geodetic network
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AbstractGeodetic networks are important for most engineering projects. Generally, a geodetic network is designed according to precision, reliability, and cost criteria. This paper provides a new criterion considering the distances between the Net Points (NPs) and the Project Border (PB) in terms of Neighboring (N). Optimization based on the N criterion seeks to relocate the NPs as close as possible to PB, which leads to creating shorter distances between NPs or those distances linking NPs with Target Points (TPs) to be measured inside PB. These short distances can improve the precision of NPs and increase the accuracy of observations and transportation costs between NPs themselves or between NPs and TPs (in real applications). Three normalized N objective functions based on L1, L2, and L∞‒norms were formulated to build the corresponding N optimization models, NL1; NL2; and NL∞ and to determine the best solution. Each model is subjected to safety, precision, reliability, and cost constraints. The feasibility of the N criterion is demonstrated by a simulated example. The results showed the ability of NL∞ to determine the safest positions for the NPs near PB. These new positions led to improving the precision of the network and preserving the initial reliability and observations cost, due to contradiction problems. Also, N results created by all N models demonstrate their theoretical feasibility in improving the accuracy of the observations and transportation cost between points. It is recommended to use multi-objective optimization models to overcome the contradiction problem and consider the real application to generalize the benefits of N models in designing the networks.

This work shows improvements of geoid undulation values obtained from a high-resolution Global Geopotential Model (GGM), applied to local urban areas. The methodology employed made use of a Residual Terrain Model (RTM) to account for the topographic masses effect on the geoid. This effect was computed applying the spherical tesseroids approach for mass discretization. The required numerical integration was performed by 2-D integration with 1DFFT technique that combines DFT along parallels with direct numerical integration along meridians. In order to eliminate the GGM commission error, independent geoid undulations values obtained from a set of GNSS/leveling stations are employed. A corrector surface from the associated geoid undulation differences at the stations was generated through a polynomial regression model. The corrector surface, in addition to the GGM commission error, also absorbs the GNSS/leveling errors as well as datum inconsistencies and systematic errors of the data. The procedure was applied to five Mexican urban areas that have a geodetic network of GNSS/leveling points, which range from 166 to 811. Two GGM were evaluated: EGM2008 and XGM2019e_2159. EGM2008 was the model that showed relatively better agreement with the GNSS/leveling stations having differences with RMSE values in the range of 8–60 cm and standard deviations of 5–8 cm in four of the networks and 17 cm in one of them. The computed topographic masses contribution to the geoid were relatively small, having standard deviations on the range 1–24 mm. With respect to corrector surface estimations, they turned out to be fairly smooth yielding similar residuals values for two geoid models. This was also the case for the most recent Mexican gravity geoid GGM10. For the three geoid models, the second order polynomial regression model performed slightly better than the first order with differences up to 1 cm. These two models produced geoid correction residuals with a standard deviation in one test area of 14 cm while for the others it was of about 4–7 cm. However, the kriging method that was applied for comparison purposes produced slightly smaller values: 8 cm for one area and 4–6 cm for the others.

The results of studies on the SSC-2011 coordinate base homogeneity carried out in the process of linking a special-purpose geodetic network’s points to this coordinate system are presented. The research consisted of multiple determinations of the differential geodetic stations (DGS) coordinates in GSK-2011 from different types of the coordinate base of this system. In the first version, they were obtained through their binding to the nearest points of the SGN with known coordinates in the SSC-2011. In the second one, the DGS was linked to SSC-2011 by GNSS vectors to four FAGS points. In the third variant, in order to obtain these coordinates in SSC-2011 the reference were four points of the IGS network. The grid coordinates of the DGS determined in GSK-2011 from the FAGS and IGS points coincided within 1,3 cm. Those of the DGS in SSC-2011, from points of the SGN, differ from the ones obtained in the FAGS and IGS by maximum values up to 21,8 cm, 22,2 cm, 27,2 cm in the abscissa, ordinate, and position, respectively. The derived data on the degree of heterogeneity of the SGN in SSC-2011 enable concluding the impracticality of using it as the coordinate basis of this system at carrying out works, requiring positioning accuracy at the level of several centimeters.

