The results of building a local quasigeoid model by various methods on the territory of the geodesic training ground of SSUGT, based on the data of geometric leveling, GNSS measurements, gravimetry and astronomical measurements, are presented. The advantages of using a two-dimensional model of a quasigeoid in ellipsoidal coordinates over the "flat model" of height calibration widely used in GNSS technologies are shown. The criteria for choosing a method for building a quasigeoid model on a local territory and criteria for evaluating the quality of the results are determined. The results of determining the deviations of the vertical line in a given area, with control according to astronomo-geodesic measurements, are presented. In particular, a method for quick determining the deviations of a vertical line from the differences in astronomical and geodetic zenith distances was tested. A conclusion about the best method for determining the parameters of the local model of the quasigeoid and the deviations of the vertical line for a given territory is made. The results of the research are of practical significance for the training of students and specialists in the field of geodesy.

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.