Search Results (239)

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

GPS GNSS position signal manipulation in shipping can lead to significant navigational challenges. Such disruptions may result from various factors, including atmospheric conditions, satellite malfunctions, or intentional positioning satellite signal disturbance. Impacts on shipping operations include delays, increased operational costs, and safety risks for crews and vessels. Understanding these disturbances and their implications is crucial for enhancing maritime safety and efficiency. Common causes of GNSS disturbances in shipping include atmospheric effects such as ionospheric and tropospheric delays, satellite signal obstructions due to terrain or buildings, satellite malfunctions or failures, and intentional interference like jamming. These factors can lead to inaccuracies in positioning, affecting navigation and safety. GPS signals are vulnerable to various cyber threats, including spoofing, jamming, and signal interference. Spoofing involves sending counterfeit GPS signals to mislead receivers, while jamming disrupts the legitimate signals. Ensuring the integrity and security of GPSs is crucial for applications like navigation, timing, and critical infrastructure. Advanced encryption and authentication methods can help safeguard the security of GPS signals. These vulnerabilities can have profound implications for navigation systems and critical infrastructure. Enhancing GPS security requires a combination of advanced technologies and policies to improve signal integrity and authentication processes. The Global Positioning System (GPS) is the most widely used GNSS positioning method in commercial shipping. Moreover, deliberate disturbance technical birth mechanisms are similar across the field of GNSS systems. Therefore, this study focuses on the deliberate disturbance of the GPS, recognising the ability to upscale the research results to other commonly used GNSSs such as Beidou, Galileo, and Glonass. This paper introduces a behavioural approach to enhancing cybersecurity and preparedness to external threats in commercial shipping through European collaboration in the CyberSEA project. 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 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

The Galileo High Accuracy Service (HAS) has been operational since January 2023, offering good and stable performance. The next phase of HAS is currently being implemented, offering enhanced performance and new functionalities. One of the improvements in HAS Phase 2 will be the provisioning of ionospheric parameters to users in the European Coverage Area (ECA). This paper focuses on the new Message Type 2 (MT2) which will contain the ionospheric parameters, i.e., ionospheric vertical delays (IVDs) and ionospheric vertical accuracies (IVAs). IVDs and IVAs will be provided for ionospheric grid points (IGPs) which receivers in the ECA can see down to a certain elevation. Data for two ionospheric layers is planned to be provided. Because transmitting the IVDs and IVAs for a vast number of IGPs requires a significant amount of bandwidth, an investigation was also launched into different approaches for compressing the IVD data. To assess the efficacy of the compression, the percentage decrease in size was assessed through post-processing of historical data. Compared to non-optimized encoding of the IVDs using a fixed number of bits, processing of historical data showed a median IVD block size reduction of about 27% and 41% under solar maximum and solar minimum conditions, respectively. The IVD block compression approach will be evaluated further during the HAS Phase 2 implementation. Full article

High-frequency (HF) sensor networks play an irreplaceable role in remote sensing and emergency communications but suffer severely from ionospheric multipath interference, which degrades Time-of-Arrival (TOA) estimation accuracy. Conventional methods, such as the Generalized Cross-Correlation (GCC) and standard Delay-Locked Loops (DLL), often treat multipath components as noise, leading to significant measurement bias in dynamic environments. To address this, we propose a Multipath Separation and Independent Tracking (MSIT) architecture. This framework transforms multipath interference into valuable observables by establishing a closed-loop synergy: a Maximum Likelihood Estimation (MLE)-based module iteratively separates signal components, while parallel tracking loops update phase and delay parameters. Additionally, a super-resolution MUSIC algorithm is employed for initialization to resolve sub-chip multipath components. Simulations demonstrate that under disturbed channel conditions, the MSIT method achieves a mean delay estimation error reduction of about two orders of magnitude relative to the GCC method. Furthermore, field experiments on the Xi’an–Ürümqi link demonstrate its capability to stably resolve and track multiple propagation paths in real-world environments. This approach significantly enhances the measurement precision and reliability of HF sensing systems. Full article

The X1.59 solar flare on 3 July 2021, was the first X-class flare of Solar Cycle 25 and the first since the X-class flare on 10 September 2017. This event was notable for producing a rare geomagnetic crochet, a temporary and localized perturbation in Earth’s magnetic field during the flare’s peak. To the best of our knowledge, this study represents the first VLF-based analysis of this event, as well as the first comprehensive multi-instrument investigation of it. VLF observations from the NAA and DHO transmitters were used to investigate the ionospheric response via amplitude and phase variations. Key low ionosphere parameters, including the effective reflection height, sharpness factor, time delay and electron density profiles were derived. The results reveal rapid ionospheric responses closely correlated with X-ray flux peaks, including sudden phase and amplitude perturbations indicative of increased low ionosphere ionization and the geomagnetic crochet effect. Simultaneously, cosmic-ray measurements from ground detectors showed negligible modulation and no significant Forbush decrease, consistent with the flare’s weak and partially Earth-directed CME. Also, the spectrum of energetic protons measured in-situ in near-Earth space shows little disturbance. This integrated study demonstrates the sensitivity of the lower ionosphere to intense solar radiation and highlights the limited short-term impact on cosmic-ray and solar energetic proton flux, providing a comprehensive assessment of flare-driven space-weather effects during the early phase of Solar Cycle 25. 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

