S1.6 - Algorithms and Methods (I)
Tracks
Track: GNSS & PNT Services
| Wednesday, April 29, 2026 |
| 4:10 PM - 5:50 PM |
| Room 1.32 |
Details
Co-Chairs: Chris Bartone & Janusz Uriasz
Speaker
Mr. Milad Bagheri
Phd Candidate
Politecnico Di Torino, DIATI, Milad Bagheri
Kriging-based interpolation of zenith wet delay from dense low-cost GNSS observations
4:10 PM - 4:30 PMAbstract text
Tropospheric zenith wet delay (ZWD) is a key parameter influencing high-precision GNSS positioning and providing valuable information on atmospheric water vapor for geodetic and meteorological applications. Spatially continuous ZWD fields are particularly important in regions where GNSS receivers are sparsely distributed or unavailable, motivating the use of network-based interpolation techniques. The increasing availability of dense low-cost GNSS networks offers new opportunities for high-resolution tropospheric monitoring, yet their applicability for ZWD spatial interpolation requires dedicated investigation.
In this study, we investigate the spatial interpolation of ZWD using an exclusively low-cost GNSS network based on an epoch-wise ordinary kriging approach. Zenith wet delays are estimated at network stations using precise point positioning with a 30 s sampling interval, and kriging interpolation is applied to predict ZWD at locations without GNSS receivers. The interpolation performance is evaluated over one year of observations using independent low-cost user stations, with particular attention to temporal variability and changing atmospheric conditions.
The results demonstrate that dense low-cost GNSS networks can provide stable and physically consistent ZWD interpolation when spatial correlations are appropriately modeled. The interpolated ZWD products are suitable not only for characterizing tropospheric conditions at uninstrumented locations, but also for supporting precise point positioning and PPP-RTK initialization, assimilation in meteorological and numerical weather prediction models.
In this study, we investigate the spatial interpolation of ZWD using an exclusively low-cost GNSS network based on an epoch-wise ordinary kriging approach. Zenith wet delays are estimated at network stations using precise point positioning with a 30 s sampling interval, and kriging interpolation is applied to predict ZWD at locations without GNSS receivers. The interpolation performance is evaluated over one year of observations using independent low-cost user stations, with particular attention to temporal variability and changing atmospheric conditions.
The results demonstrate that dense low-cost GNSS networks can provide stable and physically consistent ZWD interpolation when spatial correlations are appropriately modeled. The interpolated ZWD products are suitable not only for characterizing tropospheric conditions at uninstrumented locations, but also for supporting precise point positioning and PPP-RTK initialization, assimilation in meteorological and numerical weather prediction models.
Biography
Milad Bagheri is currently a PhD candidate at Politecnico di Torino, working with the Geomatics group at DIATI. His research interests include the quality control of GNSS positioning, monitoring techniques with Geomatics instruments, low-cost INS and GNSS systems for mobile mapping, and indoor positioning for navigation purposes.
Mr. Jiahuan Zhang
Research Postgraduate (phd)
Imperial College London
Fast GNSS Sky Obstruction Analysis with Skyline Similarity and Template Reuse
4:30 PM - 4:50 PMAbstract text
In dense urban environments, buildings severely obstruct GNSS signals, causing positioning errors and unstable satellite visibility. This study proposes a real-time method for modelling sky obstructions using vehicle-based GNSS trajectories and building height data. For each trajectory point, a local grid is constructed to estimate elevation angles of obstructed directions and generate a corresponding skyplot.
To overcome the high computational cost of frame-by-frame skyline generation, a template reuse mechanism is introduced. Skyline profiles are compared using cosine similarity, combined with spatial neighbourhood constraints and Area of Interest (AOI) overlap checks. If the current environment is similar to a stored template, its skyplot is instantly reused; otherwise, a new template is generated. This preserves local geometric characteristics while avoiding redundant computation.
Experimental results show that the method reduces average processing time from several seconds to under one second per epoch, without compromising obstruction accuracy or skyplot morphology. The proposed approach provides an efficient framework for real-time GNSS visibility modelling and urban obstruction assessment.
To overcome the high computational cost of frame-by-frame skyline generation, a template reuse mechanism is introduced. Skyline profiles are compared using cosine similarity, combined with spatial neighbourhood constraints and Area of Interest (AOI) overlap checks. If the current environment is similar to a stored template, its skyplot is instantly reused; otherwise, a new template is generated. This preserves local geometric characteristics while avoiding redundant computation.
Experimental results show that the method reduces average processing time from several seconds to under one second per epoch, without compromising obstruction accuracy or skyplot morphology. The proposed approach provides an efficient framework for real-time GNSS visibility modelling and urban obstruction assessment.
Biography
Jiahuan Zhang, PhD candidate in the Department of Civil and Environmental Engineering at Imperial College London, currently specialises in remote sensing-based earth observation for the evaluation and enhancement of PNT services.
