Search Results (211)

High-temporal-resolution vertical total electron content (VTEC) inversion is important for ionospheric delay correction in maritime GNSS applications, but offshore single-station observations often suffer from limited satellite geometry, clustered ionospheric pierce points, and noise-sensitive least-squares (LSs) solutions. This study proposes a Virtual-Observation-Based Tikhonov Regularization (TVO) method for stabilizing ill-conditioned least-square VTEC inversion. TVO links the regularization factor to the condition number of the normal-equation matrix and selectively constrains higher-order spatial-gradient parameters while preserving background VTEC and receiver-bias terms. Experiments using the European mid-latitude station OBE4 and 17 surrounding stations on 1 July 2021 show that short epoch intervals and increased model complexity aggravate ill-conditioning, especially for the full quadratic model at 30 s. Compared with LS, TVO reduces the average RMS difference relative to the GIM-interpolated VTEC reference by 56.30% across the four VTEC models for the 17 stations. Maritime validation using South China Sea buoy data collected from 19 to 25 May 2025 further shows that TVO suppresses local discontinuities and amplitude anomalies, reducing the overall RMS difference relative to the GIM-interpolated VTEC reference from 26.07 TECU to 14.74 TECU. These results suggest that TVO can improve the numerical stability of maritime single-station VTEC inversion under constrained observation geometry. Full article

Analysis of variations in the components of the Earth’s magnetic field, recorded at the magnetic observatory of the Institute of Ionosphere (Almaty, Kazakhstan) during the earthquakes of 22 January 2024 and 4 March 2024, showed that these fluctuations were not related to intrinsic variations in the magnetic field itself, but rather to mechanical oscillations of the magnetometer together with its support. Evidence supporting the seismokinetic origin of the variations in the vector magnetometer was the discrepancy between the total magnetic field measured by the absolute magnetometer and the total magnetic field calculated from the vector magnetometer readings. Equations were derived that relate variations in the components of the magnetic field to the tilt angles of the sensor, enabling the determination of the direction of arrival of seismic shock waves. Azimuths of earthquake epicenters were calculated from oscillations observed in magnetogram records for several events, and these were compared with azimuths obtained from a network of seismic stations. It is shown that, in order to improve the accuracy of geomagnetic field measurements—required for the study of seismoelectric and seismomagnetic phenomena, as well as for identifying earthquake precursors—the design of magnetic observatories should be supplemented with an inclinometer to enable correction of vector magnetometer measurement results. Full article

The emerging potential of low-Earth-orbit (LEO) satellite-based Positioning, Navigation, and Timing services has increased the need for real-time, stable, and accurate orbit determination techniques. Here, we propose a method for estimating sub-meter-level LEO satellite orbits using Global Navigation Satellite System (GNSS) code pseudorange observations. To mitigate ionospheric delay, a dual-frequency ionosphere-free combination was applied, while code-carrier smoothing was employed to reduce code observation noise. A satellite weighting model based on Signal-in-Space Range Error was developed to reflect the orbit and clock error characteristics of different GNSS, and a robust weighting scheme was applied to alleviate the impact of observation outliers. Further, Galileo High Accuracy Service corrections compensated for orbit, clock and code bias errors. The algorithm was validated using the GNSS observation data collected from the Sentinel-6A satellite on 10 August 2023. Each successively applied technique gradually improved orbit determination accuracy, achieving up to a 51% reduction in 3D root mean square error (RMSE). The final RMSE values in the radial, along-track, cross-track, and 3D components were 39.4, 18.8, 23.5, and 49.6 cm, respectively. Temporal analysis showed no distinct periodicity in orbit errors and no significant correlation with satellite visibility or ground track. Full article

