Local Global Navigation Satellite Systems Research Articles

Design of Light, Small, and High-precision Digital Servo Clock for LEO Constellation

Modern low earth orbit (LEO) satellite systems have placed increasingly stringent requirements on spaceborne time-frequency systems in the fields of constellation autonomous management, distributed synthetic aperture radar (SAR) imaging, and navigation time service. Admittedly, the original high-stability constant-temperature crystal oscillator and high-stability temperature-compensated crystal oscillator can no longer comply with the indicator requirements of clock source frequency characteristics and clock synchronization accuracy. Likewise, traditional satellites use atomic clocks (rubidium atomic clocks and cesium atomic clocks). On account of their inherent characteristics, the ground receiving system needs to observe and count the clock parameter characteristics for a long time after the satellite enters orbit and frequently modify the future working state parameters. The features of being expensive and bulky increase the operation and maintenance costs of the ground system and the complexity of engineering implementation. In this paper, a kind of light and small high-precision digital servo clock based on the deep coupling of the global navigation satellite system (GNSS) is designed for the LEO satellite constellation. The tame clock is deeply coupled with the GNSS navigation receiver, and the high precision time-frequency difference between the local clock frequency source and GNSS is obtained by using the carrier and pseudo-range measurement information of visible satellite and carrier phase measurement information of the receiver. It not only utilizes the short-term high stability of OCXO but also employs the long-term time-frequency maintenance ability of GNSS so that the tamed OCXO is locked in GNSS for a long time, which can achieve frequency calibration of local clock sources and long-term output to various space-borne systems. The system is small in size and low in power consumption, with output frequency stability better than 3E-13 (10000 s), accuracy better than ±2E-13, and timing accuracy better than ±10 ns, which is comparable to the key technical indexes of spaceborne miniaturized rubidium clocks, in line with the current demand of miniaturization, low power consumption, and low cost of LEO constellations.

Stress transmission along mid-crustal faults highlighted by the 2021 Mw 6.5 San Juan (Argentina) earthquake

Understanding the mechanisms of crustal deformation along convergent margins is critical to identifying seismogenic structures and assessing earthquake hazards for nearby urban centers. In the southern central Andes (28–33^{circ }S), differences in the style of middle to upper-crustal deformation and associated seismicity are highlighted by the January 19th, 2021 (Mw 6.5) San Juan earthquake. We integrate waveforms recorded at regional and teleseismic distances with co-seismic displacements calculated from local Global Navigation Satellite System time series, to re-estimate the source parameters of the 2021 San Juan earthquake, confirming a mid-crustal nucleation depth (21 ± 2 km) and right-lateral transpressional mechanism. Considered alongside decades of seismic observations and geological data, this event provides evidence for retroarc deformation partitioning among inherited basement faults and upper-crustal structures in response to oblique convergence of the Nazca and South American plates. As they may transfer shortening to active upper-crustal faults associated with historically devastating shallower earthquakes, a better understanding of seismogenic basement faults such as the mid-crustal structure activated during the 2021 San Juan earthquake earthquake could help future re-assessment of the seismic risk in western Argentina.

Code phase tracking error based autonomous integrity monitoring for GNSS/INS ultra-tightly integrated system

The ultra-tight integration of GNSS (Global Navigation Satellite System) and INS (Inertial Navigation System) may suffer from faults in GNSS, INS and integration filter. Both the faults occurred at the current epoch and at previous epochs affect the position solution deviation of ultra-tight integration at the current epoch, and the effect is reflected in GNSS code phase tracking errors. In this paper, a new autonomous integrity monitoring algorithm is proposed for the federated GNSS/INS ultra-tight integrations in which the code phases of local GNSS signal replicas for GNSS signal tracking are completely derived from the integrated navigation solution. In the proposed algorithm, GNSS code phase tracking errors are employed to construct the test statistics for fault detection through a MHSS (Multiple Hypothesis Solution Separation) method improved from the classical MHSS used in ARAIM (Advanced Receiver Autonomous Integrity Monitoring). With the improved MHSS, the proposed algorithm can account for GNSS nominal biases, multiple GNSS faults and the faults in INS and integration filter. The protection levels under multiple hypothesis are also derived. A semi-physical simulation of the federated ultra-tight integration of GPS (Global Positioning System) and INS in airplane approaching case and a vehicle-based field test of the federated ultra-tight integration of GPS, Galileo and INS are conducted to validate the proposed algorithm. The experiments show that the designed fault detection can effectively detect the occurred faults and the derived protection levels can correctly bound the caused position solution error.