Mr. Saqib Mehdi
Phd Student
Wrocław University of Environmental and Life Sciences
Urban GNSS Multipath Mitigation by Integrating Ray Tracing and PPP
4:50 PM - 5:10 PMAbstract text
Accurate estimation of Zenith Tropospheric Delay (ZTD) from Global Navigation Satellite System (GNSS) observations is essential for high-resolution atmospheric monitoring and numerical weather prediction. While Precise Point Positioning (PPP) achieves millimeter-level ZTD accuracy under open-sky conditions, its performance degrades severely in dense urban environments due to multipath interference and non-line-of-sight (NLOS) signal propagation. These effects limit the usability of crowdsourced and low-cost GNSS observations, including smartphone and public transport GNSS data, for urban tropospheric sensing. This study presents a geometry-aware framework that integrates 3D city models and electromagnetic ray tracing into PPP processing to enable reliable urban ZTD estimation. GNSS signal propagation is explicitly classified at each satellite–receiver epoch into line-of-sight (LOS), reflection, diffraction, mixed multipath, and NLOS components using building geometry and physically based reflection (Fresnel equations) and diffraction (Uniform Theory of Diffraction) coefficients. These classifications drive adaptive observation exclusion and reweighting within the PPP filter. In parallel, a city-scale ray-tracing analysis is used to identify “healthy urban zones” with sustained LOS visibility, suitable for crowdsourced GNSS data collection. Experiments using real urban GNSS data demonstrate that conventional PPP suffers from severe instability in urban canyons, with ZTD biases exceeding 10 m and large positioning errors. The proposed ray-tracing–assisted PPP reduces code residuals to the meter level, stabilizes carrier-phase residuals, and improves ZTD accuracy by more than two orders of magnitude, achieving sub-decimeter agreement with reference stations. Healthy-zone identification further enables systematic selection of urban locations where reliable tropospheric retrieval is feasible. These results demonstrate that physics-based, geometry-aware multipath modeling is essential for extending GNSS tropospheric sensing into dense urban environments and provides a scalable pathway toward high-resolution urban atmospheric monitoring using crowdsourced GNSS infrastructure.
Biography
Saqib Mehdi is a PhD student at the
Institute of Geodesy and Geoinformatics,
Wroclaw University of Environmental and Life Sciences, Poland.
He has a background in Physics and focuses on urban GNSS meteorology,
with emphasis on ray-tracing-based multipath mitigation and NLOS classification,
and improving tropospheric delay estimation using Precise Point Positioning.
Mr. Mohamed Ashraf Mohamed Abdelhamid
PhD Student
AGH University of Krakow
Analysis of Storm-Related GNSS-SNR Variability Using GPS and BeiDou Observations: High-Rate versus Standard Sampling Data
5:10 PM - 5:30 PMAbstract text
Global Navigation Satellite System Interferometric Reflectometry (GNSS-IR) exploits signal-to-noise ratio (SNR) variations caused by multipath interference to sense environmental changes. While GPS-based IR has been widely applied to surface monitoring applications, such as soil moisture, snow depth, and water level estimation, the use of BeiDou SNR observations for atmospheric disturbance and storm detection remains largely unexplored.
A residual-based framework is applied at three permanent GNSS stations during a storm day, in which SNR observations were compared with the days without this phenomenon. Storm sensitivity is quantified using a Storm/Quiet ratio derived from residual exceedances across multiple SNR bands (SNR1–SNR5). Results from the 30-second data show moderate storm responses at ALME station in Spain and ARA2 station in Slovenia, primarily in the lower SNR bands (SNR1 and SNR2), while BeiDou-IGSO satellites at TORI station in Italy also exhibit a moderate response. In contrast, the 1-second observations significantly enhance storm signatures for GPS, with increased Storm/Quiet ratios indicating that high-rate data capture short-lived storm-induced variations more effectively than 30-second sampling. BeiDou responses, however, remain largely unchanged between the two sampling rates, suggesting limited sensitivity gain from higher than 30s sampling resolution.
These findings demonstrate that high-rate GNSS-SNR significantly enhances storm detectability for GPS and provide, to our knowledge, the first assessment of BeiDou SNR for storm detection. The results highlight both the potential and the limitations of multi-GNSS IR for monitoring fast-evolving atmospheric phenomena.
A residual-based framework is applied at three permanent GNSS stations during a storm day, in which SNR observations were compared with the days without this phenomenon. Storm sensitivity is quantified using a Storm/Quiet ratio derived from residual exceedances across multiple SNR bands (SNR1–SNR5). Results from the 30-second data show moderate storm responses at ALME station in Spain and ARA2 station in Slovenia, primarily in the lower SNR bands (SNR1 and SNR2), while BeiDou-IGSO satellites at TORI station in Italy also exhibit a moderate response. In contrast, the 1-second observations significantly enhance storm signatures for GPS, with increased Storm/Quiet ratios indicating that high-rate data capture short-lived storm-induced variations more effectively than 30-second sampling. BeiDou responses, however, remain largely unchanged between the two sampling rates, suggesting limited sensitivity gain from higher than 30s sampling resolution.
These findings demonstrate that high-rate GNSS-SNR significantly enhances storm detectability for GPS and provide, to our knowledge, the first assessment of BeiDou SNR for storm detection. The results highlight both the potential and the limitations of multi-GNSS IR for monitoring fast-evolving atmospheric phenomena.
Biography
Mr. Mohamed Abdelhamid is a doctoral student at AGH University of Krakow, Poland, specializing in GNSS Interferometric Reflectometry (GNSS-IR) and its environmental applications. His research focuses on monitoring environmental phenomena using multi-GNSS observations, including sea-level variations and snow depth. In this presentation, he will discuss the application of GNSS-IR for detecting atmospheric disturbances, highlighting recent results from permanent GNSS stations in Europe.