Tomasz Hadas

Theoretically, it is possible to reconstruct the 3D distribution of water vapor by means of GNSS tomography using troposphere estimates from a network of GNSS stations, i.e., zenith delays mapped back into satellite directions. However, this technique is still limited by restricted satellite-to-ground observation geometry, a simplified parameterization of troposphere delays in the observation model and mandatory usage of constraints to stabilize the equation system. We propose an alternative approach, called STEPPP, in which a network of ground-based GNSS receivers is used to process GNSS observations, based on the Precise Point Positioning (PPP) technique and, instead of estimating the zenith wet delay and horizontal gradients, the estimation of the whole wet refractivity field in a grid space is performed simultaneously. Contrary to GNSS tomography, STEPPP operates on raw observation data instead of products. Values of wet refractivity at grid nodes are estimated from all stations simultaneously, i.e., they appear as common parameters in PPP. We present the functional and stochastic model of STEPPP, as well as first results of the model performance. We use GPS and Galileo dual-frequency observations generated by the Spirent simulator for 20 evenly distributed stations. The simulated observations are intentionally free of troposphere delays. However, we use a numerical weather model to retrieve reference profiles of wet refractivity and calculate slant wet delays, which are added to the simulated observations. We define a voxel space above the network of stations up to 12 km height and we recover the wet refractivity profiles by means of the STEPPP model. Several numerical experiments are performed using homogenous, inhomogeneous, constant and dynamic wet refractivity profiles. After a convergence time of a few hours, the STEPPP model accurately recovers all model states, including the 3D wet refractivity field and station coordinates.

Severe meteorological conditions, such as tropical cyclones, may contribute in electrodynamical changes of the ionospheric layer in different ways. We search for possible physical mechanisms responsible in bringing such changes by considering an extremely severe cyclone “Biparjoy” as a case study using real-time/near real-time satellite observations. A significant growth in the Atmospheric Chemical Potential (ACP) as spiral threads around the eyewall and right underneath the rainbands is observed during occurrence of numerous thunderstorms (K-index > 30), establishing a near-perfect correlation (ρ = 0.99). This observation confirms that the area under the cyclone became an ionized medium following the mutual interaction of the lightning activity and rain droplets. Moreover, the ionospheric Total Electron Content (TEC) maps derived from the COSMIC-2 satellites reveal significant ionospheric enhancements (>10 TECU) in the form of concentric TEC shells, specifically, during cyclone's peak intensity. This ionospheric intensification is driven by the mutual electric field variability from lightning activity added to the ACP growth from below that brought changes in the Global Electric Circuit (GEC) through boundary layer conductivity. In addition, Real-Time Global Ionospheric Maps (RTGIMs) and the novel Ionospheric Storm Scale Index maps (IsUG) exhibit significant performance in detecting meteorological influence onto the ionosphere, which is encouraging considering real-time ionospheric monitoring perspectives. While, ACP and TEC values exhibit a strong correlation (ρ = 0.83) providing evidence of cross-layer atmosphere coupling. Furthermore, NASA's VIIRS DNB nighttime radiance maps characterize the generation of Atmospheric Gravity Waves (AGWs) that induced spasmodic S-type ripples in topside ionospheric density. However, the production of these ripples is instantaneous that was not observed during the rest of the analyzed period. These observations confirm that the sustained ionospheric enhancements are primarily attributed to the enhanced electrical conduction in GEC, rather than oscillatory AGW effects.

Precise point positioning (PPP) has become a key technique in global navigation satellite systems (GNSS) applications, but its use in real time is limited by long convergence times. Tropospheric delay is one of the major contributors to this limitation. Accurate modeling over China is particularly challenging due to pronounced topographic variations, where empirical or conventional polynomial models fail to capture spatiotemporal characteristics. We propose a height-correction adjusted spherical harmonic model (HASH-Z) that incorporates an exponential height-decay term into a regional spherical cap expansion to account for the vertical dependence of zenith wet delay (ZWD). The model is developed from ZWD estimates obtained with PPP ambiguity resolution (PPP-AR) at a GNSS network in China (∼200 km spacing). Validation against IGS reference products confirms that centimeter-level accuracy of PPP-AR-derived ZWD estimates. Across the modeling stations, root mean square errors (RMSE) remain below 2.0 cm for all sites in winter and for more than 83% of sites in summer. A latitude-dependent variability is evident in winter, but largely obscured in summer due to pronounced atmospheric water vapor fluctuations. Independent tests at stations spanning large height differences further confirm the robustness of the model, with RMSE values of 0.5–1.9 cm in winter and 1.2–2.9 cm in summer. When applied in PPP-AR augmentation, the HASH-Z can significantly accelerate convergence by ∼20% in the vertical component and improve positioning accuracy by 4–12%. These results demonstrate that the HASH-Z model can provide an accurate and efficient representation of tropospheric delay over China.