In complex urban environments, GNSS satellite signals suffer from severe multipath errors caused by building occlusion and reflection, which significantly degrades the accuracy of precise point positioning (PPP). This paper proposes a deep-learning-based multipath hemispherical grid correction model (DL-MHM) that integrates combined filtering and satellite embedding mechanisms. The model adopts the multi-system interoperable MHM framework to achieve effective multipath error correction. First, pseudorange and carrier phase observation residuals are calculated using the ionosphere-free combination for PPP. Then, a joint median and Kalman filtering scheme is applied to suppress noise in multi-day continuous residual sequences. A transformer-based time-series learning model is constructed, which introduces satellite-specific embedding vectors to characterize the differences between individual satellites and deeply fuse temporal features. This enables the model to adaptively fit the residual variation patterns of different satellites and accurately extract multipath errors. Finally, the multipath components predicted by the deep learning model are incorporated into the multi-system interoperable MHM model to generate the final multipath corrections. Test results show that in heavily obstructed urban scenarios, the root mean square (RMS) values of the east (E), north (N), and up (U) coordinate residuals are improved by 49.27%, 1.80%, and 3.35%, respectively, after DL-MHM correction compared to the uncorrected data. In open-sky environments, the corresponding improvements are 7.70%, 5.48%, and 34.28%. In all experimental scenarios, the proposed method outperforms both the conventional multipath hemispherical map (MHM) model and the convolutional neural network-long short-term memory (CNN-LSTM)-based MHM model in terms of overall multipath correction performance. The experimental results demonstrate that the proposed DL-MHM model can effectively mitigate multipath errors in complex urban scenarios and significantly improve the accuracy of GNSS precise positioning. Full article

The ionosphere is a major error source in single-frequency GNSS positioning, and Satellite-Based Augmentation Systems (SBAS) mitigate this effect by providing real-time correction information. However, the performance of SBAS under different latitude regions and geomagnetic activity levels still requires further evaluation. Taking EGNOS as an example, this study assesses SBAS-enhanced positioning performance using data from nine IGS stations across Europe. The experiments cover relatively low-, mid-, and high-latitude regions within the EGNOS service area, four representative quarters in 2023, and two disturbed geomagnetic events. Results show: (1) SBAS significantly improves positioning accuracy in all latitude regions, with overall improvement rates ranging from 62.11% to 83.51%. (2) The relatively low-latitude region achieves the largest performance gains, while the mid-latitude region provides the most stable and accurate results. (3) Under disturbed geomagnetic conditions, SBAS still outperforms conventional SPP, but its performance decreases compared with low-Kp periods, with latitude-dependent degradation observed at both MAS1 and SOD3. (4) The integrity analysis further shows that APV II availability reaches 91.85%, whereas CAT I availability decreases to 86.95% under disturbed conditions. Overall, SBAS effectively improves single-frequency positioning accuracy, stability, and integrity, but its performance remains affected by latitude and geomagnetic activity. Full article

Positioning, navigation, and timing (PNT) services require stable time transfer, but satellite-based PNT signals are vulnerable to interference, attenuation, and limited availability in constrained environments. Very-low-frequency (VLF) signals propagate over long distances in the Earth–ionosphere waveguide and can serve as a terrestrial complement to satellite-based timing systems. Their timing performance, however, is affected by propagation-delay variation, especially the diurnal component associated with changes in the effective ionospheric reflection height. This study presents a propagation-delay correction method for VLF timing signals based on a phase-variation model. The total delay error is separated into primary path delay, secondary propagation delay, and residual random error. The primary delay is calculated from the transmitter–receiver path, while the periodic secondary delay is corrected using the predicted phase variation. Historical Alpha observations recorded at Chongqing and Guilin were used to evaluate the correction performance. The results show that the corrected standard deviation is reduced to 2.0054–2.2500 μs for the Chongqing paths and 2.7987–4.4792 μs for the Guilin paths. The corrected root mean square error (RMSE) ranges from 2.1316 μs to 4.5641 μs across the six Alpha propagation paths. These results indicate that the proposed method can suppress the main diurnal propagation-delay component in the selected historical Alpha datasets, although further validation with contemporary and multi-season VLF observations is still needed. Full article

