Methods of calculating the parameters of the reference ellipsoid according to the data of the regional gravity field of the earth ; Способи обчислення параметрів референц-еліпсоїда за даними регіонального гравітаційного поля землі

The novelty and relevance of scientific solutions lie in the necessity to establish a national reference system, namely the determination of parameters for a regional ellipsoid. The methodology of such scientific research involves the task of defining a regional ellipsoid, which practically reduces to finding corrections to the adopted global ellipsoid GRS80. The regional ellipsoid for the territory of Ukraine should best represent the geoid of this region. In other words, the geoid heights relative to the regional ellipsoid within the territory of Ukraine should be minimized as much as possible. The purpose of the article is to obtain the parameters of the regional ellipsoid for the territory of Ukraine and investigate the effectiveness of such a reference system in solving certain practical and scientific geodetic tasks. Thus, based on the results obtained from the conducted research, the following observations can be made. Determining all five parameters of the regional ellipsoid is strongly influenced by the functional dependence of these parameters on each other. This dependence (correlation) is well demonstrated by the values of mean square errors, which are proportional to the obtained parameters and even exceed them. The highest correlation arises between the correction to the major axis of the ellipsoid and the linear elements of its center displacement within the Earth's body. Taking these observations into account, it can be concluded that the simultaneous determination of all five parameters using the least squares method for the territory of Ukraine does not yield the expected good results. This is evident from the calculations of geoid heights presented in the form of a spheroidal trapezoid describing the territory of Ukraine. In contrast, research on determining only three parameters of ellipsoid displacement at given dimensions provides the opportunity to reasonably fit a regional ellipsoid that best represents the geoid constructed on the territory of Ukraine. The solution to these problems has ...