Abstract Multipath is a significant cause of inaccuracy in Global Navigation Satellite System (GNSS) signal processing, reducing the accuracy and dependability of navigation solutions. This paper provides a novel framework for multipath mitigation in GNSS signals that combines Successive Variational Mode Decomposition (SVMD) with feature-based mode selection, utilising the Power Spectral Density (PSD)-Entropy Approach. The GNSS Multipath Analysis Software tool determines the multipath errors on the GPS constellation on L1 and L2 frequencies. The GNSS receiver data for this analysis were collected on November 10, 2024, from the IISC Bangalore GNSS station, India, with a latitude of 13.0212 and a longitude of 77.570. The multipath parameters, MP1 and MP2, were computed using RINEX version 2 observation and navigation data files for the GPS constellation. SVMD decomposes these multipath signals into modes, and the power spectral density (PSD) with Shannon entropy is utilised to identify multipath-affected modes. By eliminating the multipath-affected modes, the signal is reconstructed using the remaining modes, and the approaches’ performance was measured using standard deviation (STD), variance, and RMS value as metrics. The PSD-Entropy technique generates a more minor STD than the Hilbert Transform, resulting in a more precise multipath effect reduction and outperforming traditional methods. The SVMD with the PSD-Entropy method is a data-driven approach that identifies multipath-dominant modes through an assessment of spectral information and entropy evaluation, providing an advantage over fixed-threshold methods in selecting multipath-affected modes. Advanced signal decomposition methods prove useful for GNSS multipath mitigation through this study while creating research foundations for multi-constellation analysis.
Abstract Ionospheric Total Electron Content (TEC) forecasting during geomagnetic storms is crucial for reliable Global Navigation Satellite System (GNSS) operations. Traditional single-frequency ionospheric broadcast correction models (Klobuchar and NeQuick-G models) are likely to have large ionospheric prediction errors under disturbed conditions, particularly at various latitudinal regions. In this study, a two-stage machine learning framework that integrates Light Gradient Boosting Machine (LightGBM) and an ensemble regression approach to improve storm-time TEC prediction. First stage, LightGBM is trained on the GNSS TEC data using the geomagnetic, solar, and temporal indices as inputs. In the second stage, the predictions from Klobuchar and NeQuick-G ionospheric model are integrated using traditional, optimized, and Regression based ensemble techniques. The Model performance was tested during the geomagnetic storm of October 2024 (DOY 283–287) at seven IGS stations spanning high, mid, and low-latitude regions. Results show that the ionospheric broadcast models, NeQuick-G and Klobuchar both either overestimated or underestimated storm-time TEC, while the proposed Regression-based ensemble consistently achieved better accuracy, with RMSE values reduced by more than 50 % compared to standalone ionospheric prediction TEC models. These findings demonstrate that combination of data-driven methods with physics-based models as a powerful and scalable method for real-time ionospheric modelling and GNSS position error mitigation during quiet and disturbed space weather conditions.
Abstract This study compares four online GNSS processing services AUSPOS, TrimbleRTX, OPUS, and CSRS-PPP using 72-h static GNSS data from 12 geodetic control stations in Ethiopia. Observations collected with a Leica GS10 receiver were processed by each service and evaluated against a high-precision BERNESE reference solution. One-way ANOVA showed no statistically significant differences in mean coordinates at the 95 % confidence level ( p > 0.05). However, practical precision varied notably among services, with coordinate discrepancies ranging from millimeter-level agreement to maximum differences of 44 mm (X), 30 mm (Y), and 20 mm (Z) between service pairs. CSRS-PPP and AUSPOS showed the closest agreement with the reference (mean 3D differences of 1.0 cm and 2.1 cm, respectively), while TrimbleRTX exhibited consistent systematic biases requiring datum transformation. Although statistically comparable, CSRS-PPP and AUSPOS are recommended for high-accuracy geodetic applications due to their superior consistency.
