The geodesy literature seems to offer comprehensive insight into the planar Helmert transformation with Hausbrandt corrections. Specialist literature is mainly devoted to the issues of 3D transformation. The determination of the sought values, coordinates in the target system, requires two stages of computations. The classical approach yields ‘new’ coordinates of reference points in the target system that should not be changed in principle. This requires the Hausbrandt corrections. The paper proposes to simplify the two-stage process of planar transformation by assigning adjustment corrections to reference point coordinates in the source system. This approach requires solving the Helmert transformation by adjusting conditioned observations with unknowns. This yielded transformation results consistent with the classical method. The proposed algorithm avoided the issue of correcting the official coordinates of the control network and using additional (post-transformation) corrections for the transformed points. The proposed algorithm for solving the plane Helmert transformation for �� > 2 reference points simplifies the computing stages compared to the classical approach. The assignment of adjustment corrections to coordinates of reference points in the source system helps avoid correcting coordinates of the reference points in the target system and additional corrections for transformed points. The main goal of any data adjustment process with the use of the least squares method is (by definition) obtaining unambiguous quantities that would strictly meet the mathematical relationships between them. Therefore, this work aims to show such a transformation adjusting procedure, so that no additional computational activities related to the correction of already aligned results are necessary.

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.

The purpose of this article was to provide the user with information about the number of buildings in the analyzed OpenStreetMap (OSM) dataset in the form of data completeness indicators, namely the standard OSM building areal completeness index (C Index), the numerical completeness index (COUNT Index) and OSM building location accuracy index (TP Index). The official Polish vector database BDOT10k (Database of Topographic Objects) was designated as the reference dataset. Analyses were carried out for Piaseczno County in Poland, differentiated by land cover structure and urbanization level. The results were presented in the form of a bivariate choropleth map with an individually selected class interval suitable for the statistical distribution of the analyzed data. The results confirm that the completeness of OSM buildings close to 100% was obtained mainly in built-up areas. Areas with a commission of OSM buildings were distinguished in terms of area and number of buildings. Lower values of completeness rates were observed in less urbanized areas. The developed methodology for assessing the quality of OSM building data and visualizing the quality results to assist the user in selecting a dataset is universal and can be applied to any OSM polygon features, as well as for peer review of other spatial datasets of comparable thematic scope and detail.

We present a summary of research carried out in 2019–2022 in Poland in the area of general theory and methodology in geodesy. The study contains a description of original contributions by authors affiliated with Polish scientific institutions. It forms part of the national report presented at the 28th General Assembly of the International Union of Geodesy and Geophysics (IUGG) taking place on 11-20 July 2023 in Berlin, Germany. The Polish authors developed their research in the following thematic areas: robust estimation and its applications, prediction problems, cartographic projections, datum transformation problems and geometric geodesy algorithms, optimization and design of geodetic networks, geodetic time series analysis, relativistic effects in GNSS (Global Navigation Satellite System) and precise orbit determination of GNSS satellites. Much has been done on the subject of estimating the reliability of existing algorithms, but also improving them or studying relativistic effects. These studies are a continuation of work carried out over the years, but also they point to new developments in both surveying and geodesy.We hope that the general theory and methodology will continue to be so enthusiastically developed by Polish authors because although it is not an official pillar of geodesy, it is widely applicable to all three pillars of geodesy.

The aim of this research is to evaluate the performance of four UAV image processing software for the automatic estimation of volumes based on estimated volume accuracy, spatial accuracy, and execution time, with and without Ground Control Points (GCPs). A total of 52 images of a building were captured using a DJI Mavic Air UAV at 60m altitude and 80% forward and side overlap. The dataset was processed with and without GCPs using Pix4DMapper, Agisoft Metashape Pro, Reality Capture, and 3DF Zephyr. The UAV-based estimated volume generated from the software was compared with the true volume of the building generated from its as-built 3D building information modeled in Revit 2018 environment. The resulting percentage difference was computed. The average volumes estimated from the four software with the use of GCPs were 4757.448 m3 (3.87%), 4728.1 m3 (2.54%), 4291.561 m3 (11.5%), and 4154.938 m3 (14.35%), respectively. Similarly, when GCPs were not used for the image processing, average volumes of 4631.385 m3 (4.52%), 4773.025 m3 (1.6%), 4617.899 m3 (4.89%), and 4420.403 m3 (8.92%) were obtained in the same order. In addition to the volume estimation analysis, other parameters, including execution time, positional RMSE, and spatial resolution, were evaluated. Based on these parameters, Agisoft Metashape Pro proved to be more accurate, time-efficient, and reliable for volumetric estimations from UAV images compared to the other investigated software. The findings of this study can guide decision-making in selecting the appropriate software for UAV-based volume estimation in different applications.