Low earth orbit (LEO)-enhanced global navigation satellite systems (GNSSs) (LeGNSSs) have emerged as a promising paradigm for next-generation precise point positioning (PPP). However, the highly dynamic nature of LEO satellites results in significant ionospheric variations with more frequent cycle slips. Thus, identifying fractional cycle slips and evaluating false alarms present significant challenges. In this paper, we propose an ionospheric preprocessing generalized combination (IPGC) method to improve the reliability of cycle slip detection. The ionospheric delay in the carrier phase is mitigated using the NeQuick model. Additionally, a set of specifically designed coefficients is used to combine LEO and GNSS observations, which increases the sensitivity of cycle slip detection. The simulation results indicate that the proposed method can effectively eliminate ionospheric interference of up to 4 cycles in LEO satellite cycle slip detection and can accurately detect all combinations of cycle slips with a maximum deviation of $0.14$ cycles. Compared with solutions without cycle slip repair, this method accelerates the positioning convergence time by $0.96/0.89/1.2$ min on the north/east/up (NEU) components, and the reconvergence efficiency is increased by factors of 10, $5.5$, and 2, respectively. Even with an elevated cutoff angle of ${40}^{\circ }$, the system achieves centimeter-level positioning accuracy ($0.38/1.08/1.86$ cm). These results confirm the effectiveness of the proposed method in LEO satellite cycle slip detection, providing key algorithmic guidance for the practical implementation of PPP in hybrid constellation systems. Full article

The Galileo High Accuracy Service (HAS) provides free-of-charge corrections for PPP through both the E6b signal and the internet. Currently, HAS targets a horizontal and vertical accuracy of 15 cm and 20 cm, respectively (68% confidence level) for static users. Although the service is not yet fully operational, it already delivers orbit and clock corrections, as well as satellite code biases. This paper evaluates the current performance of HAS, showing positioning errors below 5 cm in both horizontal and vertical components. However, the convergence time required to reach these accuracies remains relatively long. To address this limitation, ionospheric corrections were estimated from a European network of 34 stations and added to the processing. The results show a clear improvement in both accuracy and convergence time: horizontal and vertical errors were reduced by half, as well as the horizontal convergence time. To complete the HAS correction set, only satellite phase biases were missing. These were also generated using the same European network. Although no improvement was observed when including them, no degradation was found either. This suggests that, with further refinement, HAS could significantly benefit from phase biases and achieve even better positioning performance. Full article

Ionospheric effects constitute a key error source limiting the accuracy of surface deformation monitoring using L-band interferometric synthetic aperture radar (InSAR). Efficient identification of interferometric pairs affected by ionospheric disturbances is therefore essential for large-scale and high-throughput automated InSAR processing. To address this issue, a parameterized ionospheric detection method based on azimuth offsets derived from sub-aperture images is proposed. The proposed method integrates random-sampling pixel offset tracking (RS-POT) with piecewise Gaussian fitting to enable rapid and robust detection of ionospheric disturbances. Experimental validation was conducted using 50 interferometric pairs acquired by the LuTan-1 (LT-1) satellite, China’s first dual-satellite L-band SAR mission, covering high-, mid-, and low-latitude regions with varying ionospheric conditions. The results demonstrate that the proposed method can reliably identify ionospheric disturbances under diverse conditions while maintaining high computational efficiency. The proposed framework provides an effective solution for determining whether ionospheric correction is required, thereby improving the efficiency of automated interferometric processing workflows. Full article

Atmospheric refraction often influences the localization accuracy of ground-based radar for detecting space targets. Traditional methods generally utilize the measured troposphere and ionosphere data from the local station for atmospheric refraction correction and thus neglect the influence of atmospheric horizontal inhomogeneity. However, in practice, a horizontally inhomogeneous ionosphere often causes considerable residual errors in the measured range and elevation angle after refraction correction, especially for targets with low elevation angles. The ionospheric electron density profile along the wave propagation path is significantly different from that in the vertical direction of the local station, which further brings about challenges in the modeling and correction of atmospheric refraction errors. To address the above challenge, the effect of a horizontally inhomogeneous ionosphere on the range and elevation angle measured by ground-based radar is analyzed, and a geographic division modeling strategy for the ionospheric electron density along the propagation path for atmospheric refraction correction is proposed in this paper. The simulation results show that the oblique electron density distribution obtained from the proposed model agrees well with the results calculated by the International Reference Ionosphere (IRI) model, and the proposed methodology effectively suppresses residual errors in radar atmospheric refraction correction in the low-elevation detection case. Full article