Abstract The geodetic monitoring of engineering structures, their displacements, and deformations, carried out permanently or periodically, allows obtaining information on the technical condition of facilities. The achieved information enables determining the necessary changes in using objects and minimizing future errors in the similar object’s design. The measurement results are subject to geometric interpretation based on the determined displacement parameters of the object’s shape and the approximation of the vector displacement field. Due to the influence of random factors characterized by a change in time and varying intensity, the deformation measurements performed during the operation of the facilities are of great importance for the safety of structures and engineering structures. In actual tasks of determining the object’s deformation and building a geometric model of displacements, the dominant method is the differential method, the advantage of eliminating systematic errors in measurement results while maintaining the geometric structure of the measurement and control network. The displacement’s geometric model, built based on measurements and calculations, can build a dynamic model of a building object, additionally considering such causes of deformation as, for example, own and usable weight, wind pressure, changes in ambient temperature, or ground vibrations. The article proposes approaches using the free alignment of linear and angular observations made in a geodetic network to determine horizontal displacements of an engineering object. This method may be necessary to study displacements of various parts of the object, thus analyzing its deformation. Free alignment allows for an optimal fit of the equalized network into the approximate network by imposing additional conditions (compared to the classic least squares method) on the vector of estimates of increments to approximate coordinates and the value of the covariance matrix. As an example of applying the proposed approach, the actual data received from the geodetic monitoring of the building structure was used. The structure was a road viaduct located along Wojska Polskiego Street in Bydgoszcz. The object of measurements and analyses was represented by finite sets of fixed points, subject to periodic observations over two years. The authors tested the effectiveness of the proposed algorithm and compared the obtained results with the values of horizontal displacements, which were calculated based on the classic study of geodetic monitoring results using the least-squares method. The accuracy analysis of the obtained values of the geodetic network horizontal displacements using free alignment and the least-squares method was also performed. The results indicate the possibility of using the presented approach to identify the geometric model of horizontal displacements without losing the accuracy of their determination.

Abstract The paper is devoted to the application of photogrammetry in surveying and geomechanical studies of the state of stability of slopes in a quarry. For deep quarries a particularly important task is to ensure the stability of the slopes of the benches. The purpose of this study is to improve the survey techniques of the slopes using terrestrial photogrammetry, the establishment of the values of the basic errors in the positioning of cameras in local geodetic network. The results of photogrammetric measuring data processing, which are the coordinates of the slope points and its elements, point cloud, surface model, volume and area data, improve the quality of geomechanical monitoring at mining enterprises and provide increase safety of mining operations. The proposed method of survey consists in positioning images (projection centres) in the system of the geodetic reference network by measuring with an electronic total station. Established during the study was dependence of the accuracy of the coordinates of the three-dimensional model of the slopes on the distance between the camera and the total station, between the camera positions in a pair of images. The article contains the results of the practical implementation of the proposed survey method, the results of experiments performed for the purpose of comparison with an alternative measurement method, which was a survey by a total station, graphs of dependencies describing the effect of measurement parameters on the accuracy of work performed. The article is also supplemented by a theoretical analysis of the use of UAVs in the use of work to determine of stability of slopes in a quarry, which is based on the authors’ experience with the use of UAVs in open pit mines. In this theoretical comparison, the emphasis is mainly on the operability of the use of UAV, which in the case of open pit mines creating a practically stable wind vortex with a speed higher than the allowed speed of operation rotors UAVs.

Abstract The final result of surveys largely depends on the accuracy and timeliness of the control network. This research paper presents the relationship between the condition of the points and the area where they are located. The main goal of this study is to present the methodology of a detailed analysis of the database of vertical control points in a selected area that is used to develop a mobile application intended for the update of the existing set of points of the vertical control network on an ongoing basis. In order to prepare the mobile application for the ongoing update of the control network, it is necessary to define detailed procedures for dealing with the database of points. These procedures concern the determination of the methodology of making an inventory of the existing database, and then the determination of the rules for updating the control network using the developed application.

Abstract. The knowledge of the geoid undulation, the height of the geoid relative to a given ellipsoid of reference, is fundamental to transform the ellipsoidal heights into orthometric heights. Global geoid undulation models developed from satellite gravity measurements appropriately integrated with other data, are free accessible in internet, but their accuracy may be inadequate for specific applications. Earth Gravitational Model 2008 (EGM2008) is one of those: usually available in grid form 2.5’ × 2.5’ (a geotif is developed by Agisoft with resolution 1’ × 1’), it defines the difference between the WGS84 ellipsoid height and the mean sea level, but in some areas the discrepancies between these geoid undulations and local correspondent measured values are on the order of various decimetres. For consequence, more accurate models are necessary. This article aims to determine a geoid undulation model suitable for Campania Region (Italy), starting from the global model EGM2008 (1’ × 1’) that is locally adjusted by using geodetic network points (GNPs) and GIS interpolation functions. Three different datasets are considered including respectively 20, 40 and 60 GNPs and three deterministic interpolators are applied in global way to generate geoid undulation grids: Inverse Distance Weight (IDW), Global Polynomial 1st order (GP1), Global Polynomial 2nd order (GP2). The resultant 9 models are tested on 20 additional GNPs. The experiments demonstrate that local geoid can be produced on a little area adapting global geoid by means of GNPs: the model obtained using GP2 and 60 GNPs, the most accurate one, fits the data with ±3.2 cm root mean square error (RMSE).