The aim study is the development of the classification of agricultural enterprises, based on the properties of the distribution of enterprises depending on the size of the land bank. To achieve this aim, open databases of agricultural enterprises were used, from which data for the Dnipropetrovsk district were selected. The data is not official. They are collected according to the data provided by the agricultural enterprises themselves. Since the official statistics group of small enterprises with up to 200 ha of land includes a fairly large number of enterprises that exist only formally, and since actively functioning enterprises are voluntarily registered in the databases used for the study, the developed classification reflects the real situation with agricultural enterprises in the Dnipropetrovsk district. The proposed scheme of a grouping of agricultural enterprises is regular, logarithmically uniform and based on the exponential increase of the land bank of agricultural enterprises. Its parameters are chosen in such a way as to take into account the classification of farms used in the Tax Code of Ukraine. The developed grouping of agricultural enterprises was used to analyze such characteristics of enterprises as types of production and organizational and legal forms of management. The analysis of the distribution showed that with the decrease of the land bank the number of farms increases and the number of enterprises, whose forms of management are joint-stock companies of different types, decreases.

This paper summarizes the contribution of Polish scientific units to the development of the Global Geodetic Observing System (GGOS) in recent years. We discuss the issues related to the integration of space geodetic techniques and co-location in space onboard Global Navigation Satellites Systems (GNSS) and Low Earth Orbiters (LEO), as well as perspectives introduced by the new European Space Agency’s (ESA) mission GENESIS. We summarize recent developments in terms of the European Galileo system and its contribution to satellite geodesy and general relativity, as well as ESA’s recent initiative – Moonlight to establish a satellite navigation and communication system for the Moon. Recent progress in troposphere delay modeling in Satellite Laser Ranging (SLR) allowed for better handling of systematic errors in SLR, such as range biases and tropospheric biases. We discuss enhanced tropospheric delay models for SLR based on numerical weather models with empirical corrections, which improve the consistency between space geodetic parameters derived using different techniques, such as SLR, GNSS, and Very Long Baseline Interferometry (VLBI). Finally, we review recent progress in the development of Polish GGOS scientific infrastructure in the framework of the European Plate Observing System project EPOS-PL¸.

For over two decades, an essential information about global monthly gravity variations is provided by the GRACE mission and its successor, the GRACE Follow-On (GRACE-FO) mission. The temporal variations in gravity field from GRACE/GRACEFO are determined based on the measurement of distance changes between two identical satellites using microwave ranging instruments. This process is carried out by various processing centers, which adopt different processing strategies and background models. This causes discrepancies in the resulting gravity fields.We address this problem by determining a monthly homogenous GRACE-FO gravity field solutions from June 2018 to November 2022 as provided by different processing centers included in the Science Data System (SDS) project, i.e. the Center for Space Research (CSR), the German Research Center for Geosciences (GFZ) and the Jet Propulsion Laboratory (JPL). We test three different weighting schemes. We show that for the last 4 years, at least 65% of continental areas are characterized by water decrease. We show that proposed merged solutions contain more signal information than individual ones based on the square root of the degree variance values.We note that the largest signal differences between individual and combined solutions occur for sectoral coefficients up to degree 40, and for zonal coefficients, the signal differences are twice as small.We also present that the differences in the spherical harmonic coefficients cause differences in global and local equivalent water height (EWH) changes. For example, the proposed merged solutions reduce root mean square scatter ofEWHby 5–15% comparing to individual solutions.

This paper summarizes the activity of the chosen Polish geodetic research teams in 2019–2022 in the fields of the Earth rotation and geodynamics. This publication has been prepared for the needs of the presentation of Polish scientists’ activities on the 28th International Union of Geodesy and Geodynamics General Assembly, Berlin, Germany. The part concerning Earth rotation is mostly focused on the estimation of the geophysical excitation of polar motion using data from Gravity Recovery and Climate Experiment (GRACE) and its follow-on (GRACE-FO) missions, and on the improvement of the determination of Earth rotation parameters based on the Satellite Laser Ranging (SLR), Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS), and Global Navigation Satellite System (GNSS) satellite techniques. The part concerning geodynamics is focused on geodetic time series analysis for geodynamical purposes and monitoring of the vertical ground movements induced by mass transport within the Earth’s system, monitoring of the crustal movements using GNSS and newly applied Interferometric Synthetic Aperture Radar (InSAR), discussing the changes of the landslides and its monitoring using geodetic methods as well as investigations of seismic events and sea-level changes with geodetic methods. Finally, the recent research activities carried out by Polish scientists in the international projects is presented.