Global Navigation Satellite System (GNSS) technology, thanks to its high accuracy, is appropriate for monitoring structures, natural and anthropogenic hazards, as well as navigation and positioning. The Galileo High Accuracy Service (HAS) augmentation service recently released by the European Space Agency (ESA) is a new solution that could accelerate the development of mass-market technologies using the Global Navigation Satellite System (GNSS). Galileo HAS is designed to provide horizontal and vertical accuracies of 20 cm and 40 cm, respectively; it can be used in all legacy GNSS applications from structural monitoring to drone trajectory tracking using low-cost GNSS receivers.This study evaluates the use of Galileo HAS with geodetic grade as well as low-cost receivers, analysing the results obtained in static, pseudo-kinematic, and kinematic solutions. The results indicate that Galileo HAS currently provides positioning accuracy at a to that comparable level of less than 10 cm, regardless of the use of geodetic or low-cost receivers. The results of integrating Galileo HAS with low-cost receivers show that it represents an important step in the development of available real-time positioning solutions.In addition, the study showed that Galileo HAS meets key requirements in monitoring water vapour in the troposphere, as well as seismic displacement, by achieving real-time accuracy levels required for seismic displacement tracking and weather modelling. Comparative analyses with other GNSS correction streams show that HAS has lower accuracy in selected statistics, such as vertical accuracy. However, its near-global availability and high accuracy still make it a viable alternative.

The severe geomagnetic activities pose significant affect in modification of the electron concentrations of the ionospheric layer, especially along the equatorial and polar regions, causing challenging environments considering positioning perspectives. The recent availability of the Real-Time Global Ionosphere Maps (RT-GIMs) by some specialized IGS associated analysis centers such as Centre National d’Etudes Spatiales (CNES), Chinese Academy of Sciences (CAS), Universitat Politècnica de Catalunya (UPC), and Wuhan University (WHU), provides exciting opportunity to comprehend the ionospheric modification under these geomagnetic influences in real-time, while the RTGIMs can be integrated to the real-time precise point positioning (RT-PPP) to reduce the convergence time. Therefore, we perform the accuracy evaluation of these RT-GIM under the presence of a severe G-4 class geomagnetic storm during the year 2024. The performance of these RT-GIM products is evaluated by comparing the RT-GIM vertical Total Electron Content (VTEC) values with Final GIMs provided by Center for Orbit Determination in Europe (CODE) over land and Jason-3 altimetry satellite over oceans. The CNES RT-GIMs undergoes severe accuracy degradation across all continents recording a significant -20 to -40 TECU bias offset compared to the final CODE GIMs (CODGs) during the main phase of the geomagnetic storm. Similarly, the performance of the WHU RTGIMs sightly deteriorates upto -10 TECU along the equatorial, south pacific, and south pole regions. However, CAS and UPC RT-GIMs show a relatively consistent performances during the initial and main phase of the severe geomagnetic storm. However, during the final phase of the geomagnetic storm, both WHU and CAS RTGIMs exhibit overperformances of more than 10 TECU over the Antarctica compared to the final CODGs. Additionally, on the comparison with the Jason-3, the CNES and WHU RTGIMs shows worst performances once again with the average deviations of 10-15 TECU over the oceans during the high intensity period of the geomagnetic storm. Meanwhile, UPC RT-GIM remain the most consistent and stable performer (both, globally and over oceans) that provides accurate global ionospheric information, almost similar to the final GIMs, which is promising for their applications in real-time precise GNSS positioning.

In Precise Point Positioning (PPP), independently estimating the receiver clock parameters at each observation epoch introduces heightened noise in the estimated station coordinates and troposphere parameters due to correlations. To address this issue, stochastic modeling is applied to the receiver clock parameter, thereby enhancing the stability of PPP solutions and minimizing clock noise for precise time transfer. Importantly, the feasibility of receiver clock modeling relies on GNSS receivers being connected to exceptionally stable atomic clocks, such as hydrogen maser clocks (HM), which exhibit significantly lower noise compared to other clock types.The strategy proposed by our team involves introducing Markov stochastic process modeling for the receiver clock parameters through a random walk. We opted for this stochastic process because of its simplicity in both comprehension and implementation. We conducted tests with different levels of random walk constraints for GNSS stations equipped with various clock types, exploring both Galileo-only and multi-GNSS solutions in kinematic and static PPP modes. We compare the results against a reference solution without any additional constraints. In multi-GNSS solutions, a common clock parameter is determined alongside inter-system biases (ISBs), with the common clock parameter identified as the GPS clock.Research outcomes demonstrate that comparable results can be achieved by imposing constraints solely on the common clock parameter while treating ISBs as constant parameters. Similarly, constraints on both the common clock parameter and ISBs, with a ratio of 1:100, yield the most favorable results. However, adopting other clock-to-ISB constraint ratios, such as 1:1 and 1:10, leads to suboptimal performance. In the static PPP, the introduced clock modeling significantly enhances the precision of time transfer by effectively reducing clock noise. In the kinematic PPP, stochastic clock modeling has a marginal impact on the North and East coordinate components, whereas the Up component exhibits substantial improvement, mainly for GNSS receivers equipped with HM. An examination of Zenith Total Delay (ZTD) in both Galileo-only kinematic and static PPP modes reveals the discernible impact of clock constraints, as evidenced by observed offsets in the respective outcomes. In the case of multi-GNSS solutions, this influence is less prominent, attributed to weaker correlations between ZTD and clock parameters in multi-GNSS solutions compared to Galileo-only.

