The issue of the study of the problem of determining the geoid and quasi-geoid models is considered. Development of methods for constructing an exact geoid model using different dimensions. Analysis of the calculation of normal heights using satellite measurements, construction of geoid and quasi-geoid models by different methods is performed. Based on the results of the analytical review of existing methods for determining the geoid, it was proposed to use various data (geodetic heights, mixed gravity anomalies, anomalous potential) to construct this model, which allows building a model of a geoid with millimetre accuracy. The possibility of using the collocation method is considered. The task is to develop a methodology for constructing a geoid model using a network of low density gravity points and using pure and mixed gravity anomalies, which allows us to solve the problem of finding potential by solving the Laplace equation or using wavelets.

Local geodetic network is very important in harmonic development of city territory. On the base of the local geodetic network, cadastral and topographic surveying works, engineering geodetic works and executive measurements of newly built buildings and engineering networks are carried out. In the territory of Riga, the local geodetic network was started to create in 1880, and in the course of time, as the city expanded, necessity to have wider reference network emerged. In 2005, in the territory of Latvia, network of continuously working base stations LatPos was launched, which ensured completely new trends in execution of measurements and accuracy reached. One year later, base station network EUPOS-RIGA was launched in the territory of Riga. It can be regarded as consistent part of Riga local geodetic network. The purpose of the research was to state, what are differences between historically used coordinates of points of the local geodetic network, and coordinates that are determined by use of real time corrections of LatPos and EUPOS-RIGA base station network. Measurements were made in the territory of Riga in period from December 2016 until April 2017. In the framework of the research, 61 point of the local geodetic network was inspected and in 38 cases GNSS observations in RTK mode were completed. In the research, catalogues of coordinates of polygonometry points of sixties and eighties were used in order to compare what differences of coordinates existed historically. The main conclusion drawn during the research – historical points of the local geodetic network shall not be used for surveying works of any kind before improvement of them and before they comply with requirements of normative acts.