Abstract This study evaluates the spatial and temporal performance of static multi-GNSS Precise Point Positioning (PPP) solutions across twelve selected African International GNSS Service (IGS) stations representing diverse geographic and ionospheric environments. Using observations from the years 2013, 2018, and 2023, data were processed via the PPP-A software package (v2024.1) using dual-frequency ionosphere-free linear combinations. Coordinate differences were transformed into a local topocentric East, North, and Up (ENU) frame to accurately assess the impact of regional atmospheric delay and reference frame consistency on positioning precision. The empirical results reveal that the apparent coordinate residuals are heavily contaminated by long-term tectonic displacements of the Nubian and Somalian plates – accumulating up to several decimeters over the ten-year baseline – rather than reflecting pure PPP algorithm stochastic errors. True static PPP residuals maintained sub-decimeter geodetic precision once geophysical plate motion and terrestrial reference frame evolutions (IGS14/IGS20) were properly aligned. Statistical assessments using non-parametric Friedman tests and linear mixed-effects models confirm that spatial environmental variations and station-specific atmospheric tracking conditions significantly override temporal drift across the evaluated epochs. While multi-constellation PPP remains a highly reliable tool for geodetic infrastructure in sparse networks, this study highlights that isolating geophysical signals from operational processing artifacts is essential for meaningful accuracy assessments in the African continent.
Abstract Based on a study of the behavior of several permanently operated stations of the IGS network, the impact of ambient temperature on the heights of these stations is tested and assessed. The studies used relative GNSS determinations of very short baselines, which have very high sensitivity and are also insensitive to the influence of almost all known sources of seasonal variations in the position of stations. The following tasks were solved in this work: it was shown that the observed seasonal variations in the heights of stations possess properties characteristic of thermal deformations of antenna monuments, which testifies in favor of the effects of their thermal compression and expansion; the performed assessment of the actual values of seasonal deformations of several monuments of different types and sizes provides an idea of the typical level of values of these deformations; several methods for rigorous assessment and elimination of the influence of deformations of this type are proposed, the principle of their operation is considered and the performance of these methods is demonstrated using real examples.
Abstract The potential environmental, economic, and social repercussions of land subsidence in the Egyptian Nile Delta make it a critical geodynamic concern. As one of the oldest deltaic systems in the eastern Mediterranean Basin, the Nile Delta is particularly susceptible to ongoing tectonic processes. Factors such as relative sea-level rise, reduced sediment supply and prolonged hydrocarbon extraction contribute to progressive surface deformation, further increasing its vulnerability. This study investigates present-day crustal kinematics and short-term deformation across the Nile Delta using Global Navigation Satellite System (GNSS) measurements collected from 2013 to 2023. Time-series data from ten permanent GNSS sites were processed to estimate both regional and local velocity fields, providing a detailed assessment of the delta’s crustal motion. High-precision geodetic analysis was applied to quantify deformation parameters, including horizontal and vertical motions, principal strain components, dilatation, and maximum shear strain. The results indicate spatially variable crustal behavior across the delta, largely governed by its structural configuration. The northeastern sector exhibits relatively higher subsidence compared to the northwestern part, suggesting enhanced exposure to relative sea-level rise. Absolute velocities range from 17 to 23.8 mm/year. Horizontal motions vary between −0.76 and 2.25 mm/year in the northing direction and between −1.25 and −0.89 mm/year in the easting direction, while mean vertical displacement reaches approximately −8.25 mm/year. The derived strain field reflects moderate shear deformation, implying a low overall seismic hazard within the study area.
Abstract Precise GPS orbit and clock products released by the International GNSS Service (IGS) are referenced to the L1/L2 ionosphere-free combination, whereas using L5 observations in triple-frequency precise point positioning (PPP) introduces inter-frequency clock bias (IFCB). In this study, GPS L5 phase-specific IFCB values are estimated using observations from 110 globally distributed IGS stations during DOY 001–067, 2023, and their temporal characteristics, predictability, and impact on real-time PPP (RT-PPP) are investigated. The results show that GPS Block IIF satellites exhibit stronger IFCB variations and more evident periodic components than Block III satellites, indicating a greater need for IFCB correction. Four models, namely the harmonic function (HF), random forest (RF), support vector machine (SVM), and long short-term memory (LSTM) models, are developed for IFCB modeling and prediction. The three machine learning models outperform the HF model, with the RF model achieving the best prediction performance, yielding test coefficient of determination ( R 2 ), root mean square error (RMSE), and mean absolute error (MAE) values of 0.817, 2.642 mm, and 2.113 mm, respectively. Furthermore, the RT-PPP experiments show that IFCB correction mainly benefits the convergence stage, while its effect on final positioning accuracy is relatively limited. Moreover, RT-PPP using RF-predicted IFCB products achieves positioning accuracy and convergence performance comparable to those obtained with estimated IFCB products, demonstrating the suitability of the predicted products as external corrections for triple-frequency RT-PPP.