Satellite signals from the Global Navigation Satellite System (GNSS) are refracted as they pass through the troposphere, owing to the variable density and composition of the atmosphere, causing tropospheric delay. Typically, tropospheric delay is treated as an unknown parameter in GNSS data processing. Given the growing need for real-time GNSS applications, accurate tropospheric delay predictions are crucial to improve Precise Point Positioning (PPP). In this paper, time-series of tomography data are used for wet refractivity prediction employing Machine Learning (ML) techniques in both Poland and California, under extreme weather conditions including sweeping rain bands and storms. The predicted wet refractivity is implemented for tropospheric delay determination through ray-tracing technique. PPP processing is conducted in both static and kinematic modes using different setups. These are: (1) common PPP, called Com-PPP, (2) Ray-PPP, which applies obtained tropospheric delay on GNSS observations and thus eliminates tropospheric parameters from unknowns, and (3) Dif-PPP, which applies the difference of estimated tropospheric delay from ray-tracing and GNSS measurements to compensate for the remaining tropospheric delay in the observations. The results show that Dif-PPP reduces the Mean Absolute Error (MAE) of the Three-Dimensional (3-D) component between 8 and 33% in static mode compared to the Com-PPP method. Additionally, it can improve the convergence time of the up component in the kinematic mode by between 6 and 17%.

The Galileo High Accuracy Service (HAS) is a free of charge Global Navigation Satellite System (GNSS) augmentation service provided by the European Union. It is designed to enable real-time Precise Point Positioning (PPP) with a target accuracy (at the 95% confidence level) of 20 cm and 40 cm in the horizontal and vertical components, respectively, to be achieved within 300 s. The performance of the service has been confirmed with geodetic-grade receivers. However, mass market applications require low-cost GNSS receivers connected to low-cost antennae. This paper focuses on the performance of the real-time static and kinematic positioning achieved with Galileo HAS and low-cost GNSS receivers. The study is limited to GPS + Galileo dual-frequency positioning, thus exploiting the full potential of Galileo HAS SL1. We demonstrate that the target accuracy of Galileo HAS SL1 is reached with both geodetic-grade and low-cost receivers in dual-frequency static and kinematic applications in open-sky conditions. Precision of a few centimeters is reached for static positioning, while kinematic positioning results in subdecimeter precision. Vertical accuracy is limited by missing phase center offset models for low-cost antennas. In general, the performance of low-cost hardware using Galileo HAS for real-time PPP is comparable to that of geodetic-grade hardware. Therefore, combining low-cost GNSS receivers with Galileo HAS is feasible and justified.

Vertical displacements are traditionally measured with precise levelling, which is inherently time consuming. Rapid or even real-time height determination can be achieved by the Global Navigation Satellite System (GNSS). Nevertheless, the accuracy of real-time GNSS positioning is limited, and the deployment of a network of continuously operating GNSS receivers is not cost effective unless low-cost GNSS receivers are considered. In this study, we examined the use of geodetic-grade and low-cost GNSS receivers for static and real-time GNSS levelling, respectively. The results of static GNSS levelling were processed in four different software programs or services. The largest differences for ellipsoidal/normal heights reached 0.054 m/0.055 m, 0.046 m/0.047 m, and 0.058 m/0.058 m for points WRO1, BM_ROOF, and BM_CP, respectively. In addition, the values depended on the software used and the location of the point. However, the multistage experiment was designed to analyze various strategies for GNSS data processing and to define a method for detecting vertical displacement in a time series of receiver coordinates. The developed method combined time differentiation of coordinates estimated for a single GNSS receiver using the Precise Point Positioning (PPP) technique and Butterworth filtering. It demonstrated the capability of real-time detection of six out of eight displacements in the range between 20 and 55 mm at the three-sigma level. The study showed the potential of low-cost GNSS receivers for real-time displacement detection, thereby suggesting their applicability to structural health monitoring, positioning, or early warning systems.