Ionospheric delay is a dominant error source in global navigation satellite systems (GNSSs). Conventional ionospheric estimation relies on dense networks of expensive geodetic receivers, limiting accessibility and coverage. With the widespread availability of multi-frequency, multi-constellation smartphones capable of carrier-phase tracking, this study investigates smartphone-based ionospheric estimation. Using a single-reference Precise Point Positioning Real-Time Kinematic (PPP-RTK) framework, ionospheric delays are estimated from smartphone data and evaluated using real-time correction products from BeiDou PPP-B2b and Centre National d’Études Spatiales (CNES). Quality control is performed via solution separation testing with time-differenced carrier phase and time-differenced pseudorange. Field experiments with two Google smartphones and a geodetic receiver demonstrate that the estimated slant ionospheric accuracy is comparable to geodetic receivers within the meter level under both static and kinematic scenarios. Additionally, the horizontal positioning performance demonstrates that the positioning performance of the user smartphone with ionospheric corrections broadcast from the base smartphone is significantly improved, with 74.7% and 54.9% for CNES and PPP-B2b products compared with the conventional PPP solution. Furthermore, a comparison between ionospheric corrections generated from the smartphone and those obtained from the geodetic receiver reveals that the positioning performance of the user smartphone becomes comparable after convergence. Full article

This study evaluates the quality of ionosphere-corrected bending angle products from 12 satellite radio occultation (RO) missions, with data provided by the ROM SAF and CDAAC data centers. The missions include MetOp-B/C, Sentinel-6, Spire, COSMIC-2, KOMPSAT-5, and TerraSAR-X. The assessment focuses on bending angle quality control (QC), bias and noise characteristics at 65–80 km altitude, and statistical errors, with ERA5 data used as the reference. For quality control, Spire products achieved the highest pass rate, exceeding 99%. Products from the two MetOp satellites and Sentinel-6 exhibited pass rates above approximately 90%. The COSMIC-2 series had a pass rate of ~81%, while KOMPSAT-5 and TerraSAR-X had pass rates of 62% and 68%, respectively. Concerning bending angle biases, slightly larger biases were observed in MetOp setting events. Biases from other missions were mostly within the range of 0–0.05 μrad. Regarding noises, Sentinel-6 recorded the smallest bending angle noise (0.87 μrad), whereas TerraSAR-X (2.3 μrad) and KOMPSAT-5 (1.9 μrad) showed the largest noise magnitudes. Systematic differences in bending angles from all 12 RO missions were generally consistent below 60 km, while their standard deviations show good consistency below 35 km. In the middle stratosphere (35–50 km), MetOp-B/C and Sentinel-6 displayed the smallest standard deviations. Spire values are 1–2% larger, COSMIC-2 values 5–10% larger, and TerraSAR-X values the largest. Since ERA5 data also contain inherent uncertainties, particularly above 60 km, the findings of this study can only serve as a preliminary reference for users applying these datasets in weather and climate research. Future work will investigate the detailed causes of discrepancies among different datasets at high altitudes. Full article

Precise characterization of the thermospheric neutral wind is essential for comprehending the dynamic interactions within the ionosphere-thermosphere system, as evidenced by the development of models like HWM and the need for localized data. However, numerical models often suffer from biases due to uncertainties in external forcing and the scarcity of direct wind observations. This study examines the influence of incorporating actual neutral wind profiles from the Michelson Interferometer for Global High-resolution Thermospheric Imaging (MIGHTI) on the Ionospheric Connection Explorer (ICON) satellite into the Thermosphere Ionosphere Electrodynamics General Circulation Model (TIE-GCM) via an ensemble-based data assimilation framework. To address the challenges of assimilating real observational data, a robust background check Quality Control (QC) scheme with dynamic thresholds based on ensemble spread was implemented. The assimilation performance was evaluated by comparing the analysis results against independent, unassimilated observations and a free-running model Control Run. The findings demonstrate a substantial improvement in the precision of the thermospheric wind field. This enhancement is reflected in a 45–50% reduction in Root Mean Square Error (RMSE) for both zonal and meridional components. For zonal winds, the system demonstrated effective bias removal and sustained forecast skill, indicating a strong model memory of the large-scale mean flow. In contrast, while the assimilation exceptionally corrected the meridional circulation by refining the spatial structures and reshaping cross-equatorial flows, the forecast skill for this component dissipated rapidly. This characteristic of “short memory” underscores the highly dynamic nature of thermospheric winds and emphasizes the need for high-frequency assimilation cycles. The system required a spin-up period of approximately 8 h to achieve statistical stability. These findings demonstrate that the assimilation of data from ICON/MIGHTI satellites not only diminishes numerical inaccuracies but also improves the representation of instantaneous thermospheric wind distributions. Providing a high-fidelity dataset is crucial for advancing the modeling and understanding of the complex interactions within the Earth’s ionosphere-thermosphere system. Full article

