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Vertical total electron content (VTEC) parameters estimated using global navigation satellite system (GNSS) data are of great interest for ionosphere sensing. Satellite differential code biases (SDCBs) account for one source of error which, if left uncorrected, can deteriorate performance of positioning, timing and other applications. The customary approach to estimate VTEC along with SDCBs from dual-frequency GNSS data, hereinafter referred to as DF approach, consists of two sequential steps. The first step seeks to retrieve ionospheric observables through the carrier-to-code leveling technique. This observable, related to the slant total electron content (STEC) along the satellite–receiver line-of-sight, is biased also by the SDCBs and the receiver differential code biases (RDCBs). By means of thin-layer ionospheric model, in the second step one is able to isolate the VTEC, the SDCBs and the RDCBs from the ionospheric observables. In this work, we present a single-frequency (SF) approach, enabling the joint estimation of VTEC and SDCBs using low-cost receivers; this approach is also based on two steps and it differs from the DF approach only in the first step, where we turn to the precise point positioning technique to retrieve from the single-frequency GNSS data the ionospheric observables, interpreted as the combination of the STEC, the SDCBs and the biased receiver clocks at the pivot epoch. Our numerical analyses clarify how SF approach performs when being applied to GPS L1 data collected by a single receiver under both calm and disturbed ionospheric conditions. The daily time series of zenith VTEC estimates has an accuracy ranging from a few tenths of a TEC unit (TECU) to approximately 2 TECU. For 73–96% of GPS satellites in view, the daily estimates of SDCBs do not deviate, in absolute value, more than 1 ns from their ground truth values published by the Centre for Orbit Determination in Europe.

The relationship between ionospheric research and global navigation satellite systems (GNSS) can be analysed through two approaches. The direct approach utilises ionospheric models to mitigate its influence, while the indirect approach leverages GNSS data to model ionospheric parameters. This study presents an indirect approach in which the total electron content (TEC), a fundamental parameter for ionospheric conditions, is modelled as a harmonic function using spherical harmonic (SH) expansion. Station-specific (local) and regional ionospheric models are developed by decomposing ionospheric influence into deterministic and stochastic components. GNSS data from seven evenly distributed stations in Serbia were used to estimate TEC coefficients. Local models were provided in the ION format as SH coefficients, allowing TEC determination at any epoch, while regional models had a 0.5∘×0.5∘ spatial and 2 h temporal resolution. The TEC root mean square (RMS) values ranged from 0.2 to 0.5 TECU (total electron content unit), with a mean of 0.3 TECU. Validation against global ionospheric maps showed agreement within 5.0 TECU. The impact of the SH expansion degree and order on TEC values was also analysed. These results refine regional ionospheric modelling, improving GNSS positioning accuracy in Serbia and beyond.

The precise description of the topside ionosphere using an ionospheric empirical model has always been a work in progress. The NeQuick topside model is greatly enhanced by adopting radio occultation data from the FORMOSAT-7/COSMIC-2 constellation. The topside scale height H formulation in the NeQuick model is simplified into a linear combination of an empirically deduced parameter H 0 and a gradient parameter g . The two-dimensional grid maps for the H 0 and g parameters are generated as a function of the foF 2 and hmF 2 parameters. Corrected H 0 and g values can be interpolated easily from two grid maps, allowing a more accurate description of the topside ionosphere than the original NeQuick model. The improved NeQuick model (namely NeQuick_GRID model) is statistically validated by comparing it to Total Electron Content (TEC) integrated from COSMIC-2 electron density profiles and space-borne TEC derived from onboard Global Navigation Satellite System observations, respectively. The results show that the NeQuick_GRID model can reduce relative errors by 38% approximately when compared to the integrated TEC from COSMIC profiles and by 15% approximately when compared to the space-borne TEC. Furthermore, a long-term statistical analysis during years of both high and low solar activities reveals that grid maps of the scale factor H 0 and the gradient parameter g have very similar features, allowing rapid and efficient acquisition of high-precision electron density during different solar activity.

