With the widespread availability of Android’s raw GNSS API, there is a growing demand for reliable tools that convert smartphone GNSS logs into standard RINEX files for post processing. Existing solutions often omit observables, mislabel frequencies, or provide unstable outputs, limiting their use in high-precision applications. This paper introduces the Nottingham Smartphone GNSS Raw to RINEX (NSGRX) converter, a novel Python-based GUI application that overcomes these limitations by producing complete, standards-compliant RINEX files. NSGRX supports GPS, Galileo, GLONASS, and BeiDou dual frequency observations without external dependencies and generates precise pseudorange, carrier phase, and Doppler observables using robust algorithms. In static tests with data from Samsung S23 FE and Xiaomi Mi 11T devices, RINEX files generated by NSGRX achieved fixed solution rates of up to 100
To improve ambiguity fixing in real‑time precise orbit determination (RTPOD) for low Earth orbit satellites, this study proposes a hierarchical integer ambiguity resolution (IAR) approach that addresses the critical need for reliable validation and rapid convergence. The hierarchical approach uses a two-level (normal and strict) integer ambiguity validation. The criteria for normal and strict validation are derived from a one-layer and six-layer decision tree model, respectively, both trained on one month of GRACE‑C data. The integer constraint is added to a temporary filter after passing the normal validation while further propagated into the main filter after passing the strict validation. By applying the hierarchical integer constraint, two-month RTPOD for GRACE-C and GRACE-D are conducted using CNES real-time products. An ambiguity fixing rate of about 78
Precision and safety-critical Global Navigation Satellite System (GNSS) applications require high-fidelity monitoring of space weather conditions, particularly ionospheric disturbances. These systems are highly sensitive to sharp spatial gradients and rapid Total Electron Content (TEC) variations. To support both operational and scientific needs, this study proposes and evaluates two variants of the Gradient Ionosphere indeX (GIX): GIXM and GIXV. Derived from absolute TEC measurements at pairs of ionospheric piercing points (IPPs), the GIX quantifies gradients by dividing the TEC difference by the distance between IPPs. The GIXM method calculates the scalar average of these gradients, while GIXV computes the resultant gradient vector over regional scales (typically ≥ 500 × 500 km2) to capture both magnitude and direction. Comparative analysis reveals a strong correlation between GIXM and the operational geodetic I95 index, confirming GIXM’s utility for disturbance scaling and reliability assessment. Accurate estimation of the GIXV vector requires sufficient spatial coverage, typically involving 35–45 IPPs. Furthermore, analyzing GIX dynamics within the Magnetosphere-Ionosphere-Thermosphere (MIT) framework demonstrates potential for predictive modeling. By tracking the equatorward propagation of high-latitude gradient structures, this framework enables the forecasting of GIXMI95 levels, offering a robust tool for mitigating GNSS risks.
With Solar Cycle (SC) 25 approaching its maximum, the heightened frequency and intensity of solar-driven geomagnetic storms present significant challenges for precise orbit determination (POD) of low Earth orbit (LEO) satellites. Given the limited capability of non-gravitational (NG) force models to capture space weather variability, the ultra-sensitive accelerometer can measure NG accelerations with high precision and may provide a more reliable means of obtaining them during storms. This study investigates the performance of model-based POD (MB POD) and accelerometer-based POD (AB POD) for the Gravity Recovery and Climate Experiment Follow-On (GRACE-FO) mission during two intense geomagnetic storms on 10–12 May and 10–12 October, 2024. The MB POD solutions achieve an external orbit difference of 1.8 cm during quiet periods, which degrades to 3.6 cm during storms. This degradation is corroborated by deteriorated SLR residuals and storm-correlated carrier phase residuals, indicating a mismatch between the satellite dynamics and GNSS observations. By comparison, POD using only quiet-period data yields an external orbit difference of 1.1 cm, suggests that the inclusion of storm periods in the processing degrades the MB POD performance over the entire arc. Regarding AB POD, twelve accelerometer calibration schemes are developed and categorized into the well-tuned and untuned calibration groups based on their corresponding POD performance. Using schemes from the well-tuned group, AB POD achieves orbit differences below 0.8 cm during quiet periods and maintains sub-centimeter accuracy during geomagnetic storms. However, it is not completely unaffected by storms, as the STD time series of the bias estimates exhibit prominent peaks during storms that align temporally with spikes in MB POD carrier phase residuals, suggesting that the robustness of AB POD is largely due to the absorption of storm-induced effects by the accelerometer bias parameters. Nevertheless, these sub-centimeter accuracy orbits and corresponding NG accelerations are promising for providing maneuvering references for collision avoidance under dynamic atmospheric conditions and for better characterizing neutral density variations during storms, but their application in gravity field recovery requires caution because the POD process involves short bias estimation intervals ( ≤ 1 orbital period) and the inclusion of 1 cycle-per-revolution acceleration.