The accurate and rapid estimation of ionospheric delays is essential for PPP-RTK positioning. While traditional spatial interpolation methods like Kriging rely solely on geographic correlations, they often fail to capture rapid temporal variations in the ionosphere. To overcome this limitation, this paper proposes a long short-term memory (LSTM)-based interpolation method for interpolating ionospheric delays between satellites. The method leverages both spatial and short-term temporal correlations to generate accurate ionospheric corrections at user locations. The model uses a sliding window approach, taking the most recent 10 min of historical data as input to predict ionospheric delays at the current epoch. Experimental validation using data from a reference network in Australia—with average and maximum baseline lengths of 280 km and 650 km, respectively—demonstrates that the proposed LSTM method achieves a centimeter-level interpolation accuracy, with RMS errors between 0.06 m and 0.07 m under both quiet and geomagnetic storm conditions, significantly outperforming the Kriging method (0.27–0.44 m). In PPP-RTK, the LSTM model achieved a 3D positioning accuracy of 8.99 cm RMS during quiet periods, representing improvements of 51.9% and 28.8% over the No Constraint and Kriging methods, respectively. Under geomagnetic storm conditions, it maintained a 3D RMS of 24.54 cm—over 44% more accurate than other methods—and reduced the average time-to-first-fix (TTFF) to just 7.0 min, a 39.1% improvement. This study provides a novel approach for ionospheric spatial interpolation, demonstrating a particular robustness even during geomagnetic storms. Full article

The 27-day oscillation in total electron content (TEC) is analysed by means of world maps of TEC. The TEC maps are derived from measurements of the ground receiver network of the Global Navigation Satellite System (GNSS) and are provided by the International GNSS Service (IGS). The observed 27-day oscillation in TEC is mainly due to the 27-day solar rotation period, which induces a 27-day oscillation in extreme ultraviolet radiation (EUV) of the Sun. Analysing the time interval from 2003 to 2020, cross-correlation of the 27-day oscillation of the solar MgII-index of the Solar Radiation and Climate Experiment (SORCE) and the 27-day oscillation in TEC shows an average time delay of about 1.1 days for the ionospheric response with respect to the solar EUV variation. The average correlation coefficient of the solar and the ionospheric variation is 0.85. The cross-correlation of the 27-day oscillation in solar radio flux F10.7 and the 27-day oscillation in TEC gives a time lag of about 1.3 days and an average correlation coefficient of 0.78. The world maps of the amplitude of the 27-day oscillation in TEC are discussed for the TEC data from 1998 to 2024. Finally, TEC composites are derived for F10.7 enhancement events and geomagnetic storms. Full article

We present experimental results related to the features and geophysical conditions for the occurrence of the long-delay echo (LDE) signals in the medium-wave (MW) frequency range observed on 20 January 2025, at the Gor’kovskaya observatory near St. Petersburg (60.27° N, 29.38° E). A total of 19 series of experiments on guiding MF in the magnetosphere were carried out, while LDE signals were only registered on January 20, 2025, in evening hours, when the most disturbed conditions were observed (Kp = 4+, ΣKp = 27−). It was found that the LDE signals, with delay times of 310–322 ms, were observed in the evening hours under disturbed magnetic conditions. In such a case, the MW propagates into the magnetosphere to the magnetically conjugate point, is reflected from the topside ionosphere, and returns. The frequency of sounding signal f_SS exceeded the critical frequency of the F2 layer at Gor’kovskaya observatory foF2_GRK but was less than the critical frequency at the magnetic conjugated point foF2_MCP, foF2_GRK < f_SS < foF2_MCP. The LDE signals were observed in the narrow frequency range from 2100 to 2400 kHz. The background geophysical conditions during the occurrence of LDE signals were analyzed using the CADI ionosonde data and Swarm satellite observations. The plausible generation mechanisms for MW guiding in the magnetosphere are discussed. Full article