Assessing the Impact of Positioning Errors in Car-Borne Repeat-Pass SAR Interferometry With a Controlled Rail-Based Experiment

Agile synthetic aperture radar (SAR) platforms such as car-borne and UAV-borne SAR systems require combined inertial navigation systems (INS) and global navigation satellite systems (GNSS) to measure the radar sensor trajectories used for focusing and interferometric processing. Measurement inaccuracies from INS/GNSS systems lead to residual phase errors in the SAR products whose minimisation is crucial to derive accurate topographic and deformation information. In this work, we analyse the impact of residual positioning errors on car-borne repeat-pass SAR interferometry at L-band for different INS/GNSS measurement configurations and for the typical car-borne acquisition geometry. The positioning errors are evaluated both during single SAR acquisitions with long integration times and between different acquisitions as a function of the distance of the radar platform from the GNSS reference stations. We show the reduction of interferometric phase errors achievable by additionally using a GNSS receiver mounted in the vicinity of the SAR platform as compared to remote reference stations of the national network of permanent GNSS receivers. Test results obtained in a controlled setup with a rail-based SAR system equipped with a navigation-grade INS/GNSS system show maximum repeat-pass trajectory errors on the order of 1–2 cm using a local GNSS reference station and up to 10–15 cm using the remote reference stations, leading to azimuth and range phase trends in the interferometric products.

A satellite-based method for modeling ionospheric slant TEC from GNSS observations: algorithm and validation

Total Electron Content (TEC) modeling is critical for Global Navigation Satellite System (GNSS) users to mitigate ionospheric delay errors. The mapping function is usually used for Vertical TEC ionospheric correction models for slant and vertical TEC conversion. But the mapping function cannot characterize TEC variation in different azimuths between the user and satellites. The ionospheric modeling error resulting from the mapping function tends to be bigger in middle and low latitudes. Therefore, a new algorithm for ionospheric Slant TEC (STEC) modeling with Satellite-based Ionospheric Model (SIM) is proposed in this contribution. Validation tests are carried out with GNSS observation data from the Crustal Movement Observation Network of China during different solar activities and in different seasons. The performance of SIM is compared with that of several commonly-used Global Ionospheric Map (GIM) and Regional Ionospheric Map (RIM) products. The results show that the STEC bias and STD of SIM are within 1.0 TECU and about 2.0 TECU, respectively, and SIM can correct over 90% STEC RMS errors, outperforming the GIM and RIM products. Consequently, the SIM algorithm can be a new option for high-accuracy ionospheric delay correction in regional and local GNSS networks.

Creating a thematic geodatabase for monitoring the landslide processes of the landslide circus “Dalgia yar”

Impact on the process of landslide origin and activation is result of many factors both endogenous and exogenous. The purpose of this study is to provide possibility for analysis and assessment of the geo-processes in the “Dalgia yar” landslide located at Northern Black Sea coast of Bulgaria in order to prevent risks and disasters of natural and anthropogenic origin. An important stage was to seamlessly include data from different sources such as geodetic measurements, satellite SAR (Synthetic-aperture radar) data as well as geological and geophysical data. The established geodatabase structures the collected information on dangerous geo-processes in the mentioned area and introduces them into the GIS (Geographic information system) environment. Its purpose is to facilitate the analysis of the available geological data for this landslide and to integrate them with results of measurements from regular monitoring. Interferometric images (IFIs), data from permanent GNSS (Global Navigation Satellite Systems) stations and from local geodynamic GNSS network, geological, seismic and geophysical data, updated geological maps and maps of the risk of landslide processes are included in the database. The IFIs have been produced using well established procedure for processing large number of Sentinel-1 SAR data of the purposely created local archive. Other key element used to improve the final results of SAR data processing and important part of the geodatabase is the precise Digital Elevation Model (DEM), which is much better in terms of horizontal and vertical resolutions than the open accessed ones (SRTM). The coordinates and velocities of the GNSS points are obtained from adjustment and analysis of two epoch measurements of the geodynamic control network of landslides “Dalgia yar”. Since the area has complex geological structure, small scale maps reflecting the geological and geophysical hazards are integral part of the geodatabase. Having all this information the analysis concerning the ongoing geodynamical processes in the study area is significantly improved and more reliable information is produced for better regional planning by the local authorities and residents.

