The paper attempts to determine an optimum structure of a directional measurement and control network intended for investigating horizontal displacements. For this purpose it uses the notion of entropy as a logarithmical measure of probability of the state of a particular observation system. An optimum number of observations results from the difference of the entropy of the vector of parameters X X ˆ H ' corresponding to one extra observation. An increment of entropy interpreted as an increment of the amount of information about the state of the system determines the adoption or rejection of another extra observation to be carried out.

The adjustment problem of the so-called combined (hybrid, integrated) network created with GNSS vectors and terrestrial observations has been the subject of many theoretical and applied works. The network adjustment in various mathematical spaces was considered: in the Cartesian geocentric system on a reference ellipsoid and on a mapping plane. For practical reasons, it often takes a geodetic coordinate system associated with the reference ellipsoid. In this case, the Cartesian GNSS vectors are converted, for example, into geodesic parameters (azimuth and length) on the ellipsoid, but the simple form of converted pseudo-observations are the direct differences of the geodetic coordinates. Unfortunately, such an approach may be essentially distorted by a systematic error resulting from the position error of the GNSS vector, before its projection on the ellipsoid surface. In this paper, an analysis of the impact of this error on the determined measures of geometric ellipsoid elements, including the differences of geodetic coordinates or geodesic parameters is presented. Assuming that the adjustment of a combined network on the ellipsoid shows that the optimal functional approach in relation to the satellite observation, is to create the observational equations directly for the original GNSS Cartesian vector components, writing them directly as a function of the geodetic coordinates (in numerical applications, we use the linearized forms of observational equations with explicitly specified coefficients). While retaining the original character of the Cartesian vector, one avoids any systematic errors that may occur in the conversion of the original GNSS vectors to ellipsoid elements, for example the vector of the geodesic parameters. The problem is theoretically developed and numerically tested. An example of the adjustment of a subnet loaded from the database of reference stations of the ASG-EUPOS system was considered for the preferred functional model of the GNSS observations.

Mining activity influence on the environment belongs to the most negative industrial influences. Land subsidence can be a consequence of many geotectonic processes as well as due to anthropogenic interference with rock massif in part or whole landscape. Mine subsidence on the surface can be a result of many deep underground mining activities. The presented study offers the theory to the specific case of the deformation vectors solution in a case of disruption of the data homogeneity of the geodetic network structure in the monitoring station during periodical measurements in mine subsidence. The theory of the specific solution of the deformation vector was developed for the mine subsidence at the Košice-Bankov abandoned magnesite mine near the city of Košice in east Slovakia. The outputs from the deformation survey were implemented into Geographic Information System (GIS) applications to a process of gradual reclamation of whole mining landscape around the magnesite mine. After completion of the mining operations and liquidation of the mine company it was necessary to determine the exact edges of the Košice-Bankov mine subsidence with the zones of residual ground motion in order to implement a comprehensive reclamation of the devastated mining landscape. Requirement of knowledge about stability of the former mine subsidence was necessary for starting the reclamation works. Outputs from the presented specific solutions of the deformation vectors confirmed the multi-year stability of the mine subsidence in the area of interest. Some numerical and graphical results from the deformation vectors survey in the Košice-Bankov abandoned magnesite mine are presented. The obtained results were transformed into GIS for the needs of the self-government of the city of Košice to the implementation of the reclamation works in the Košice-Bankov mining area.

Generally, gross errors exist in observations, and they affect the accuracy of results. We review methods to detect the gross errors by Robust estimation method based on L1-estimation theory and their validity in adjustment of geodetic networks with different condition. In order to detect the gross errors, we transform the weight of accidental model into equivalent one using not standardized residual but residual of observation, and apply this method to adjustment computation of triangulation network, traverse network, satellite geodetic network and so on. In triangulation network, we use a method of transforming into equivalent weight by residual and detect gross error in parameter adjustment without and with condition. The result from proposed method is compared with the one from using standardized residual as equivalent weight. In traverse network, we decide the weight by Helmert variance component estimation, and then detect gross errors and compare by the same way with triangulation network In satellite geodetic network in which observations are correlated, we detect gross errors transforming into equivalent correlation matrix by residual and variance inflation factor and the result is also compared with the result from using standardized residual. The results of detection are shown that it is more convenient and effective to detect gross errors by residual in geodetic network adjustment of various forms than detection by standardized residual.

Slope deformations, i.e., all types of landslides of rock masses (flow, creep, fall down, etc.), caused by gravitational forces, are the most widespread implementation of geological hazards and a negative geomorphological phenomenon that threatens the security of the population, destroy all utility values of the affected regions, negatively affects the environment, and cause considerable economic damage. Nowadays, the Global Navigation Satellite Systems (GNSS) provide accurate data for precise observations around the world due to the growing number of satellites from multiple operators, as well as more powerful and advanced technologies and the implementation of mathematical and physical models more accurately describing systematic errors that degrade GNSS observations such as ionospheric, tropospheric, and relativistic effects or multipath. The correct combination of measurement methods provides even more precise, i.e., better measurement results or estimates of unknown parameters. The combination of measurement procedures and their significant evaluations represent the essential attribute of deformation monitoring of landslides concerning the protection of the environment and the population’s safety in the interest areas for the sustainable development of human society. This article presents the establishment and use of a local geodetic network in particular local space for various needs. Depending upon the specific conditions, it is possible to use GNSS technology to obtain accurate observations and achieve the results applicable to the deformation survey for subsequent processing of the adjustment procedure.

The aim of this study was to evaluate millimeter-scale deformations in Tallinn, the capital of Estonia, by using repeated leveling data and the synthetic aperture radar (SAR) images of Sentinel-1 satellite mission. The persistent scattered interferometric SAR (PS-InSAR) analysis of images from ascending and descending orbits from June 2016 to November 2021 resulted the line-of-sight (LOS) displacement velocities in the Tallinn city center. Velocity solutions were estimated for the full period of time, but also for shorter periods to monitor deformation changes in yearly basis. The gridded LOS velocity models were used for the decomposition of east-west and vertical velocities. Additionally, the uncertainty of 2D velocity solutions was estimated by following the propagation of uncertainty. The 3D velocity of permanent GNSS station “MUS2” in Tallinn was used to unify the reference of all PS-InSAR velocity solutions. The results of the latest leveling in Tallinn city center in 2007/2008 and 2019 showed rather small subsidence rates which were in agreement with InSAR long-termsolution. However, the short-termInSAR velocity solutions revealed larger subsidence of city center with a rate about –10 mm/yr in 2016–2017, and the uplift around 5 mm/yr in 2018–2019 with relatively stable periods in 2017–2018 and 2019–2021. The inclusion of groundwater level observation data and the geological mapping information into the analysis revealed possible spatiotemporal correlation between the InSAR results and the groundwater level variations over the deep valleys buried under quaternary sediments.