Volume 19, Issue 2

Processing measurement data is an essential part of surveying engineering. One can list several methods in such a context: least squares estimation, M-estimation, R-estimation, etc. Some methods were developed by surveyors, e.g., the Danish method, IGG scheme, or M split estimation. The last method is, in fact, a class of estimation procedures dedicated to different problems. As a new approach to processing data, M split estimation is still being developed and improved. That paper concerns the local robustness of M split estimation and introduces a new M split estimation variant that is less sensitive to local outliers. Such a property seems important, especially in big data processing, such as observations from Light Detection and Ranging systems. The new variant modifies the squared M split estimation (SMS estimation) by implementing the adapted Tukey weight function, hence its acronym SMSTL estimation. The basic theoretical and empirical analyses, which were performed for the univariate model using, among others, the appropriate measures of robustness, confirmed the expected property of the method. The further tests, based on simulated as well as real data, show that the new method might overperform other M split estimation variants and classical methods for the chosen types of observation sets.

In this paper we propose a monitoring method that allows the inclusion of point clouds into a geodetic monitoring network. Consequently, network adjustment and a rigorous deformation analysis can be performed allowing consistent error propagation and trustful significance calculation. We introduce a supervised pipeline based on ICP-matching of small-scale laser scan patches. It is specially designed for geo-monitoring applications and allows to improve the spatial resolution as well as the network geometry of monitoring networks in inaccessible hazardous areas in the mountains, where the installation of a sufficient number of targets is difficult. We apply our method to two datasets. The first is a monitoring setup in the laboratory, where we establish the parameters for the supervised patch selection and demonstrate how the network geometry is improved. Second is the real case study of Mt. Hochvogel, where the proposed method helps to clearly improve the spatial resolution of deformation vectors.

Accurate geoid modelling in marine areas requires the integration of gravity data from multiple sources including shipborne gravity measurements, global geopotential models, and satellite altimetry-derived gravity data. This study aims to develop homogenized gravity data for the coastal region of Nigeria to improve geoid modelling accuracy. Residual linear drifts in the shipborne gravity dataset from the Bureau Gravimétrique International (BGI) were corrected using crossover adjustments for each survey leg. We eliminated gross errors for each survey leg by using the 2-sigma method. Outliers in the historical shipborne gravity data were identified and removed using the leave-one-out cross-validation technique, resulting in a refined shipborne gravity dataset. The refined shipborne data were compared with the gravity data predicted by DTU21GRA, SSv29.1, SGG-UGM-2, XGM2019e_2159, GECO, EIGEN-6C4, and EGM2008. Our findings show that DTU21GRA outperformed the other models in the same region when compared with shipborne gravity data. The refined shipborne gravity data were merged with the DTU21GRA data using Least-Squares Collocation (LSC) to create a combined gravity dataset. The results of comparison between the complete refined shipborne gravity data and DTU21GRA before and after the integration process, shows that both the mean offset and the SD values decreased from 0.43 to −0.02 mGal and 3.14 to 2.69 mGal, respectively, which reveal an improvement in the final combined data. The geoid model constructed using the combined gravity data before and after the integration process showed an improvement in the SD values, decreasing from 0.023 m to 0.016 m when evaluated against the CNES-CLS22 MDT.

The development of global geoid models became feasible following the launch of specialised satellite missions. Today, the root mean square deviation of the heights in global models of high degree & order varies from centimetres to decimetres across different countries. In countries where the accuracy of such models is lower, there is potential to enhance their precision by applying specific corrections. This study presents a novel methodology for locally modelling the height errors of high degree & order global geoid models using levelling sub-benchmarks for GNSS stations. The methodology is based on a combination of optimal interpolation methods, filtering, and the concept of data weighting by gravity anomaly differences. The methodology is aimed at creating a hybrid model that aligns with the local characteristics of the geoid (or quasi-geoid) derived from the traditional levelling network. The advantage of this methodology lies in its ability to reduce the residual height errors of the EGM2008 and EIGEN6C4 models to less than 1 cm when using only four control points. Such results exceed the initial values of the systematic height errors of these models by 90–96 %. For the GECO model, the residual errors are around 2 cm, while for the XGM2019e_2159 model, they reach 3 cm. These results indicate that this methodology can be applied to all global models of high degree & order, although its effectiveness may vary depending on the specifics of a particular model.