For many situations in geodesy and allied disciplines, data are collected that not only enter the usual observation vector y , but also the coefficient matrix A after linearization. Such models fall into the category of errors-in-variables (EIV) models and may be treated by total least-squares (TLS) adjustment. However, if stochastic prior information is available for the unknown parameters of the model that follows certain quantifiable "expectations," these normally non-random parameters will turn into "random effects," in which case the standard estimation procedure needs to be replaced by one that resembles collocation, but is here obviously based on the TLS principle. While early work by Schaffrin on this topic admitted only iid (independent and identically distributed) data from the side of the EIV Model, eventually the authors presented models for TLS collocation with a more arbitrary cofactor matrix Q 1 of full rank, which will be extended herein to admit an even larger class of singular covariance matrices. Use of the developed formulas will be demonstrated by a 3D similarity transformation in the context of a geodetic network.
The Dnister Pumped Storage Power Plant (PSPP) is subject to significant natural and anthropogenic loads, requiring millimeter-level precision in determining vertical displacements. The purpose of this study is to develop a local geometric geoid model to establish a high-precision verti-cal datum for satellite geodetic monitoring. The input data were derived from high-precision geometric leveling and Global Navigation Satellite System (GNSS) measurements conducted in 2022. Modeling was performed using the least-squares collocation method within the Remove-Compute-Restore Procedure, using the EGM2008 global geopotential model and Legendre functions of non-integer degree. The model was computed on a regular 8 ''& times;8 '' grid. The result-ing local geoid model has a standard deviation of 3.4 mm relative to the GNSS leveling data. Spatially, a 60-80 mm increase in geoid height from east to west is observed, with a sharp gradient in the Dnister River right-bank zone, consis-tent with the terrain morphology. No systematic trends were detected in the residuals. The developed model enables conversion of ellipsoidal heights to normal heights with millimeter-level accuracy over an area of approximately 10 km & sup2;, providing a reliable basis for real-time GNSS mon-itoring of vertical deformations of hydraulic structures in both static and kinematic modes.
This paper estimates the zero-level geopotential of South Africa's Land Levelling Datum (LLD) and its offset to the International Height Reference System (IHRS) using a height-geopotential combination tailored to the country's spheroidal-orthometric height practice. Geopotential at GNSS/levelling benchmarks is synthesized directly from satellite-only Global Geopotential Models (GGMs), GOSG02S, WHU-SWPU-GOGR2022S, and Tongji-GMMG2021S, by summing gravitational and centrifugal potentials at each GPS/levelling station's geocentric position. The estimator forms pointwise values of W-0(LVD), with (gamma) over bar* the Vignal mean-normal gravity consistent with South African height datum, and averages these over a quality-controlled national network (138 stations) under harmonized frame, tide system, and epoch. The three GGMs yield tightly clustered W-0(LVD) estimates: 62,636,857.5890, 62,636,857.6179, 62,636,857.6551 m(2) s(-2), implying a consistent potential offset delta W approximate to 4.221 m(2) s(-2) relative to the IHRS conventional value. Converted using (gamma) over bar*, this corresponds to a national height shift of delta h approximate to 0.431 m. Diagnostic checks show near-unity normalization of synthesized potentials and negligible spatial variability in the height conversion (sitewise SD similar to 0.1 mm; weak latitude trend). The inter-model spread in delta W similar to 0.07 m(2) s(-2) (<1 cm in height), indicating robust, model-insensitive results at sub-decimetre level. Main residual uncertainties stem from short-wavelength omission in satellite-only GGMs, legacy levelling distortions, spheroidal-orthometric approximations, and remaining tide/epoch nuances. A single national conversion (delta h(LLD)(S) approximate to 0.431 m) is therefore recommended for transforming LLD heights to IHRS-compatible vertical coordinates, with optional millimetric sitewise refinements.
Low-cost GNSS antennas have enabled a wide range of new applications where traditional GNSS equipment is associated with substantial financial cost. However, low-cost equipment also has a serious drawback: low-cost GNSS antennas are typically characterized by high susceptibility to multipath, poorly known or unavailable PCO/PCV calibrations, and large inter-antenna PCV variability even among antennas of the same model, which significantly limits their performance in high-precision applications. The goal of this study is to verify whether, with the low-cost GNSS antennas, it is feasible to provide precise ellipsoidal heights, that is, an intermediate step in GNSS geodetic levelling. In this way, we address a scientific question on the potential usability of low-cost antennas for precise normal height determination in geodetic and surveying applications. We pay particular attention to the impact of antenna phase center characteristics on height determination with GNSS. In this regard, we apply, for the first time, a web service-derived PCC to obtain more accurate antenna phase patterns of low-cost antennas. The usability of these patterns is examined, and the results are validated against those obtained with high-grade GNSS antennas. We demonstrated that low-cost antennas can achieve ellipsoidal heights with accuracy comparable to that of high-grade antennas. Finally, we show that applying web-based calibrations may enhance the accuracy of the GNSS height determinations using mass-market GNSS antennas.