The undifferenced and uncombined (UDUC) model preserves raw code and carrier-phase observations for each frequency, avoiding differencing or ionosphere-free combinations. This approach enables the direct estimation of atmospheric parameters. However, the stochastic characteristics of these parameters, particularly ionospheric delay, are often oversimplified or based on empirical assumptions, limiting the accuracy and convergence speed of Precise Point Positioning (PPP). To address this issue, this study introduces a stochastic constraint model based on the power spectral density (PSD) of ionospheric variations. The PSD describes the distribution of ionospheric delay variance across temporal frequencies, thereby providing a physically meaningful constraint for modeling their temporal correlations. Integrating this PSD-derived stochastic model into the UDUC framework improves both ionospheric delay estimation and PPP performance, especially under disturbed ionospheric conditions. This paper presents a BDS PPP/PPP-AR method that estimates the ionospheric power spectral density (IPSD) in real time. Vondrak smoothing is applied to suppress noise in ionospheric observations before IPSD estimation. Experimental results demonstrate that the proposed approach significantly improves convergence time and positioning accuracy. Compared to the empirical IPSD model, the PPP mode using the estimated IPSD reduced horizontal and vertical convergence times by 11.1% and 13.2%, and improved the corresponding accuracies by 15.7% and 12.6%, respectively. These results confirm that real-time IPSD estimation, coupled with Vondrak smoothing, establishes an adaptive and robust ionospheric modeling framework that enhances BDS PPP and PPP-AR performance under varying ionospheric conditions. Full article

Currently, the PPP-B2b service faces challenges such as long convergence times and re-convergence issues after signal interruptions due to the lack of high-precision atmospheric enhancement. To address this, this study develops a multi-frequency uncombined Precise Point Positioning (PPP) model that accounts for Clock Constant Bias (CCB) based on PPP-B2b products, extracting atmospheric delays from reference stations and performing regional modeling. Considering the spatiotemporal characteristics of the ionosphere, a stochastic model for enhancement information that varies with time and satellite elevation is established. The performance of atmospheric-enhanced PPP-B2b is validated on the user end. Results demonstrate that zenith wet delay (ZWD) and ionospheric modeling generally achieve centimeter-level accuracy. However, during certain periods, ionospheric modeling errors are significant. By adjusting the stochastic model, approximately 98% of modeling errors can be enveloped. With atmospheric constraints, both convergence speed and positioning accuracy of PPP-B2b are significantly improved. Using thresholds of 30 cm horizontally and 40 cm vertically, the convergence times for horizontal and vertical components are approximately (16.7, 21.3) min for single BDS-3 and (3.8, 5.0) min for the dual-system combination, respectively. In contrast, with atmospheric constraints applied, convergence thresholds are met almost at the first epoch. Within one minute, single BDS-3 and the dual-system combination achieve accuracies better than (0.15, 0.3) m and (0.1, 0.2) m horizontally and vertically, respectively. Furthermore, even under high-elevation cutoff conditions, stable and rapid high-precision positioning remains achievable through atmospheric enhancement. Full article

To address the problem of the degraded positioning accuracy of the long-baseline undifferenced network RTK (URTK) under extreme space weather conditions, herein, we propose a user-side atmospheric delay estimation strategy based on the undifferenced network RTK concept to enhance positioning performance in geomagnetic storm environments. First, an ambiguity-resolution model that jointly estimates atmospheric error parameters is used to fix the carrier-phase integer ambiguities for long-baseline reference stations. The accurately fixed inter-station ambiguities are then linearly transformed to recover station-specific undifferenced integer ambiguities; undifferenced observation errors at each reference station are computed to generate corresponding undifferenced correction terms. Lastly, recognizing that ionospheric delays vary sharply during geomagnetic storms and can severely compromise the availability of regional undifferenced correction models, we estimate the residual atmospheric parameters on the user side after applying regional corrections. Experimental results show that the server side is not significantly impacted during geomagnetic storms and can continue operating normally. On the user side, augmenting the solution with atmospheric parameter estimation effectively improves positioning availability. Under strong geomagnetic storms, the proposed mode improves user-station positioning accuracy by 63.7%, 60.7%, and 64.4% in the east (E), north (N), and up (U) components, respectively, relative to the conventional user-side solution; under moderate storm conditions, the corresponding improvements are 16.7%, 10.0%, and 11.1%. Full article

A practical methodology for estimating regionally optimized Klobuchar coefficients using only International GNSS Service (IGS) Global Ionosphere Map (GIM) data is proposed. The method preserves computational simplicity, enabling near-real-time corrections suitable for accurate GNSS positioning. Utilizing both slant and vertical total electron content (STEC and VTEC) values extracted from GIM as inputs to estimate eight Klobuchar coefficients, robust parameter sets were obtained. Root mean square error (RMSE) analysis was used to compare these models to the standard Klobuchar model. Comprehensive performance evaluations using STEC-derived parameters, encompassing both seasonal and spatial analyses across South Korea, demonstrated significant reductions in ionospheric delay errors, with improvements reaching up to 57% compared to the conventional Klobuchar model. The far less computationally intensive VTEC-based model was applied over a wider region with 120 grid points. Continuous testing of this model over an entire year confirmed consistent enhancements in correction accuracy every day, demonstrating stable performance throughout the period. The developed regional Klobuchar models were further validated indirectly through satellite positioning performance, demonstrating daily RMSE improvements over the standard Klobuchar model ranging from 17.3% to 44.6%. Full article