Knowledge of ionospheric plasma altitudinal distribution is crucial for the effective operation of radio wave propagation, communication, and navigation systems. High-frequency sounding radars—ionosondes—provide unbiased benchmark measurements of ionospheric plasma density due to a direct relationship between the frequency of sound waves and ionospheric electron density. But ground-based ionosonde observations are limited by the F2 layer peak height and cannot probe the topside ionosphere. GNSS Radio Occultation (RO) onboard Low-Earth-Orbiting satellites can provide measurements of plasma distribution from the lower ionosphere up to satellite orbit altitudes (~500–600 km). The main goal of this study is to investigate opportunities to obtain full observation-based ionospheric electron density profiles (EDPs) by combining advantages of ground-based ionosondes and GNSS RO. We utilized the high-rate Ebre and El Arenosillo ionosonde observations and COSMIC-2 RO EDPs colocated over the ionosonde’s area of operation. Using two types of ionospheric remote sensing techniques, we demonstrated how to create the combined ionospheric EDPs based solely on real high-quality observations from both the bottomside and topside parts of the ionosphere. Such combined EDPs can serve as an analogy for incoherent scatter radar-derived “full profiles”, providing a reference for the altitudinal distribution of ionospheric plasma density. Using the combined reference EDPs, we analyzed the performance of the International Reference Ionosphere model to evaluate model–data discrepancies. Hence, these new profiles can play a significant role in validating empirical models of the ionosphere towards their further improvements.

Purely data‐driven ionospheric modeling fails to adequately obey fundamental physical laws. To overcome this shortcoming, we propose a novel ionospheric inversion model, Physics‐Informed Neural Network based on fully physical models SAMI3 (PINN‐SAMI3). The model incorporates the governing equations of the ionospheric physical model SAMI3 into the neural network to reconstruct the temporal‐spatial distribution of ionospheric plasma parameters. The objective of this study is to investigate the feasibility of integrating physical models with machine learning for ionospheric modeling. The PINN‐SAMI3 framework enforces physical laws through the multiple ion species of continuity, momentum, temperature equations in the magnetic dipole coordinate system. The simulation results show that if sparse ion densities are used as training data, it is possible to retrieve ionospheric electron densities, ion velocities and ion temperatures, respectively. The optimal physical constraints have been also investigated for different inversion quantities. Furthermore, the impact of incorporating E × B velocity terms on inversion results during the periods of ionospheric calm and geomagnetic storm is analyzed. The PINN‐SAMI3 achieves good inversion results even using sparse data in comparison to the traditional artificial neural networks (ANN). The framework will contribute to advance the future space weather prediction capability with artificial intelligence (AI).

The International Reference Ionosphere (IRI) model is widely used in the ionospheric community and considered the gold standard for empirical ionospheric models. The development of this model was initiated in the late 1960s using the FORTRAN language; for its programming approach, the model outputs were calculated separately for each given geographic location and time stamp. The Consultative Committee on International Radio (CCIR) and International Union of Radio Science (URSI) coefficients provide the skeleton of the IRI model, as they define the global distribution of the maximum useable ionospheric frequency foF2 and the propagation factor M(3,000)F2. At the U.S. Naval Research Laboratory, a novel Python tool was developed that enables global runs of the IRI model with significantly lower computational overhead. This was made possible through the Python rebuild of the core IRI component (which calculates ionospheric critical frequency using the CCIR or URSI coefficients), taking advantage of NumPy matrix multiplication instead of using cyclic addition. This paper explains in detail this new approach and introduces all components of the PyIRI package.

A comprehensive evaluation of Global Positioning System (GPS) Klobuchar, Galileo broadcast NeQuick2, international reference ionosphere (IRI) and global ionospheric map (GIM) models in estimating ionospheric total electron content (TEC) is performed using GPS-derived, constellation observing system for meteorology, ionosphere, and climate and JASON-2 TECs under various solar conditions in the Arctic and Antarctic. The performances of the four ionospheric models are first analysed for the overall polar regions. In addition, according to the temporal and spatial characteristics of the polar regions, the accuracies of the four models are evaluated for the polar days and nights, the Antarctic ice sheet (AIS) and the Arctic Ocean (AO), the Weddell Sea Anomaly (WSA) as well as for ionospheric storm. The results show that Klobuchar, NeQuick2, IRI2016 and GIM can mitigate the ionospheric delay by 28.69–29.41%, 44.57–56.09%, 43.38–55.99% and 67.17–77.56%, respectively. The performances of the four models during the polar days are obviously worse than those during the polar nights. In the AIS and AO, the Galileo broadcast NeQuick outperforms the GPS broadcast Klobuchar, and the root-mean-square error of IRI2016 performs almost the same as NeQuick2, but IRI2016 has a greater deviation. In addition, the GIM model can only mitigate the ionospheric delay by 46.81–56.72%, which is lower than other regions due to the lack of GPS ground station observations. Under the WSA conditions, the four models underestimate the real TEC to varying degrees, and the night-time deviations of the Klobuchar, NeQuick2 and IRI2016 models are significantly greater than the daytime deviations. The relative accuracy of four ionospheric models is lower during the ionospheric storm period than that in the ionospheric quiet period, especially the NeQuick2 and IRI2016 over the Antarctic.