Global Navigation Satellite Systems (GNSS) provide accurate and reliable positioning and timing information to the users. However, GNSS signals are inherently weak due to their low transmission power, making them vulnerable to interference and intentional disruptions. Radio frequency interference (RFI) from man-made sources, such as intentional jamming and spoofing, as well as unintentional signal disruptions, can severely compromise the accuracy, availability, and integrity of GNSS services. Both threats highlight the vulnerability of GNSS-dependent systems and emphasize the importance of resilient receiver designs, monitoring, and countermeasures. In this paper, RFI detection and its effects on GNSS signal quality and positioning performance are investigated. To detect variations in the signal due to RFI, a cubic spline fitting method is employed to approximate the expected signal's behavior. A total of 67 RFI events were identified from seven IGS GNSS stations, with a notable increase from 21 events in 2023 to 46 events in 2024 for SNR deviation and Precise Point Positioning (PPP) positioning error analysis. It is observed that the RFI due to positioning errors exceeds +/- 15-20 m during interference periods, with pronounced fluctuations in the afternoon hours. The analysis can be used to get a better idea of the effects of RFI and to continue developing better methods of monitoring GNSS and reducing its impact.
Rapid and reliable earthquake source characterization is essential for seismic hazard mitigation in subduction environments. This study integrates high-rate (1 Hz) and daily GNSS observations to analyze the 24 April 2023 M w 7.1 Mentawai earthquake, Indonesia. High-rate GNSS data from stations operated by the Geospatial Information Agency of Indonesia (BIG) were processed using Precise Point Positioning with Ambiguity Resolution (PPP-AR) to obtain three-component displacement time series. Peak ground displacement (PGD) values were calculated and converted to moment magnitude using empirical scaling relations proposed by Melgar et al. (Earthquake magnitude calculation without saturation from the scaling of peak ground displacement. Geophys Res Lett 2015;42:5197-205), Ruhl et al. (A global database of strong-motion displacement GNSS recordings and an example application to PGD scaling. Seismol Res Lett 2019;90:271-9), and Crowell et al. (Demonstration of the Cascadia G-FAST geodetic earthquake early warning system for the Nisqually, Washington, earthquake. Seismological Research Letters 2016;87:930-43). Static GNSS solutions were used to derive coseismic offsets, which were subsequently inverted using an elastic half-space model to estimate the slip distribution. All empirical approaches detected rapid magnitude growth within seconds, significantly earlier than institutional releases. The Crowell formulation provides the best agreement with the official magnitude evolution. The static inversion reproduces observed displacements with a mean absolute error of 0.530 mm and yields a seismic moment of 6.1 & times; 1019 N m (M w similar to 7.12), consistent with the reference magnitude. These results highlight the effectiveness of integrated GNSS analysis for rapid and robust earthquake source characterization in Indonesian subduction zones.
Accurate acquisition of meteorological parameters is fundamental for improving the performance of Global Navigation Satellite System (GNSS) applications, especially in water vapor retrieval and precise point positioning. As an effective and reliable method, parametric modeling supports robust global-scale estimation of essential variables, including surface temperature (Ts), weighted mean temperature (Tm), and surface pressure (P). Among existing models, the second-generation Hourly Global Pressure and Temperature (HGPT2) model has attracted considerable attention due to its capability to provide meteorological parameters with high spatiotemporal resolution. However, a systematic assessment of its accuracy and applicability across the European region has been lacking. To address this gap, this study presents the first comprehensive evaluation of HGPT2 in Europe, utilizing quality-controlled data from 61 radiosonde stations spanning 2019 to 2021, with outlier removal performed using the Interquartile Range (IQR) method. Results show that for Ts, the bias, root mean square error (RMSE), and mean absolute percentage error (MAPE) are 0.03 K, 4.00 K, and 1.13 %, respectively; for Tm, the corresponding values are -0.09 K, 4.56 K, and 1.34 %; and for P, they are 0.22 hPa, 8.43 hPa, and 0.68 %. Further analysis indicates clear geographic heterogeneity in model accuracy, as well as periodic variations across interannual and seasonal scales. Overall, the HGPT2 model demonstrates favorable accuracy and stability in the European region, establishing it as a reliable reference for practical applications; however, given the spatiotemporal distribution characteristics of its accuracy, there remains considerable potential for further optimization of the model in future studies.