Currently, solar activity is in its 25th peak year, with frequent occurrences of ionospheric scintillation, resulting in a significant increase in cycle slip events in Global Navigation Satellite System (GNSS) observation data and significantly affecting the reliability of precise positioning services. Accurate cycle slip detection is key to improving positioning performance. However, the fixed-threshold detection method often fails to adapt to ionospheric scintillation variations, resulting in high false alarm rates, frequent misjudgments, and subsequently reduced positioning accuracy. To address the limitation that the existing Hatch-Melbourne-Wübbena (HMW) combination cycle slip threshold cannot adapt to variations in ionospheric scintillation intensity, this paper analyzes the variation patterns between the scintillation factor Rate Of Total Electron Content (TEC) Index (ROTI) and the cycle slip detection values, i.e., Extra-Wide-Lane (EWL), Wide-Lane (WL), and Narrow-Lane (NL), and finds that the fluctuation range of the detection values increases with rising ROTI. Based on previous findings, a regional threshold model is proposed. Under low scintillation conditions, a fixed threshold is selected; under strong scintillation conditions, an adaptive cycle slip threshold detection model is constructed by performing quadratic fitting based on the relationship between ROTI and the detection values. The proposed model is validated using GNSS observations collected from nine high-latitude stations during 2023–2024 and is compared with both the conventional fixed-threshold method and the dynamic threshold method proposed by Zhao et al. (2019). Compared to the fixed-threshold method, the false alarm rate of this scheme is reduced by 39.1
Accurate representation of the topside ionosphere is essential for GNSS ionospheric delay correction, but the effective scale height H used in NeQuick remains weakly constrained at high altitudes because of the limited availability of direct electron density observations. In this study, ISIS-2 topside sounder profiles from 1976 to 1979 are used to develop a continuity-constrained height-segmented correction for the NeQuick topside formulation. The correction is evaluated against alternative correction schemes and applied to NeQuick for topside electron density reconstruction and TEC estimation under different solar activity conditions. The experimental results show that the upper topside above 800 km exhibits clearer nonlinear scale-height behavior under lower solar activity. The quadratic upper-topside model reduces the MRE from 42.3 to 38.4
Low Earth orbit (LEO) satellite constellations have significant potential to enhance Global Navigation Satellite System (GNSS)-based positioning, navigation, and timing (PNT) applications. Spaceborne GNSS observations and inter-satellite link (ISL) measurements establish observation links between GNSS and LEO satellites and among LEO satellites, enabling more robust autonomous ephemeris generation. However, centralized processing imposes substantial communication and computational burdens, whereas conventional distributed approaches may neglect ISL-induced inter-satellite correlations, degrading orbit prediction performance. To address this issue, this study proposes a two-step distributed autonomous orbit determination (AOD) and broadcast ephemeris generation framework. In the first step, each satellite independently performs real-time orbit determination using only spaceborne GNSS observations, ensuring mutual independence of state estimates across the constellation. In the second step, ISL observations are incorporated to refine orbit states and dynamic parameters for orbit prediction and broadcast ephemeris fitting, while only the GNSS-based solutions are propagated in the time update to prevent correlation propagation. The proposed method is validated using real spaceborne GPS and K-band ranging (KBR) observations from the GRACE-FO mission, as well as simulated data from a Walker (120/12/0) constellation. Real-time orbit determination, orbit prediction, and 21-parameter broadcast ephemeris generation are evaluated and compared with GPS-only, conventional GPS+ISL distributed, and GPS+ISL centralized processing strategies. The results demonstrate that the proposed method reduces the broadcast ephemeris user range error (URE) by more than 19
Mixed-integer (MI) estimation theory is fundamental to carrier-phase GNSS, where real-valued parameters are coupled with integer ambiguities. The class of integer-equivariant (IE) estimators is the largest class that properly respects this structure. Its unbiased minimum mean-squared-error member is the best integer equivariant (BIE) estimator, whose precision is never worse than that of the BLUE and whose performance is often close to that of integer least-squares. Its practical drawback, however, is the need to evaluate an infinite sum. We introduce the projected-BIE (PBIE) estimator, a new unbiased minimum-variance IE-estimator with a finite representation. It is obtained by restricting the admissible periodic corrections in the canonical IE-representation and solving the resulting optimization problem. PBIE is valid for general observation distributions, has an exactly computable variance matrix, and is obtained from normal equations. We further show that PBIE has a dual optimality property: it is both minimum-variance in its class and the closest estimator in that class to the BIE. For normally distributed data, PBIE simplifies considerably and can be computed efficiently from the BLUE of the integer ambiguities.