NRTK, PPP or Static, That Is the Question. Testing Different Positioning Solutions for GNSS Survey

Worldwide, the determination of the coordinates from a Global Navigation Satellite System (GNSS) survey (in Network Real Time Kinematic, Precise Point Positioning, or static mode) has been analysed in several scientific and technical applications. Many of those have been carried out to compare Precise Point Positioning (PPP), Network Real Time Kinematic (NRTK), and static modes’ solutions, usually, using the latter as the true or the most plausible solution. This approach is not always possible as the static mode solution depends on several parameters (baseline length, acquisition time, ionospheric, and tropospheric models, etc.) that must be considered to evaluate the accuracy of the method. This work aims to show the comparison among the GNSS survey methods mentioned above, using some benchmark points. The tests were carried out by comparing the survey methods in pairs to check their solutions congruence. The NRTK and the static solutions refer to a local GNSS CORS network’s analysis. The NRTK positioning has been obtained with different methods (VRS, FKP, NEA) and the PPP solution has been calculated with two different software (RTKLIB and CSRS-PPP). A statistical approach has been performed to check if the distribution frequencies of the coordinate’s residual belong to the normal distribution, for all pairs analysed. The results show that the hypothesis of a normal distribution is confirmed in most of the pairs and, specifically, the Static vs. NRTK pair seems to achieve the best congruence, while involving the PPP approach, pairs obtained with CSRS software achieve better congruence than those involving RTKLIB software.

Estimation and Analysis of GNSS Differential Code Biases (DCBs) Using a Multi-Spacing Software Receiver

In the use of global navigation satellite systems (GNSS) to monitor ionosphere variations by estimating total electron content (TEC), differential code biases (DCBs) in GNSS measurements are a primary source of errors. Satellite DCBs are currently estimated and broadcast to users by International GNSS Service (IGS) using a network of GNSS hardware receivers which are inside structure fixed. We propose an approach for satellite DCB estimation using a multi-spacing GNSS software receiver to analyze the influence of the correlator spacing on satellite DCB estimates and estimate satellite DCBs based on different correlator spacing observations from the software receiver. This software receiver-based approach is called multi-spacing DCB (MSDCB) estimation. In the software receiver approach, GNSS observations with different correlator spacings from intermediate frequency datasets can be generated. Since each correlator spacing allows the software receiver to output observations like a local GNSS receiver station, GNSS observations from different correlator spacings constitute a network of GNSS receivers, which makes it possible to use a single software receiver to estimate satellite DCBs. By comparing the MSDCBs to the IGS DCB products, the results show that the proposed correlator spacing flexible software receiver is able to predict satellite DCBs with increased flexibility and cost-effectiveness than the current hardware receiver-based DCB estimation approach.

Study on Seasonal Variations of Plasma Bubble Occurrence over Hong Kong Area Using GNSS Observations

In this study, the characteristics and causes of the seasonal variations in plasma bubble occurrence over the Hong Kong area were investigated using the local Global Navigation Satellite System (GNSS) network. Generally, the occurrences of plasma bubbles were larger in the two equinoxes than in the two solstices. Furthermore, two seasonal asymmetries in plasma bubble occurrence were observed: plasma bubble activity was more frequent in the spring equinox than in the autumn equinox (equinoctial asymmetry), and more frequent in the summer solstice than in the winter solstice (solstitial asymmetry). The equinoctial asymmetry could be explained using the Rayleigh–Taylor (R–T) instability mechanism, due to larger R–T growth rates in the spring equinox than in the autumn equinox. However, the R–T growth rate was smaller in the summer solstice than in the winter solstice, suggesting the R–T instability mechanism was inapplicable to the solstitial asymmetry. Our results showed there were more zonally propagating atmospheric gravity waves (GWs) induced by thunderstorm events over the Hong Kong area in the summer solstice than the winter solstice. So, the solstitial asymmetry could be attributed to the seeding mechanism of thunderstorm-driven atmospheric GWs.