To obtain the vertical component of crustal tectonic movement in the Sichuan-Yunnan region, non-tectonic deformations induced by environmental loading and common mode errors must be removed from GNSS vertical displacements. Based on GNSS data and corresponding Hydrological Loading (HYDL) deformation data from 48 continuous stations in the Sichuan-Yunnan region from January 2012 to June 2023, this study systematically analyzes the quantitative relationship and temporal variation characteristics between GNSS vertical displacements and HYDL deformation. Additionally, wavelet analysis is employed to investigate the time-frequency periodic characteristics of both time series. The results indicate that the average correlation coefficient between GNSS vertical displacements and HYDL deformation is 0.62. After removing the HYDL deformation from the GNSS vertical displacements, the root mean square (RMS) decreases by an average of 33.98 %. Wavelet analysis further reveals that most stations exhibit consistent variations at the annual cycle scale, demonstrating that HYDL deformation is a crucial controlling factor for the annual variations in GNSS. The vertical velocity field obtained after correcting for both hydrological loading and common mode errors indicates that the entire Sichuan-Yunnan region is generally uplifting at a rate of 0.16-2.41 mm/a. These findings demonstrate that environmental loading correction is of significant importance for recovering the true vertical tectonic deformation in the Sichuan-Yunnan region, providing a reliable basis for high-precision monitoring of regional vertical crustal movements.
In urban environments, global navigation satellite system (GNSS) signals are prone to obstruction and reflection caused by surrounding structures, leading to the reception of non-line-of-sight (NLOS) signals. This effect significantly impairs the accuracy and reliability of satellite-based positioning. This paper proposes an NLOS signal identification method based on a hybrid model that integrates long short-term memory (LSTM) networks with light gradient boosting machine (LightGBM). Firstly, the relationships between signal types and seven key features - including pseudorange standard deviation, carrier phase standard deviation, Doppler frequency standard deviation, carrier phase lock-time counter, and carrier-to-noise ratio - are systematically analysed. Then, the LSTM network is employed to extract deep temporal features from the GNSS signal sequences. These learned representations are subsequently fused with the original observation data to construct a comprehensive hybrid feature space. Finally, a LightGBM classifier is utilised to perform signal classification. Experimental results demonstrate that the proposed method achieves an accuracy of 95.03 % and an F1-score of 93.96 % on the test dataset, showing significant improvements over baseline models such as random forest, K-nearest neighbours, gradient boosted decision trees, standalone LSTM and stand-alone LightGBM. Notably, the model maintains an accuracy of 95.90 % even under class-imbalanced conditions, confirming its robustness and generalisation capability in complex urban canyon scenarios.
The high cost of geodetic-grade GNSS receivers limits the development of dense early warning systems for earthquakes. While high-rate GNSS observations enable direct displacement measurements without cumulative integration errors, the deployment of dense GNSS networks remains economically challenging and thus low-cost receivers have gained attention for such monitoring. In this study, we assess the performance of the low-cost Septentrio Mosaic-X5 GNSS module for dynamic displacement detection under a controlled field experiment. The results were compared with those obtained from a geodetic-grade Trimble Alloy receiver. Harmonic oscillations with frequencies ranging from 0.5 to 4 Hz and amplitudes from 20 to 2.5 mm were generated using a Quanser I-40 shake table. Both receivers were connected to a common antenna, and the recorded data were processed using the Variometric Approach for Displacements Analysis Stand-Alone Engine (VADASE) algorithm. While both devices reproduced sinusoidal motions and correctly identified frequencies, we observed a consistent amplitude overestimation. The highest deviation occurred at the 2 Hz frequency and 10 mm amplitude motion. In this scenario, the Trimble and Septentrio receivers output 17.0 mm and 11.6 mm amplitudes, respectively. Despite the amplitude offsets, the system reliably detected the minimum 2.5 mm excitation at 4 Hz, demonstrating its utility for precise monitoring. Moreover, the analysis showed that the low-cost sensor has a lower noise level in the high-frequency domain than the reference device. These findings indicate that low-cost GNSS receivers combined with the VADASE algorithm are sufficient for detecting microseismic events, enabling the mass deployment of low-cost monitoring networks.