Accurately monitoring the change of mine area in the mining process is beneficial to mine safety management. This paper briefly introduces the collection of remote sensing images by unmanned aerial vehicles (UAVs) and its application in measuring surface mining subsidence and surrounding vegetation in the mining area. A case study was carried out in some mining areas of Nanshan Mountain, Yuncheng City, Shanxi Province. The surface mining subsidence value and vegetation-related parameters were measured by comparing the digital elevation model and multi-spectral images collected on May 12 and June 12, 2023. The validity experiment verified that the UAV image data could be used to measure the mining subsidence and vegetation parameters. Moreover, it was found that mining underground coal could lead to significant ground subsidence and pollute the surrounding environment, reducing vegetation. The innovation of this article lies in using UAV-collected remote sensing images instead of manually collecting ground elevation data and vegetation distribution data, providing effective references for safe mining in mining areas.

This study delves into ionospheric characteristics during solar cycle 24 using data from the Global Positioning System (GPS) and Low Earth Orbit (LEO) satellites, GOCE. The present study fills the gap of not assessing and studying GOCE satellite data before in Egypt. Focusing on spatial and temporal variations of ionospheric Total Electron Content (TEC) over Egypt and the Middle East across a 4-year dataset, monthly average Vertical Total Electron Content (VTEC) variations are scrutinized, emphasizing extremes during heightened and reduced solar and geomagnetic activities. Results TEC typically decreases with latitude’s increase, with peak ionization during equinoxes and troughs during solstices. Notably, VTEC values consistently reach maximum values on days of heightened solar and geomagnetic activities. GOCE data is evaluated against International Reference Ionosphere (IRI) model and NeQuick2 model by selecting 10 days from all data by using a statistical comparison via t -tests. There is not significant difference between them except for two days between GOCE-IRI. The values of Root Mean Square Error (RMSE) are 3.7403 and 4.4655 for GOCE – NeQuick2 model and GOCE – IRI model, respectively. Ionospheric scintillation, signifying rapid electron density fluctuations, is assessed through amplitude scintillation index (S4), S4 proxy, and Rate Of TEC Index (ROTI). A robust correlation between S4 and S4 proxy is noted, thus scintillation can be studied by using S4 proxy instead of S4. Temporal variations indicate heightened scintillation during geomagnetic storms and peak solar activity, contrasting with reduced activity during solar minimum. Throughout the study period the maximum scintillation index values for ROTI, S4, and S4 proxy are 0.3, 0.15, and 0.05, indicating minimal scintillation. This comprehensive analysis, rooted in GOCE data, illuminates spatial and temporal dynamics of ionospheric TEC and elucidates ionospheric scintillation characteristics in the Egypt region. These findings are crucial for refining ionospheric models, improving scintillation prediction, and enhancing satellite communication and navigation systems, especially in the study region.

In recent weeks, there have been reports of gas emanations from the crater of the dormant Taftan volcano in Iran. In this study, due to the limitations of ground stations and the advantages of satellite remote sensing, it has been tried to detect possible anomalies using the plasma data measured by Swarm (A, B and C) and GPS (Global Positioning System) satellites around the location of the mentioned volcano. Also, lithospheric and atmospheric data including OLR (Outgoing Longwave Radiation), water vapor, ozone, relative humidity, surface and air temperature, AOD (Aerosol Optical Depth), sulfur dioxide (SO 2 ) and nitrogen dioxide (NO 2 ) using the Giovanni website in a period of about 5 months, were downloaded and analyzed. Using the median and interquartile method, possible anomalies were detected in the pre-processed time series of the desired parameters. To justify some of the non-volcanic anomalies, synoptic data including precipitation and temperature were prepared from the nearest ground station. By rejecting the possibility that some detected anomalies are related to volcanic activities, hypotheses were presented for other proposed anomalies. As a result of this research, the capabilities of Swarm satellites and GPS-TEC (Total Electron Content) are emphasized in studies related to the prediction, detection and tracking of volcanic activities and it is shown that by comparative comparison with other lithospheric and atmospheric precursors, uncertainty in eruption prediction can be reduced.

The extended operation of Ukrainian hydroelectric power plants has caused spatial deformations and aging of hydrostructures. This can lead to man-made disasters, especially after explosions resulting from missile attacks. As a result, various defects can appear in the concrete structures of the dam. Continuous structural monitoring of hydropower plants is essential to prevent man-made accidents. The research paper also demonstrates that changes in water temperature can affect the dam’s vertical and horizontal displacements. A model was developed and analysed to determine the spatial deformations of the Dnister HPP based on water temperature and distance from the dam’s edge. It was determined that horizontal displacement rates range from −2.2 to 2.7 mm/month, and vertical displacement rates range from −2 to 1.3 mm/month. They are also seasonal in nature. The studies conducted enable the prediction and identification of seasonal spatial deformations of the Dnister HPP dam. The research also helps to find their variations due to water temperature at the definite depth. If the temperature deformation model deviates from the measurement results, the structure in those areas should be more thoroughly inspected and analysed. This may indicate the structure’s weakening due to natural aging processes or construction-related deficiencies. Deformations in the dam’s structure can lead to cracks, compromising its stability and watertightness. Dams can vary in shape, design features, depth, volume, and water temperature. So, it is important to customize the displacement model for each dam. Any deviation from the specified model may suggest defects due to abnormal temperature distribution and spatial displacements.