Support Vector Machines (SVMs) are widely used in critical decision-making applications, such as precision agriculture, due to their strong theoretical foundations and their ability to construct an optimal separating hyperplane in high-dimensional spaces. However, the effectiveness of SVMs is highly dependent on the efficiency of the optimization algorithm used to solve their underlying dual problem, which is often complex and constrained. Classical solvers, such as Sequential Minimal Optimization (SMO) and Stochastic Gradient Descent (SGD), present inherent limitations: SMO ensures numerical stability but lacks scalability and is sensitive to heuristics, while SGD scales well but suffers from unstable convergence and limited suitability for nonlinear kernels. To address these challenges, this study proposes a novel hybrid optimization framework based on Open Competency Optimization and Particle Swarm Optimization (OCO–PSO) to enhance the training of SVMs. The proposed approach combines the global exploration capability of PSO with the adaptive competency-based learning mechanism of OCO, enabling efficient exploration of the solution space, avoidance of local minima, and strict enforcement of dual constraints on the Lagrange multipliers. Across multiple datasets spanning medical (diabetes), agricultural yield, signal processing (sonar and ionosphere), and imbalanced synthetic data, the proposed OCO-PSO–SVM consistently outperforms classical SVM solvers (SMO and SGD) as well as widely used classifiers, including decision trees and random forests, in terms of accuracy, macro-F1-score, Matthews correlation coefficient (MCC), and ROC-AUC. On the Ionosphere dataset, OCO-PSO achieves an accuracy of $95.71\%$, an F1-score of $0.954$, and an MCC of $0.908$, matching the accuracy of random forest while offering superior interpretability through its kernel-based structure. In addition, the proposed method yields a sparser model with only 66 support vectors compared to 71 for standard SVC (a reduction of approximately $7\%$), while strictly satisfying the dual constraints with a near-zero violation of $1.3\times {10}^{-3}$. Notably, the optimal hyperparameters identified by OCO-PSO ($\mathrm{C}=2$, $\gamma \approx 0.062$) differ substantially from those obtained via Bayesian optimization for SVC ($\mathrm{C}=10$, $\gamma \approx 0.012$), indicating that the proposed approach explores alternative yet equally effective regions of the hypothesis space. The statistical significance and robustness of these improvements are confirmed through extensive validation using 1000 bootstrap replications, paired Student’s t-tests, Wilcoxon signed-rank tests, and Holm–Bonferroni correction. These results demonstrate that the proposed metaheuristic hybrid optimization framework constitutes a reliable, interpretable, and scalable alternative for training SVMs in complex and high-dimensional classification tasks. Full article

Ionospheric delay errors significantly reduce the positioning accuracy of global navigation satellite systems (GNSSs), whereas precise ionospheric modeling can effectively mitigate this issue. The ionosphere exhibits large-scale symmetry, and spherical harmonics (SHs) can effectively describe this property due to their rotational symmetry on the sphere. However, mathematical fitting models such as spherical harmonic functions and polynomial models encounter boundary inaccuracies caused by edge effects. To address this problem, we developed a spherical harmonic–radial basis function (SH-RBF) hybrid method based on the integration of spherical harmonics and radial basis function interpolation techniques. This method leverages the global symmetry of spherical harmonics and utilizes the local adaptability of radial basis functions to correct regional distortions. Validation using European GNSS data during both geomagnetically quiet and active periods, in comparison with the CODE global ionospheric map (GIM), demonstrates that the modeling accuracy of spherical harmonics surpasses that of POLY during geomagnetically quiet periods. Compared to spherical harmonics, SH-RBF improves overall modeling accuracy by 8.87–27.27% and enhances accuracy in edge regions by 34.16–83.91%. During geomagnetically active periods, the SH-RBF method also achieves notable improvements. This study confirms that SH-RBF is a reliable technique for significantly reducing edge effects in regional ionospheric modeling. Full article