The article is devoted to the study of changes in geodesy, land management, State land cadastre and urban planning. It is proved that changes in certain areas are related to changes in the main directions of land reform in Ukraine, namely the formation of territorial communities and the introduction of a full and open land market. The process of formation of communal property in Ukraine and formation of territorial communities are investigated. At the same time, a special type of documentation appears – a comprehensive plan of spatial development of territorial communities, which is both land management documentation and urban planning documentation at the local level and includes topographic and geodetic data. To determine the boundaries of the territory of the community, a new type of land management documentation was introduced – a land management project to establish the boundaries of the territory of the territorial community. It is established that the number and area of territorial communities are different and can differ dozens of times. It is determined that the issue of creating geospatial data infrastructure is becoming more and more developed in Ukraine, because it combines data from the State Geodetic Network, information from the State Land and Urban Cadastre, which provides additional amplification and data entry, development of documentation using its current data. The issue of land market regulation is considered. Its subjects and features of acquisition of the property right to land plots of agricultural purpose are defined. The maximum size of the total area of agricultural land plots is presented – no more than ten thousand hectares, but until January 1, 2024 for the citizens of Ukraine this value should not exceed 100 hectares. The tendency of changes in establishing the sale price of the land plot, namely in carrying out the normative monetary assessment is determined. It is proposed to create a single assessment procedure for all land plots, regardless of their purpose, but taking into account the boundaries of the territorial community. The average cost of agricultural land by regions of Ukraine is analyzed. It is determined that it is uneven and can differ by 2-2.5 times. It is established that the introduction of real-time electronic auctions for the purchase and sale of agricultural land of all forms of ownership allows to achieve openness and transparency of the land market, as well as attracting a wider range of potential buyers.

Mining activity influence on the environment belongs to the most negative industrial influences. 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 was developed for the mine subsidence at the abandoned magnesite mine of Košice-Bankov near the city of Košice in East Slovakia. The outputs from the deformation survey were implemented into Geographical Information System (GIS) applications to a process of gradual reclamation of whole mining landscape in the magnesite mine vicinity. After completion of the mining operations and liquidation of the mine company it was necessary to determine the exact edges of the mine subsidence of Košice-Bankov 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 work. 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 abandoned magnesite mine of Košice-Bankov are presented. The obtained results were transformed into GIS for the needs of the Municipality of the city of Košice to the implementation of the reclamation activities in the mining territoryof Košice-Bankov.

The article highlights the issues of creating with the necessary accuracy a planned control on the industrial site of the engineering structures under construction using satellite technologies and total stations. Depending on the design features of the engineering structures under construction, as well as the technological scheme for the installation of building constructions and industrial equipment, various schemes for creating such control are considered, based on the application of the inverse linear-angular notch. Errors in the source data are one of the main errors that affect the accuracy of geodetic constructions, including the solution of the inverse linear-angular notch. When creating a geodetic network in several stages, the errors of the initial data of the first stage affect the values of the root-mean-square errors (RMS) of determining the position of the second stage points, the errors of which affect the value of the RMS of the position of the third stage points, etc. The reason for their occurrence is the errors of geodetic measurements that occur at each stage of control creating, as well as the stability violation of the points during the production of excavation, construction and installation works. When determining the coordinates of a separate project point at the stage of its removal in-situ by a total station, the entire network is not equalized in the vast majority of cases, and the coordinates of the starting points to which the total station is oriented are considered error-free. As a result, the RMS determination of the points coordinates of the control network or the removal of the design points of the elements of building structures and equipment will also be considered satisfying the requirements, i.e. the measurement accuracy will be artificially overestimated and will not correspond to the actual one obtained. This is due to the fact that the accumulation of errors in the initial data is not taken into account when the number of steps (stages) of control creating increases. The purpose of this work is to analyze the influence of measurement errors and initial data when creating a geodetic control on an industrial site by several stages of its construction based on inverse linear-angular notches and a priori estimation of the accuracy of the determined points position.