The article presents the reviewed and summarised research activities of Polish research groups on reference frames and reference networks in a period of 2019–2022. It contains the results on the implementation of latest resolutions on reference systems of the International Union of Geodesy and Geophysics and the International Astronomical Union focusing on changes in the consecutive issues of the Astronomical Almanac of the Institute of Geodesy and Cartography, Warsaw. It further presents the status of the implementation of the European Terrestrial Reference System 1989 (ETRS89) in Poland, monitoring the terrestrial reference frame, including research on global terrestrial reference frames, GNSS data analysis within the EUREF Permanent Network, research on GNSS receiver antenna phase centres, research on impact of non-tidal loading effects on position solutions, and on station velocities. Then the activities concerning the realization of ITRS and ETRS89 in Poland are discussed, including operational work of GNSS IGS/EPN stations as well as operational work of the laser ranging station of the International Laser Ranging Service, with special emphasis on the Polish active GNSS network for the realization of ETRS89 and maintenance of the vertical control network. Extensive research activities are observed in the field of implementation of the International Terrestrial Gravity Reference Frame in Poland, maintenance and modernization of gravity control network in Poland but also in Sweden, establishment of gravity control network in Ireland based on absolute gravity survey as well as maintenance of the national magnetic control network in Poland which is traditionally performed on a regular basis.

This paper reviews the key studies concerning GNSS positioning and applications conducted at leading Polish research institutions from 2019 until 2022. The review also constitutes a contribution to the national report of Poland for the International Union of Geodesy and Geodynamics (IUGG) presented at the 28th General Assembly of IUGG held in 2023 in Berlin, Germany. In particular, we discuss the advances in theory and applications of relative and absolute positioning, troposphere and ionosphere sounding, smartphone and low-cost GNSS data processing, and other specific studies such as those on satellite antenna calibration and clock stability. In light of these recent advances by the Polish scientific community, continuous progress in GNSS theory and processing algorithms is thought to be maintained in the future, and GNSS applications are expected to continue to proliferate.

The article presents the reviewed and summarised research activities of the Polish research groups on gravimetry and gravity field modelling in the period of 2019–2022. It contains the results of absolute gravity surveys for the maintenance of the international gravity reference level in Poland and Europe, and for geodynamic research with an emphasis on metrological aspects. It also contains relative gravimetry issues as well as the results of marine gravity surveys in the southern Baltic Sea. Non-tidal gravity changes were extensively investigated. Long-term gravity variations were monitored at the Borowa Gora Geodetic-Geophysical Observatory and in a few other locations in Poland. The contribution of gravimetric records to seismic studies was investigated. Temporal variations of the gravity field from GRACE (Gravity Recovery and Climate Experiment) and GRACE-FO (GRACE Follow-On) data, in particular, deformations of the Earth’s surface as well as temporal variations of heights, total water storage and groundwater storage were investigated. Moreover, GRACE-based products and the performance of monthly Global Geopotential Models (GGMs) were a subject of research. GGMs developed in last years were evaluated. The research on developing new approaches in geoid modelling and their validation was conducted. New regional and local geoid models were determined for Poland and Ethiopia. The use of different techniques for estimating the absolute sea level at sites of the selected network in the Baltic Sea was investigated.

In this paper, the climate and environmental datasets were processed by the scripts of Generic Mapping Tools (GMT) and R to evaluate changes in climate parameters, vegetation patters and land cover types in Burkina Faso. Located in the southern Sahel zone, Burkina Faso experiences one of the most extreme climatic hazards in sub-saharan Africa varying from the extreme floods in Volta River Basin, to desertification and recurrent droughts.. The data include the TerraClimate dataset and satellite images Landsat 8-9 Operational Land Imager (OLI) and Thermal Infrared (TIRS) C2 L1. The dynamics of target climate characteristics of Burkina Faso was visualised for 2013-2022 using remote sensing data. To evaluate the environmental dynamics the TerraClimate data were used for visualizing key climate parameter: extreme temperatures, precipitation, soil moisture, downward surface shortwave radiation, vapour pressure deficit and anomaly. The Palmer Drought Severity Index (PDSI) was modelled over the study area to estimate soil water balance related to the soil moisture conditions as a prerequisites for vegetation growth. The land cover types were mapped using the k-means clustering by R. Two vegetation indices were computed to evaluate the changes in vegetation patterns over recent decade. These included the Normalized Difference Vegetation Index (NDVI) and the Soil-Adjusted Vegetation Index (SAVI) The scripts used for cartographic workflow are presented and discussed. This study contributes to the environmental mapping of Burkina Faso with aim to highlight the links between the climate processes and vegetation dynamics in West Africa.