Reconstructing vertical ionospheric electron density profiles from ground-based GNSS-derived total electron content (TEC) is a fundamentally ill-posed inverse problem, as TEC represents only an integral constraint on the electron density distribution. In this study, we propose TEC2Ne, a physics-informed deep learning framework that reconstructs station-level electron density profiles by explicitly embedding the intrinsic coupling between TEC and vertical ionospheric structure. The key innovation of TEC2Ne is the introduction of a physically fitted TEC feature (TECfit), derived using a genetic programming–based symbolic regression algorithm. TECfit quantitatively bridges global TEC maps and locally integrated digisonde electron densities, effectively constraining the solution space of the inverse problem and guiding the neural network toward physically consistent reconstructions. The model also incorporates empirical background profiles from IRI-2020, solar and geomagnetic indices, and lunar-phase–related parameters, forming a hybrid, data-driven and physics-guided reconstruction framework. TEC2Ne is validated against more than one solar cycle of digisonde observations at representative mid- and low-latitude stations. The reconstructed electron density profiles exhibit strong agreement with observations, achieving coefficients of determination (R2) exceeding 0.85 and substantially reducing reconstruction errors compared with the IRI-2020 model, empirical-NmF2 methods, and state-of-the-art data assimilation products. Feature attribution analysis based on integrated gradients demonstrates that TECfit is the dominant non-spatiotemporal contributor, accounting for over 20
The RINEX format has been around for many decades, providing an essential element to process GNSS data. Going from a RINEX file to a GNSS solution requires however a number of additional computation steps, in order to compute corrections to be applied to the GNSS observations, or information used in the estimation algorithm such as the Jacobian matrix of the observation models or weights attributed to a particular GNSS observation. This essential information is not readily available in existing GNSS open-source software. Our tool prx is an open-source python library that processes RINEX observation files, computes the typical parameters required by GNSS positioning algorithms and provides them to the user in a csv file. By providing such data, we propose a tool for GNSS researchers and engineers that will help dealing with low-level GNSS data processing, so that they can focus on positioning algorithms. This article provides information about the parameters computed by prx, and provides a comparison to rtklib, a widespread reference tool in the GNSS domain.