<i>Corrigendum to</i>: Using global navigation satellite system data for real-time moisture analysis and forecasting over the Australian region I. The system

The use of high spatial and temporal resolution data assimilation and forecasting around Australia’s capital cities and rural land provided an opportunity to improve moisture analysis and forecasting. To support this endeavour, RMIT University and Geoscience Australia worked with the Bureau of Meteorology (BoM) to provide real-time GNSS (global navigation satellite system) zenith total delay (ZTD) data over the Australian region, from which a high-resolution total water vapour field for SE Australia could be determined. The ZTD data could play an important role in high-resolution data assimilation by providing mesoscale moisture data coverage from existing GNSS surface stations over significant areas of the Australian continent. The data were used by the BoM’s high-resolution ACCESS-C3 capital city numerical weather prediction (NWP) systems, the ACCESS-G3 Global system and had been used by the ACCESS-R2-Regional NWP model. A description of the data collection and analysis system is provided. An example of the application of these local GNSS data for a heavy rainfall event over SE Australia/Victoria is shown using the 1.5-km resolution ACCESS-C3 model, which was being prepared for operational use. The results from the test were assessed qualitatively, synoptically and also examined quantitatively using the Fractions Skills Score which showed the reasonableness of the forecasts and demonstrated the potential for improving rainfall forecasts over south-eastern Australia by the inclusion of ZTD data in constructing the moisture field. These data have been accepted for operational use in NWP.

Comparative analysis of modern deformation and the newest motions of the Earth surface in the territory of Ukraine

Currently, the data of the Global Navigation Satellite Systems (GNSS) are widely used in the field of navigation, geodesy, cartography and regional geodynamic studies, in particular, in monitoring the movement of lithospheric plates, etc. Further development and creation of local GNSS networks, as well as the long-term replenishment of databases regarding the determination of the coordinates of individual stations and the speeds of their movement allows obtaining reliable more detailed information on the current deformation of the Earth's surface. The article discusses the current deformation of the Earth’s surface based on the analysis of the Global Navigation Satellite Systems data from the GAO NAS of Ukraine in comparison with the heights of the UGK2012 quasi-geoid and the latest lineament zones and faults, as well as with the late Pliocene-Quaternary vertical movements of the Earth’s crust. According to the results of the analysis of high-precision coordinates of displacement vectors of permanent GNSS stations in the territory of Ukraine, deformation parameters of the Earth’s surface were obtained, areas of prevailing compression values — tension and left-right-side rotation of the Earth’s surface were identified, the boundaries between which can be drawn along the latest lineament zones and faults. The areas of the predominant stretching of the Earth’s surface correspond to the zones of the newest tectonic uplifts (Volyn-Podolsk and Periazov hills) and maximum amplitudes of the Pliocene-Quaternary movements and positive geoid anomalies, and the areas of prevailing compression are zones of tectonic descents (Polissian and Peridnieper lowland), minimal amplitudes of Pliocene-Quarternary movements and minor heights of the geoid. Four large modern geoblocks have been identified: North-West and North-East, which rotate clockwise, and South-West and South-East rotating counterclockwise. At a qualitative level, the mechanism of interconnection of modern and newest movements of the Earth’s crust, namely, the presence of the latest tectonic zones of uplifting and lowering with corresponding tensions and movements of its surface, on which modern tensions (and corresponding movements) are imposed that are associated with the tectonic movement of the Eurasian Plate in northeastern direction and the irregular rotation of the Earth.

Rate of Magma Supply Beneath Mammoth Mountain, California, Based on Helium Isotopes and CO2 Emissions

AbstractMammoth Mountain, California, has exhibited unrest over the past ~30 years, characterized by seismicity over a broad range of depths, elevated 3He/4He ratios in fumarolic gas, and large‐scale diffuse CO2 emissions. This activity has been attributed to magmatic intrusion, but minimal ground deformation and the presence of a shallow crustal gas reservoir beneath Mammoth Mountain pose a challenge for estimating magma supply rate. Here, we use the record of fumarolic 3He/4He ratios and CO2 emissions to estimate that of the ~5.2 Mt of CO2 released from Mammoth Mountain between 1989 and 2016, 1.6 Mt was associated with active intrusion and degassing of ~0.05–0.07 km3 of basaltic magma. Intrusion at an average rate of ~0.002–0.003 km3/year into a postulated zone of partial melt at ~15‐km depth could occur without detection by local Global Navigation Satellite System stations.