This study presents an innovative approach to improving the accuracy and reducing the error convergence time of static Precise Point Positioning (PPP) in Global Positioning System (GPS) navigation. The research focuses on the impact of the high spatial and temporal resolution of a regional ionospheric data assimilation model on PPP over Taiwan. The study further evaluates the performance of both static PPP with the ionospheric information using commonly used models such as Klobuchar and International Reference Ionosphere (IRI), as well as a global ionospheric data assimilation model. Compared to the default IRI, the data assimilated IRI model can improve the overall ionospheric total electron content by approximately 83%. Additionally, it can significantly reduce horizontal positioning errors and shorten the error convergence time more than 52% for static PPP, even during geomagnetic storm events. The study concludes that the high resolution of a regional ionospheric data assimilation model can enhance the accuracy and reduce the error convergence time of PPP navigation and positioning. This research provides valuable insights for future studies in this field, especially in the development of more precise and efficient models for correcting ionospheric delay in GPS navigation.

This study applies the zero‐differenced integer ambiguity method, named PPP‐Fixed, to extract real‐time ionospheric data and eliminate the latencies of rapid/final Global Ionosphere Maps (GIMs). The PPP‐Fixed method is also used to derive ionospheric data for post‐processed GIM generation, named SGG Post‐GIM, combined with low earth orbit satellite data. The obtained hardware delays are applied to revise real‐time ionospheric data. Meanwhile, the estimated multi‐source ionospheric model is regarded as historical data to estimate an ionospheric prediction model for constraint using the semi‐parameter model. Then, the Kalman filter is employed to estimate the parameters to generate real‐time GIM. Finally, the accuracy of estimated real‐time GIM, named SGG RT‐GIM, and SGG Post‐GIM is assessed. During the experimental period, the mean differences of SGG Post‐GIM and SGG RT‐GIM relative to GIMs provided by the international Global Navigation Satellite System service, named IGSG, are −0.46 and −0.57 Total Electron Content Unit (TECU), respectively. The corresponding Root Mean Square (RMS) values are 1.64 and 3.08 TECU. Over the test period, the mean positioning errors of the single‐frequency precise point positioning corrected by IGSG, SGG Post‐GIM, SGG RT‐GIM, and Klobuchar model are 0.14, 0.19, 0.21, and 0.25 m in the horizontal direction, respectively, while the corresponding errors are 0.36, 0.33, 0.38, and 0.64 m in the up direction. Further, the mean biases of experimental days for the self‐consistency assessment are 0.06, −0.01, and −0.07 TECU for IGSG, SGG Post‐GIM, and SGG RT‐GIM, respectively. The corresponding RMS values are 1.19, 1.15, and 1.57 TECU.

The ionosphere is one of the important error sources that affect the communication of radio signals. The international reference ionosphere (IRI) model is a commonly used model to describe ionospheric parameters. The driving parameter IG12 of the IRI-2016 model was optimally updated based on GNSS-TEC data from 2015 and 2019. The electron density profiles and NmF2 calculated by the IRI-2016 model (upda-IRI-2016) driven by the updated IG12 value (IG-up) were evaluated for their accuracy using ionosonde observations and COSMIC inversion data. The experiments show that both the electron density profiles and NmF2 calculated by upda-IRI-2016 driven by IG-up show significant optimization effects, compared to the IRI-2016 model driven by IG12. For electron density, the precision improvement (PI) for both MAE and RMSE at the Beijing station exceed 31.2% in January 2015 and 16.0% in January 2019. While the PI of MAE and RMSE at the Wuhan station, which is located at a lower latitude, both exceed 32.5% in January 2015, both exceed 42.1% in January 2019, which is significantly higher than that of the Beijing station. In 2015, the PI of MAE and RMSE compared with COSMIC are both higher than 20%. For NmF2, the PI is greater for low solar activity years and low latitude stations, with the Wuhan station showing a PI of more than 11.7% in January 2019 compared to January 2015. The PI compared to COSMIC was higher than 17.2% in 2015.