpose of the article is to obtain the parameters of the regional ellipsoid for the territory of Ukraine and to study the effectiveness of such a reference system in solving some practical and scientific problems of geodesy. Thus, based on the results of the above studies, the following can be noted. The determination of all five parameters of the re- gional ellipsoid is caused by a strong functional dependence of the parameters among themselves. This dependence (correlation) is quite well demonstrated by the mean square error values, which are commensurate with the obtained parameters and even exceed the latter. Moreover, the greatest correlation occurs between the correction to the semimajor axis of the ellipsoid and the linear elements of the displacement of its center in the body of the Earth. Taking into account these remarks, we can conclude that the joint finding of all five parameters by the least squares method for the territory of Ukraine does not give us the expected good results. This is clearly visible from the calculations of geoid heights, presented in the form of a spheroidal trapezoid, which describes the territory of Ukraine. In contrast to such a solution, research on the determination of only three parameters of the displacement of the ellipsoid with its given dimensions makes it possible to quite well choose such a regional ellipsoid that would best represent the geoid (quasi-geoid) built on the territory of Ukraine. Solving these problems showed us very different results obtained from the same data for the same territory. This leads us to the need to conduct additional research on obtaining correct solutions to so-called unstable or ill-conditioned problems