The Global Navigation Satellite System (GNSS) inherently exhibits sensitivity to geocenter motion. Inter-satellite links (ISLs) play a crucial role in both current and future GNSS developments, with the potential to offer enhanced precision and robustness in geocenter motion derived from GNSS. In this study, we investigate geocenter motion determined by individual GNSS systems and the combined multi-GNSS based on L-band and ISL data. L-band solutions show that the a priori solar radiation pressure (SRP) model reduces the STandard Deviations (STD) of the BDS-based geocenter coordinates X (GCC-X), Y (GCC-Y), and Z (GCC-Z) components by approximately 17
The BeiDou Global Navigation Satellite System (BDS) provides multi-frequency signals that facilitate carrier phase Ambiguity Resolution (AR). The widely known Three-Carrier Ambiguity Resolution (TCAR) method is proven to achieve rapid AR under open-sky conditions. However, in complex urban environments, signal blockages from buildings and multipath effects induced by Non-Line-of-Sight (NLOS) propagation contribute to significant pseudorange errors, which severely degrade TCAR performance and overall positioning accuracy. To address this challenge, an improved Multi-Layer Perceptron (MLP) model is developed to directly predict and correct Double-Differenced (DD) pseudorange errors. The corrected observations are integrated into the TCAR framework to enhance ambiguity resolution performance in challenging urban environments. Results from urban vehicular experiments demonstrate that the proposed method significantly outperforms conventional TCAR, achieving an average improvement of 41.2
Precise point positioning (PPP) is a key technology for achieving high-precision global navigation satellite system (GNSS) timing service. As one of the essential products for multi-frequency PPP, the differential code bias (DCB) products provided by International GNSS Service (IGS) analysis centers meet the requirements of precise positioning. However, due to inconsistencies in the reference definition between these DCB products and the hardware delay calibration values provided by the International Bureau of Weights and Measures (BIPM) time laboratories, existing DCB products cannot be directly applied to PPP timing. To address this issue, we propose a traceable DCB estimation method that establishes a link between the DCB reference and the UTC(k) maintained by time laboratories, thereby fulfilling the requirements of PPP timing. Our approach is validated using observation data from 236 Multi-GNSS Experiment (MGEX) stations and 9 time laboratories. The results demonstrate that: For satellite-specific traceable DCB, the stability of the proposed traceable products shows a maximum improvement of 0.20 ns (57
This study presents a simulation-based analysis to evaluate the impact of satellite clock stability, particularly that of emerging optical clocks, on global navigation satellite systems (GNSS) positioning performance. A controlled single-station precise point positioning-real time kinematic (PPP-RTK) framework is employed, with the provider and user receivers located over a short baseline to minimise spatially correlated errors, such as atmospheric delays and satellite orbit mismodelling, thereby isolating clock-induced effects. Seven representative satellite clocks are evaluated, including four atomic clocks currently onboard GNSS satellites and three prospective optical clocks: the compact rubidium optical clock (CROC), iodine modulation transfer spectroscopy (IMTS), and strontium lattice (SRL) clocks. Each clock is modelled using its respective Allan deviation (ADEV) profile under identical measurement conditions, ensuring that performance differences reflect only clock characteristics. Intentional delays in the delivery of state space representation (SSR) corrections are introduced to simulate realistic operational disruptions, with holdover time defined as the maximum period during which carrier-phase ambiguity resolution success rates remain above 99
Modeling real-time zenith total delay (ZTD) remains a challenge owing to the rapidly changing water vapor conditions influenced by geography and climate. In this contribution, we propose Trop_XS, an innovative architecture that integrates the extreme gradient boosting (XGBoost) and spherical cap harmonic analysis (SCHA) algorithms with multi-source heterogeneous data, to support real-time wide-area tropospheric augmentation services. With North America serving as the study region due to its representative complex topography and diverse climatic conditions, XGBoost rapidly fuses epoch-wise features and generates ZTD corrections at predefined grid points with a mean RMS below 11 mm. Building on the empirical ZTD mfodel, the enhanced SCHA-E solution is employed to model the ZTD corrections from reference sites and regular grids, achieving a favorable trade-off between accuracy and communication burden. Validated against 6-month post-processing ZTD from 31 external test stations, Trop_XS-derived ZTD achieves a mean RMS of 13.4 mm, outperforming MOFC, VMF3_SCHA, and GNSS_interp solutions by 25.3