Ionospheric irregularities affect the propagation of Global Navigation Satellite System (GNSS) signals, often leading to positioning errors, signal degradation, and occasional loss of lock. Although research-grade ionospheric monitoring stations provide highly accurate measurements, their cost and fixed infrastructure limit large-scale deployment and real-time accessibility. To address this gap, this paper presents the development and field validation of IonoAPI, a low-cost, Internet of Things (IoT)-enabled GNSS-based ionospheric monitoring platform designed for continuous and autonomous operation. The system integrates a dual-frequency u-blox ZED-F9P receiver with a Raspberry Pi-based processing unit. Raw GNSS observables recorded at 1 Hz are processed through a structured Python pipeline to estimate satellite geometry (elevation and azimuth), Dilution of Precision (DOP), total amplitude scintillation index (S 4) derived from C/N 0 measurements, and uncalibrated relative slant Total Electron Content (STEC) using dual-frequency pseudorange combinations. To enhance data reliability, post-processing includes missing-data filtering, a 15 degrees elevation mask, and statistical outlier detection prior to cloud transmission. Processed results are automatically uploaded to an Amazon Web Services Relational Database Service (AWS RDS) database via Node-RED and visualized through Grafana dashboards, while a Flask-based REST API enables structured programmatic access. The system operates in a near-real-time batch mode with an overall end-to-end latency of approximately 3-5 min. Validation was conducted through simultaneous observations with a co-located Septentrio PolaRx5 receiver. The platform was validated through simultaneous observations with a co-located Septentrio PolaRx5 receiver. Quantitative evaluation was performed using correlation coefficient (r), root mean square error (RMSE), mean absolute error (MAE), bias, normalized RMSE (NRMSE), and mean absolute percentage error (MAPE). Satellite geometry parameters showed near-unity correlation with minimal error, while the total S 4 values showed moderate agreement under the nominal daytime ionospheric conditions considered in this study. The uncalibrated relative STEC estimates followed the same temporal pattern, although a nearly constant offset was present due to the absence of Differential Code Bias (DCB) correction. After removal of the mean bias, differential STEC variations remained bounded without long-term drift, indicating reliable tracking of ionospheric variability. These results demonstrate that, although absolute calibration is not performed, the low-cost IonoAPI architecture reliably captures relative ionospheric dynamics and satellite geometry behavior. The integrated cloud-based framework supports scalable, distributed, and cost-effective ionospheric monitoring for research and space-weather applications.
Ecuador's Vertical Control Network has been established through gravimetric and spirit leveling surveys conducted by the Military Geographic Institute since the 1960s. Continuous maintenance and updates have ensured the network's consistency. Height determination in Ecuador is based on the propagation of elevation differences from the La Libertad tide gauge, which is currently regarded as the Local Vertical Datum, with plans to adopt a new datum linked to the International Height Reference Frame. Adjustments or compensations to network segments have been made based on leveled height differences and geopotential numbers; however, in all cases, they have not considered the entire leveling loops. This study outlines the procedure and results for compensating the Ecuadorian Vertical Control Network based on leveled height differences and geopotential numbers. The least-squares adjustment results yield adjusted leveled, orthometric, and normal heights with an average adjustment precision of about 4 cm, applicable to both the network adjustment and the internal or line adjustment.
The Real-Time Kinematic (RTK) method of Global Navigation Satellite Systems (GNSS) technology allows the position of points to be determined with centimeter accuracy. The vertical component of the position is determined less accurately than the horizontal component. Two cases were analyzed to ensure higher accuracy of the vertical component on a set of test measurements obtained using 11 GNSS receivers under different observation conditions, at different times of day, with different vector lengths, and different averaging lengths. In the first case, it was found that if the maximum elevation angle - the elevation angle of the satellite closest to the zenith - is greater than 70 degrees, better accuracy of the vertical component is achieved for most of the tested GNSS receivers. In the second case, it was found that averaging measurements at three specified times of day - 6 a.m., 3 p.m., and 9 p.m. - ensures greater accuracy of the vertical component, whose unit mean error is 21 % lower than the unit mean error of a single height measurement. The accuracy of the final average of three measurements is 54 % higher than the accuracy of a single measurement.
