The purpose of the study is to attempt to determine the deviation of vertical lines using trigonometric levelling and Global Navigation Satellite System (GNNS) measurements. For the last decades with the emergence of highprecision electronic theodolites and tacheometers, trigonometric levelling becomes a competitor of the geometric levelling of the II and III accuracy classes. This is primarily the definition of exceedances at distances up to 1-2 km for topographic surveying and the study of geodynamic processes in zones of the man-made load. Today, high precision robotic electronic tacheometers have been developed, which allow to significantly improve the accuracy of the measurement of zenith distances by automatically guiding the target to the maximum reflected signal. Such robotic tacheometers carry out measurements of anti-aircraft distances and distances without the direct participation of the observer. The method of achieving this goal is provided by theoretical and experimental studies to improve the accuracy of trigonometric alignment and the use of high-precision GNSS measurements. It is also important here to switch from the spatial geodetic coordinates B, L, H to local topocentric coordinates in order to provide control over the deformation of hydraulic structures and the territory of man-caused loading of the main structures in the area at the Dniester hydroaccumulation power plant (DHPP). The main result of the study is the possibility of taking into account the influence of the refraction and the gravitational field of the earth on the accuracy of the trigonometric levelling and the determination of the deviations of vertical lines from a two-way trigonometric levelling with short distances from 500 to 1000 m. Scientific novelty: the proposed approach allows to calculate the effect of the refraction and the gravitational field of the Earth on the resulting trigonometric levelling with high accuracy. In addition, using trigonometric levelling and GNSS measurements, it is possible to independently determine the deviation of the vertical lines. Practical significance: the proposed method makes it possible to estimate the effect of vertical lines on the results of two-way synchronous trigonometric levelling.

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The main goal of our research is to show the need to use modern methods of processing GNSS observations time series by non-classical error theory of measurements (NETM), which is characterized by large sample sizes n > 500. The errors of high-precision observations, for the most part, cannot be represented by the classical law of Gaussian distribution. With the increase in sample size, the empirical error distribution will increasingly deviate from the classical Gaussian error theory of measurements (CETM). Methods. For this research we pre-processed GNSS observation at five permanent stations in Ukraine (SULP, GLSV, POLV, MIKL and CRAO). After applying the "clean" procedures based on the iGPS software package, we obtained the GNSS observation time series for 2018-2020. The verification of empirical error distributions was ensured by the procedure of non-classical error theory of measurements, based on the recommendations offered by G. Jeffreys and on the principles of hypothesis testing according to Pearson criteria. Results. It has been established that the coordinate time series of permanent stations obtained from precision GNSS observations do not confirm the hypothesis of their conformity to normal Gaussian distribution law. NETM diagnostics of the accuracy of high-precision GNSS measurements, which is based on the use of confidence intervals for estimates of asymmetry and kurtosis of a large sample, followed by the Pearson test, confirms the presence of weak, non-GNSS-treated sources of systematic errors. Scientific novelty. The authors use the possibility of NETM to improve the method of processing high-precision GNSS measurements and necessity to take into account sources of systematic errors. The failure to account for individual factors creates the effect of shifting the coordinate time series, which, in turn, leads to subjective estimates of station movement velocities, their geodynamic interpretation. Practical significance is based on the application of NETM diagnostics of probabilistic form of permanent stations topocentric coordinates distribution and improvement of the method of their determination. Research of the causes of the error distribution deviations from the established norms ensures the metrological literacy of large amount high-precision GNSS measurements.

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