Global Navigation Satellite System (GNSS) signals are increasingly affected by man-made intentional interferences, such as jamming and spoofing, underscoring the need for reliable and extensively evaluated interference detection techniques in protected GNSS frequency bands. This paper presents a GNSS signal anomaly detection method based on a Chi-Square statistical test applied directly to raw digitized intermediate-frequency (IF) samples, where an anomaly is defined as any man-made interference signal. A key contribution of this work lies in its extensive experimental evaluation, which spans a wide range of datasets, including multiple publicly available spoofing datasets that have been widely used by the research community, as well as data collected during a real-world GNSS jammer test campaign held in Norway in 2023 (JammerTest2023). The proposed method is implemented using the open-source software-defined receiver FGI-GSRx and evaluated under diverse and realistic signal propagation conditions. The results demonstrate anomaly detection rates exceeding 99
Precise forecasting of ionospheric Total Electron Content (TEC) is critical for safeguarding the reliable operation of satellite navigation and communication systems. However, the severe spatiotemporal heterogeneity exhibited during intense geomagnetic storms poses formidable challenges to existing modeling approaches. To address this, we propose TransTCN-XA, a hybrid deep learning architecture. Featuring an innovative dual-stream decoupled design, the model utilizes a Temporal Convolutional Network (TCN) and a spatial Transformer to extract temporal and spatial features, respectively, while introducing a Cross-Attention mechanism to achieve seamless feature integration. Leveraging Global Ionosphere Maps (GIM) released by the Center for Orbit Determination in Europe, a representative dataset covering representative geomagnetic storm events from 2012 to 2023 was constructed for training and validation. Experimental results indicate that during the main phase of extreme magnetic storms—characterized by a Dst index dropping to − 163 nT—TransTCN-XA exhibits exceptional robustness, achieving an accuracy improvement of approximately 21.9
In urban canyons, severe multipath and Non-Line-of-Sight (NLOS) reception caused by buildings and foliage severely degrade GNSS positioning reliability. Currently, data-driven machine-learning models that integrate signal-to-noise ratio, elevation angle, and other features, are widely used to identify signal-quality levels in complex environments. However, existing methods primarily rely on three-dimensional (3D) city models or panoramic cameras for NLOS signal labeling, which are prone to mislabeling at obstruction edges. Moreover, line-of-sight (LOS) category contains a large proportion of multipath interfered signals, making conventional stochastic models ineffective. To address these issues, this study proposes a fine-grained GNSS signal classification and stochastic-model optimization framework that operates without external auxiliary information. The method employs IQR and Jenks Natural Breaks to automatically stratify observations according to pseudorange errors, with category-specific optimized stochastic models fitted accordingly. Concurrently, an XGBoost-based machine learning model incorporating multiple features is developed for robust signal classification, with adaptive weighting factors assigned to different signal categories to enhance positioning performance. Experimental results demonstrate that the proposed classification stochastic model achieves better consistency with observation true errors, while significantly improving data utilization efficiency and terminal positioning accuracy. In a low-rise district of Hong Kong, 92.6
Soil moisture fulfills a critical role in hydrological processes, climate modeling, and agricultural management. Therefore, obtaining accurate soil moisture distributions with high spatiotemporal resolution has become increasingly essential for understanding land surface dynamics. The data provided by the Cyclone Global Navigation Satellite System (CYGNSS) mission via the use of spaceborne Global Navigation Satellite System Reflectometry (GNSS-R) technology offer the advantage of high temporal resolution, while synthetic aperture radar (SAR) data can provide information on surface features with high spatial resolution. Thus, these two types of data can be combined to generate soil moisture measurements with high spatial–temporal resolution. In this paper, a new soil moisture retrieval method is proposed by fusing CYGNSS (GNSS-R) and Sentinel-1 (SAR) data to simultaneously achieve high spatial and temporal resolutions. In this method, a functional relationship between the surface reflectivity of the spaceborne GNSS-R sensor and the backscattering coefficient of the SAR is established. By fusing Sentinel-1 and CYGNSS data, a two-layer machine learning framework is constructed for soil moisture retrieval. The machine learning-based model was trained on the basis of Soil Moisture Active Passive (SMAP) products to learn regional soil moisture patterns, and the retrieval independence and accuracy were rigorously validated using in situ measurements from the International Soil Moisture Network (ISMN) over a grassland region in the southern–central United States. The results indicated that the retrieved soil moisture is comparable to the SMAP product, with an average unbiased root mean square error (ubRMSE) of 0.070 cm3/cm3 and an average correlation coefficient of 0.65, but the temporal resolution was significantly enhanced, namely, by 3.9 times on average. This study demonstrates the feasibility of bridging the spatiotemporal gaps of current satellite products through GNSS-R and SAR data fusion.