Using global navigation satellite system data for real-time moisture analysis and forecasting over the Australian region I. The system

The use of high spatial and temporal resolution data assimilation and forecasting around Australia’s capital cities and rural land provided an opportunity to improve moisture analysis and forecasting. To support this endeavour, RMIT University and Geoscience Australia worked with the Bureau of Meteorology (BoM) to provide real-time GNSS (global navigation satellite system) zenith total delay (ZTD) data over the Australian region, from which a high-resolution total water vapour field for SE Australia could be determined. The ZTD data could play an important role in high-resolution data assimilation by providing mesoscale moisture data coverage from existing GNSS surface stations over significant areas of the Australian continent. The data were used by the BoM’s high-resolution ACCESS-C3 capital city numerical weather prediction (NWP) systems, the ACCESS-G3 Global system and had been used by the ACCESS-R2-Regional NWP model. A description of the data collection and analysis system is provided. An example of the application of these local GNSS data for a heavy rainfall event over SE Australia/Victoria is shown using the 1.5-km resolution ACCESS-C3 model, which was being prepared for operational use. The results from the test were assessed qualitatively, synoptically and also examined quantitatively using the Fractions Skills Score which showed the reasonableness of the forecasts and demonstrated the potential for improving rainfall forecasts over south-eastern Australia by the inclusion of ZTD data in constructing the moisture field. These data have been accepted for operational use in NWP.

Assessment of local GNSS baselines at co-location sites

As one of the major contributors to the realisation of the International Terrestrial Reference System (ITRS), the Global Navigation Satellite Systems (GNSS) are prone to suffer from irregularities and discontinuities in time series. While often associated with hardware/software changes and the influence of the local environment, these discrepancies constitute a major threat for ITRS realisations. Co-located GNSS at fundamental sites, with two or more available instruments, provide the opportunity to mitigate their influence while improving the accuracy of estimated positions by examining data breaks, local biases, deformations, time-dependent variations and the comparison of GNSS baselines with existing local tie measurements. With the use of co-located GNSS data from a subset sites of the International GNSS Service network, this paper discusses a global multi-year analysis with the aim of delivering homogeneous time series of coordinates to analyse system-specific error sources in the local baselines. Results based on the comparison of different GNSS-based solutions with the local survey ties show discrepancies of up to 10 mm despite GNSS coordinate repeatabilities at the sub-mm level. The discrepancies are especially large for the solutions using the ionosphere-free linear combination and estimating tropospheric zenith delays, thus corresponding to the processing strategy used for global solutions. Snow on the antennas causes further problems and seasonal variations of the station coordinates. These demonstrate the need for a permanent high-quality monitoring of the effects present in the short GNSS baselines at fundamental sites.

Low-Cost GNSS Receivers for Local Monitoring: Experimental Simulation, and Analysis of Displacements.

The geodetic monitoring of local displacements and deformations is often needed for civil engineering structures and natural phenomena like, for example, landslides. A local permanent GNSS (Global Navigation Satellite Systems) network can be installed: receiver positions in the interest area are estimated and monitored with respect to reference stations. Usually, GNSS geodetic receivers are adopted and provide results with accuracies at the millimeter level: however, they are very expensive and the initial cost and the risk of damage and loss can discourage this approach. In this paper the accuracy and the reliability of low-cost u-blox GNSS receivers are experimentally investigated for local monitoring. Two experiments are analyzed. In the first, a baseline (65 m long) between one geodetic reference receiver and one u-blox is continuously observed for one week: the data are processed by hourly sessions and the results provide comparisons between two processing packages and a preliminary accuracy assessment. Then, a network composed of one geodetic and two u-blox receivers is set up. One u-blox is installed on a device (slide) that allows to apply controlled displacements. The geodetic and the other u-blox (at about 130 m) act as references. The experiment lasts about two weeks. The data are again processed by hourly sessions. The estimated displacements of the u-blox on the slide are analyzed and compared with the imposed displacements. All of the results are encouraging: in the first experiment the standard deviations of the residuals are smaller than 5 mm both in the horizontal and vertical; in the second, they are slightly worse but still satisfactory (5 mm in the horizontal and 13 mm in vertical) and the imposed displacements are almost correctly identified.

Estimating the Baseline between CERN Target and LNGS Reference Points

AbstractThis work is part of the European Organization for Nuclear Research (CERN) Neutrinos to Gran Sasso (CNGS) Project, aimed at estimating the velocity of neutrino beams directed from CERN in Geneva toward the Gran Sasso National Laboratory (LNGS) in Assergi, Italy. In particular, the distance has to be estimated between the Large Volume Detector, Icarus, and Borexino reference points, located inside LNGS, and the CERN laboratory target. All the points at LNGS and CERN are placed in underground laboratories. Traditional surveying methods must then be applied for connecting the reference points to benchmarks established outside the underground laboratories in the open field. In this way, the two local LNGS and CERN geodetic networks can be connected by the Global Navigation Satellite System (GNSS) technique. The CERN target was already estimated with respect to a local GNSS network in the International Terrestrial Reference Frame 97. To estimate the position of LNGS points, a new local GNSS network has...