The purpose of this study is to analyse the use of agricultural land on the territory of united communities and their individual districts of Zhytomyr region as the smallest units of the administrative territorial division of Ukraine. The relevance of this study, due to current changes in national land relations, dictates the need to have information about agricultural lands, their owners, tenants and the lands status for planning agricultural production, the land-leases development, sale of land. The analysis of land use was carried out according to the following indicators: location of land plots of all owners within the community district and the whole community; their area; monetary evaluation; status of documents for each land plot, in particular the availability of lease, land cultivation presence. The initial data of the researches is the data of the state land cadastre database, and data of the real property rights register, both in general access and in need of special access. As a result of the research there were defined areas and location of lands of some landowners, who leased their lands and areas of lands not leased, also there were defined areas of lands, used illegally, without any documents on land use, defined areas of lands, used or owned by agricultural producers (farms, physical persons, legal entities). A cartographic core was created for the purpose of convenient planning of agricultural land use and land management within selected districts on the territory of the community.

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.

Real objects in horizontal projection often have a complex geometry. Their irregular shape causes issues during analyses and calculations that consider their geometry. The paper proposes the replacement of real-world objects with equivalent rectangles (ER). The paper also defines the geometric criteria of ER as well as ER parameters and methods for calculating them. The paper also demonstrates the difference in the duration of calculations for different types of rectangles (equivalent rectangle with the same area, surrounding rectangle with the smallest area, inscribed rectangle with the largest area). The presented approach has been illustrated with three case studies. The first one is the application of ER to underground mining cavities to determine post-mining deformations of the ground surface. In the second study, an ER was applied to analyse the geometry of agricultural parcels in a selected part of a rural settlement. ER can help assess whether the spatial layout is faulty and if a planning intervention is necessary. The third example describes a building’s geometry with an ER. Regarding the simplification of building’s geometry, it is crucial to replace a simplified building with a model that has the same centroid location and the same area. It is the perfect solution for rapid analyses of displaying objects on maps in various scales.

The article analyses the development of metrological control technologies for electronic distance measurement rangefinders to determine their main characteristic of accuracy – the root mean square error of distance measurement. It is established that the current reference linear bases are reliable and serve as the main means of transmitting a unit of length from the standards to the working means of measuring length. The article describes the existing linear reference bases and specifies their accuracy and disadvantages. It is concluded that the disadvantages of linear reference bases are deprived of the reference linear bases built in special laboratories. They use distances measured by the differential method with laser interferometers as reference distances. The application of such technology allowed to automate the processes of measurements and calculations. There is development of fibre-optic linear bases, in which optical fibres of known length are used as model lines. The article offers a new technical solution – a combination of fiber-optic and interference linear bases, which allows to qualitatively improve the system of metrological support of laser rangefinders. This is achieved by having a fiber-optic unit, which allows you to create baselines of increased length, while ensuring small dimensions of the baseline, and relative interference base, which provides high accuracy of linear measurements and does not require calibration of the base with a precision rangefinder, which eliminates several difficulties associated with changes in the refractive index, makes measurements independent of the wavelength of the radiation source and almost independent of the ambient temperature.

In the article publications have been analyzed and summarized on this topic: studied the experience of implementing building information models and geographic information models for administrative and economic management of transport infrastructure facilities on the example of the regional airport activity. After the stage of collecting geospatial data from various sources and sensors, the data is imported into CAD-systems or GIS-systems. Different software products are used to work with both of these models. The processes of data organization in the process of creating building information models and geographic information models differ to some extent. The issues of integration of such models are not yet fully addressed and need to be addressed. In the process of integration of spatial data, solutions to the integration of semantics, topology, formats and standards of geospatial data are needed. An important task is to develop and study the experience of creating software modules that allow you to integrate BIM-models into geographic information systems. Based on the research, it is established that the current area of research is the development of technologies that allow the generation of information from BIM and GIS to create a more interconnected infrastructure. The integration of BIM and GIS information to create a spatial data infrastructure (SDI) is a perspective direction.