The ionosphere, partially ionized by solar radiation, is rich in free electrons and ions, affecting satellite navigation signals by altering their speed and path. This interaction often leads to signal delays of 5–10 m, complicating accurate positioning in satellite-based systems. This paper investigates the influence of global ionospheric models (GIMs) with varying Temporal Resolutions (TR) on satellite positioning accuracy and convergence time under different solar activities, represented by the years 2009 (low solar activity) and 2014 (high solar activity). The study utilizes Global Positioning System (GPS) data from three GIMs: CODG, representing the Center for Orbit Determination in Europe (CODE) GNSS model with a 2-h TR; bcom, with a 1-h TR; and b5mg, with a 5-min TR. Analysis was conducted using the GNSS Analysis Software for Multi-constellation and Multi-frequency Precise Positioning across 46 international GNSS service stations under single and dual-frequency strategies. The results indicate that precise point positioning convergence time improved by approximately 18 % and 78 % using single and dual frequencies, depending on the GIM applied. Consequently, positioning accuracy after convergence improved by about 16 % and 27 % in the horizontal and up components for ionospheric-constrained single-frequency PPP models and by 68 % and 79 % in the horizontal and up components for dual-frequency PPP models. Furthermore, vertical total electron content analysis at the MARS station revealed significant variations correlating with solar activity, underscoring the importance of selecting appropriate GIMs for accurate GNSS positioning. Future studies, including multi-solar events, are recommended for comprehensive analysis.

This study utilizes Precise Point Positioning (PPP) for accurate GNSS-based positioning with a single receiver. Seven PPP techniques (GAPS, APPS, CSRS, Magic-GNSS, gLAB, Pride, GAMP) are evaluated for zenith tropospheric delay (ZTD) estimates, comparing them with Radiosonde (RS) and Radio Occultation (RO) data from the same day (36th in 2014). RO data is categorized based on RO Events (ROE) – GNSS observation distances (10 km, 50 km, 50:100 km), while RS data is limited to three stations (ASWN, FARF, PHLW). Generally, the differences among PPP techniques are within 5 cm, except for PRIDE-PPPAR, which exhibits semi-constant zenith wet delay (ZWD) values. Root Mean Square (RMS) and t -test comparisons with RO data reveal that APPS has the lowest RMS values for ZWD at 10 km, while CSRS-PPP performs well with increasing distance. Magic-GNSS demonstrates the highest RMS values at 10: 50 km, while APPS at 50:100 km. RMS values typically increase with greater ROE-GNSS distances, except for Magic-GNSS, which decreases. t -tests indicate statistically insignificant differences across PPP techniques, except for APPS and gLAB in the 50:100 km case. Comparisons with RS data indicate that CSRS-PPP achieves the lowest RMS values for ZWD at ASWN and PHLW, while Magic-GNSS and CSRS-PPP excel at FARF. However, Magic-GNSS, GAMP, GAPS, and Pride yield the highest RMS values at ASWN (00:00), (12:00), FARF, and PHLW, respectively. t -tests show statistically insignificant differences across PPP techniques for the three stations, except for APPS and Pride at ASWN and gLAB at PHLW. These findings demonstrate that CSRS-PPP consistently provides reliable ZWD assessments across various conditions, contributing to enhanced accuracy in GNSS-based atmospheric studies. The comparison of PPP techniques offers valuable insights into the strengths and limitations of each method, with implications for improving atmospheric modeling, positioning applications, and broader GNSS-based research in weather forecasting and climate monitoring.

This study conducts an evaluation of the performance of seven ultra-high-degree Global Geopotential Models (GGMs) across Egypt, utilizing GNSS/leveling data as a basis for assessment. The models under investigation include SGG-UGM-2, XGM2019e_2159, SGG-UGM-1, GECO, EIGEN-6C4, EGM2008, and GGMplus. The evaluation procedure comprises three principal steps: an absolute assessment, the implementation of Residual Terrain Modelling (RTM), and the fitting of GGMs to GNSS/leveling data. Among the models assessed, GECO exhibited the highest performance in the absolute assessment, achieving a standard deviation (STD) of 0.310 m, while SGG-UGM-1 recorded the largest STD at 0.353 m. Given Egypt’s predominantly flat topography, the application of RTM yielded only modest benefits. Nonetheless, all models demonstrated significant enhancements in accuracy through the fitting process, with EIGEN-6C4 emerging as the most successful model, attaining an STD of 0.116 m in external assessment. The accuracy improvements following the fitting procedure ranged from 49 % to 63 % across all models assessed.