Tomographic reconstruction of wet and total refractivity fields from GNSS receiver networks

One of the most attractive scientific issues in the use of GNSS (Global Navigation Satellite System) signals, from a meteorological point of view, is the retrieval of high resolution tropospheric water vapour maps. The real-time (or quasi real-time) knowledge of such distributions could be very useful for several applications, from operative meteorology to atmospheric modelling. Moreover, the exploitation of wet refractivity field reconstruction techniques can be used for atmospheric delay compensation purposes and, as a very promising activity, it could be applied for example to calibrate SAR or Interferometric-SAR (In-SAR) observations for land remote sensing. This is in fact one of the objectives of the European Space Agency project METAWAVE (Mitigation of Electromagnetic Transmission errors induced by Atmospheric Water vapour Effects), in which several techniques are investigated and results were compared to identify a strategy to remove the contribution of water vapour induced propagation delays in In-SAR products. Within this project, the tomographic reconstruction of three dimensional wet refractivity fields from tropospheric delays observed by a local GNSS network (9 dual frequency GPS receivers) deployed over Como area (Italy), during 12–18 October, 2008, was performed. Despite limitations due to the network design, internal consistency tests prove the efficiency of the adopted tomographic approach: the rms of the difference between reconstructed and GNSS observed Zenith Wet Delays (ZWD) are in the order of 4 mm. A good agreement is also observed between our ZWDs and corresponding delays obtained by vertically integrating independent wet refractivity fields, taken by co-located meteorological analysis. Finally, during the observing period, reconstructed vertical wet refractivity profiles evolution reveals water vapour variations induced by simple cloud covering. Even if our main goal was to demonstrate the effectiveness in adopting tomographic reconstruction procedures for the evaluation of propagation delays inside water vapour fields, the actual water vapour vertical variability and its evolution with time is well reproduced, demonstrating also the effectiveness of the inferred 3D wet refractivity fields.

Integration and verification of meteorological observations and NWP model data for the local GNSS tomography

GNSS meteorology applies the Global Navigation Satellite Systems (GNSS) to derive information about the state of the atmosphere (particularly troposphere). The tomography is one of the methods used in GNSS meteorology. The input data of GNSS tomography are the signal troposphere delays, results of GNSS data processing and additionally meteorological observations and Numerical Weather Prediction (NWP) models data. Different types of the input data have heterogeneous character, but give broad spectrum of information. The paper presents the methodology of integration and verification of GNSS, meteorological and NWP data for GNSS tomography. Because of the data inhomogeneity, original methods of meteorological data validation and NWP model calibration are proposed. In order to verify the ground meteorological observations, the differential wavelet method is proposed. The results of analysis show that pressure should be measured as accurately as possible (uncertainty below 1.0 hPa) with homogenous instruments and in the similar conditions. Whereas the temperature could be measured less accurately (uncertainty below 2.4 K), however usage of meteorological radiation shelters (e.g. Stevenson screens) or mathematical algorithms to mitigate the influence of direct insolation is a must. The integration procedure of the COAMPS NWP model shows that the model output parameters are squaring with the meteorological observations from the synoptic stations. The best match is found between pressures from both sources, a good match is also found in case of temperature, whereas relative humidity measurements are less consistent. Moreover, the presented methodology could be used for assimilation of meteorological observations into numerical weather models.

Local tomography troposphere model over mountains area

The term GNSS meteorology refers to the utilization of the Global Navigation Satellite System's (GNSS) radio signals to derive information about the state of the troposphere. GNSS tomography allows to resolve the spatial structure and temporal behavior of the tropospheric water vapor. This paper presents the verification of GNSS tomography over dense local GNSS network. The paper addresses the problem of obtaining a stable tomographic solution from an ill-conditioned system of linear equations. The main interests are in suitable horizontal and vertical resolution in given conditions. Here the Moore–Penrose pseudo inverse of variance–covariance matrix is used. The minimum constraints solution is obtained with no additional assumptions. The results are validated with the help of simulated weather conditions. Three various scenarios are tested. As general output of this paper the optimal model construction scheme is presented with possible further improvements. The verification of the tomography model based on the local GPS KARKONOSZE, situated in the Karkonosze mountains area in Poland.