The problem of outlying observations is very well-known in the surveying data processing. Outliers might have several sources, different magnitudes, and shares within the whole observation set. It means that it is not possible to propose one universal method to deal with such observations. There are two general approaches in such a context: data cleaning or robust estimation. For example, the robust M-estimation has found many practical applications. However, there are other options, such as R-estimation or the absolute M _split estimation. The latter method was created to be less sensitive to outliers than the squared M _split estimation (the basic variant of Msplit estimation). From the theoretical point of view, the absolute M _split estimation cannot be classified as a robust method; however, it was proved that it could be used in such a context under certain conditions. The paper presents the primary comparison between that method and a conventional robust M-estimation. The results show that the absolute M _split estimation predominates over the classical methods, especially when the percentage of outliers is high. Thus, that method might be used to process LiDAR data, including mismeasured points. Processing synthetic data from terrestrial laser scanning or airborne laser scanning confirms that the absolute M _{split / estimation can deal with outliers sufficiently.}

The applications of the machine learning and programming approaches in cartography has been increasing in recent years. This paper presents a case study of the scripting techniques used for cartographic mapping using Generic Mapping Tools (GMT) and R language (raster and tmaps packages). The aim of the study is environmental mapping of Ghana. The materials include high-resolution raster grids: topography by the General Bathymetric Chart of the Oceans (GEBCO), climate and environmental datasets (TerraClimate) and Shuttle Radar Topography Mission (SRTM) Digital Elevation Model (DEM) for geomorphometric analysis (slope, aspect, hillshade and elevations). The methodology includes code snippets commented and explained with details of scripts. It is argued that using consolebased scripting tools for mapping is effective for cartographic workflow due to the logical structure and repeatability of scripts. The results include eight new thematic maps of Ghana performed using scripting approach inGMTscripting toolset and R language for quantitative and qualitative environmental assessment. Maps show correlations between the landforms of Ghana and certain environmental variables (drought index and soil moisture) showing the effects of the topographic relief on the distribution of the continuous geographic fields. These varied in several geographically distinct regions of Ghana: Ashanti (Kumasi), Volta, Savannah, coastal and northern regions. Demonstrated maps show that scripting method works effectively on a wide range of geosciences including environmental, topographic and climate studies. In such a way, this paper contributes both to the regional studies of Ghana and development of cartographic techniques.

M _split estimation is a novel method developed to process observation sets that include two (or more) observation aggregations. The main objective of the method is to estimate the location parameters of each aggregation without any preliminary assumption concerning the division of the observation set into respective subsets. Up to now, two different variants of M _split estimation have been derived. The first and basic variant is the squared M _split estimation, which can be derived from the assumption about the normal distribution of observations. The second variant is the absolute M _split estimation, which generally refers to the least absolute deviation method. The main objective of the paper is to compare both variants of M _split estimation by showing similarities and differences between the methods. The main dissimilarity stems from the different influence functions, making the absolute M _split estimation less sensitive to gross errors of moderate magnitude. The empirical analyses presented confirm that conclusion and show that the accuracy of the methods is similar, in general. The absolute M _split estimation is more accurate than the squared M _split estimation for less accurate observations. In contrast, the squared M _split estimation is more accurate when the number of observations in aggregations differs much. Concerning all advantages and disadvantages of M _split estimation variants, we recommend using the absolute M _split estimation in most geodetic applications.

The applicability of integratedUnmannedAerialVehicle (UAV)-photogrammetry and automatic feature extraction for cadastral or property mapping was investigated in this research paper. Multi-resolution segmentation (MRS) algorithm was implemented on UAVgenerated orthomosaic for mapping and the findings were compared with the result obtained from conventional ground survey technique using Hi-Target Differential Global Positioning System (DGPS) receivers. The overlapping image pairs acquired with the aid of a DJI Mavic air quadcopter were processed into an orthomosaic using Agisoft metashape software while MRS algorithm was implemented for the automatic extraction of visible land boundaries and building footprints at different Scale Parameter (SPs) in eCognition developer software. The obtained result shows that the performance of MRS improves with an increase in SP, with optimal results obtained when the SP was set at 1000 (with completeness, correctness, and overall accuracy of 92%, 95%, and 88%, respectively) for the extraction of the building footprints. Apart from the conducted cost and time analysis which shows that the integrated approach is 2.5 times faster and 9 times cheaper than the conventional DGPS approach, the automatically extracted boundaries and area of land parcels were also compared with the survey plans produced using the ground survey approach (DGPS) and the result shows that about 99% of the automatically extracted spatial information of the properties fall within the range of acceptable accuracy. The obtained results proved that the integration of UAVphotogrammetry and automatic feature extraction is applicable in cadastral mapping and that it offers significant advantages in terms of project time and cost.