In this contribution we consider mixed-integer least-squares problems, where the integer ambiguities a ∈ Z n $a\in {\mathbb{Z}}^{n}$ and real-valued parameters b ∈ R p $b\in {\mathbb{R}}^{p}$ are estimated. Both a primal and a dual formulation can be considered, with the latter concerning the ambiguity resolution process taking place into the parameters’ domain. We study the p = 1 case, where an ad hoc ‘P1’ algorithm is introduced, and some geometrical insights are provided. It is demonstrated how the algorithm’s complexity (i.e. number of candidate integer solutions to be evaluated) grows linearly with the ambiguity dimensionality n , differently from the primal formulation where an exponential growth is observed. By means of numerical simulations, here based on Global Navigation Satellite System (GNSS) models, we show the efficiency of this proposed ‘P1’ algorithm, meanwhile also demonstrating its quasi-optimal statistical performance.

Assessing the quality of a trajectory is a prerequisite for correctly interpreting and using the trajectory in applications such as kinematic laser scanning. Evaluation is for example done empirically by comparison with a ground-truth trajectory recorded simultaneously. Depending on the measurement and sensor configuration, both trajectories have to be aligned before comparison. Usually, either a similarity transformation or a rigid-body transformation is used for this purpose. We propose an extended spatio-temporal alignment, which additionally supports the estimation of a lever arm and a time offset between both trajectories. Our method can be used to align two trajectories of the same vehicle captured simultaneously by different sensors. We apply the approach on several recorded data sets and evaluate it empirically. We show that although real-world data sets can lead to high correlations between parameters, they can still be successfully aligned and evaluated using the methodology. To enable replication of our research, we publish the code which is available here: https://github.com/gereon-t/trajectopy.

Networked Real-Time Kinematic (NRTK) is the most widely used GNSS (Global Navigation Satellite Systems) positioning technique in surveying practice due to its speed, operability and sufficient accuracy. Positioning using NRTK methods in the European Terrestrial Reference System ETRS89 obligatory coordinate system is tied to the positioning of reference stations of the RTK network. Monitoring of GNSS reference stations provides both the determination of the position of individual stations in the obligatory coordinate system and the monitoring of daily position deviations of individual stations. The application to four networks of GNSS reference stations in the Czech Republic has demonstrated the accuracy of the positioning of stations from the daily solution at the level of 1.2 mm in the horizontal components and 3.8 mm in the vertical component. This accuracy is quite suitable for NRTK methods that determine position with centimetre accuracy. At the same time, it allows to detect the behaviour of time series of coordinates of individual stations – sudden jumps, linear and periodic trends. The accuracy achieved also allows tracking geokinematic movements.

The area located East to Cairo, the Capital of Egypt, represents an obvious example for the rapid urban expansion, as it contains many new housing cities. Beside its socio-economic importance, it’s located in the Cairo-Suez seismic zone. We utilized Persistent Scatterer Interferometry (PSI) of 2015–2021 Sentinel-1 SAR scenes along with two GNSS stations (KATA and PHLW) to assess the distribution and rates of crustal deformation of this region. The PSI analysis is applied to 140 Sentinel-1 SAR images collected from the ascending track number (58) and the descending track number (167). The Bernese software V. 5.0 is used for the processing of the GNSS data. A good agreement between the rates estimated from the PSI analysis and GNSS data is observed. Based on results, most of the new cities showing land subsidence with variable rates. The rates at Obour, New Cairo, Shorouk, Madinty, and Capital Gardens are 0.54 ± 0.30 mm/year, 0.58 ± 0.30 mm/year, 1.01 ± 0.30 mm/year, 0.58 ± 0.30 mm/year, and 0.99 ± 0.30 mm/year, respectively. The highest recorded subsidence rates are at Asher, Administrative Capital, and Badr with 2.18 ± 0.30 mm/year, 1.89 ± 0.30 mm/year, and 1.69 ± 0.30 mm/year, respectively. Nasr city is the only city with an uplift of 0.82 ± 0.30 mm/year. Our new findings introduce the probable use of integrated techniques such as GNSS and InSAR to evaluate the extent of crustal deformation connected to rapid urbanization in arid areas. Beside tectonic setting, it should be considered while executing mega-projects for sustainable development especially within Egypt’s Vision 2030.