Ionospheric Vertical Total Electron Content Research Articles

Reconstruction of ionospheric VTEC using empirical orthogonal function and its performance during extreme geomagnetic storm

This paper demonstrates that the spatial distribution of the ionospheric TEC over the Indian region can be reconstructed with appreciable accuracy using minimal numbers of empirical orthogonal functions as a basis. These basis functions were derived using the Singular Value Decomposition of a matrix composed of pragmatic vertical Total Electron Content (VTEC) values collected across varied ionospheric conditions and measured over the region of interest. The reconstruction was achieved by linearly combining the appropriately chosen significant bases with corresponding weight factors. The reconstruction accuracy of the algorithm was found to be better than 4 TECU (TECU = 1016 electrons/m2) for more than 99.9 % of the time when tested over the complete year of 2016 with only eight basis vectors. The containment factor, defined here, indicates the goodness of the chosen bases in representing the arbitrary VTEC distributions and is found to remain typically high, aiding in improved algorithm performance. The performance, however, was found to be sensitive to the seasons and geomagnetic conditions. Deteriorated performance was observed when tested for the St. Patrick's Day storm data. The deterioration was attributed to the structural alteration of the ionospheric plasma density and the presence of atypical modes during the storm. The results ascertain the prospect of a faithful representation of the spatial distribution of the ionospheric VTEC using limited parametric variables, which may find utility in navigation, radar, and various other applications.

Machine learning based storm time modeling of ionospheric vertical total electron content over Ethiopia

Geomagnetic storms can cause variations in the ionization levels of the ionosphere, which is commonly studied using the total electron content (TEC). TEC is a crucial parameter to identify the possible effects of ionospheric variations on satellite communication and navigation. This paper assesses the performance of light gradient boosting machine (LGB) and deep neural network (DNN) machine learning algorithms in modeling ionospheric vertical TEC (VTEC) during geomagnetic disturbances. GPS VTEC data for years 2011–2016 from 13 dual-frequency receiver stations over Ethiopia was utilized. Input parameters for the models were derived from the factors that influence VTEC, such as time, location, geomagnetic activity, solar activity, solar wind, and the interplanetary magnetic field. The LGB model improved the predictions of the DNN model from root mean squared error (RMSE), mean absolute percentage error (MAPE), and R2 values of 5.45 TECU, 21%, and 0.93 to 4.98 TECU, 18%, and 0.94 on the testing data, respectively. The two machine learning models significantly outperformed the International Reference Ionosphere (IRI 2020) model during the selected geomagnetic storm periods. This study could provide insight into the impacts of ionosphere variations on satellite communication and navigation systems in the low-latitude ionospheric region.

A stacked machine learning model for the vertical total electron content forecasting

We design four Artificial Neural Network (ANN) models, namely a Multilayer Perceptron (MLP), a Convolutional Neural Network (CNN), an Extreme Learning Machine network (ELM) and an ensemble model based on stacking (STACKED) to forecast the ionospheric vertical Total Electron Content (vTEC) from 1 to 24 hours in advance on a single station at mid latitude. The time series used, spanning from January 2006 to December 2018, includes vTEC, provided by the Global Navigation Satellite System (GNSS) receiver at Tsukuba (TSKB), Japan (36.06o N, 140.05o E) and suitable external drivers selected among several helio-geophysical parameters. The selection of appropriate external drivers is made by rating their relevance on the vTEC at forecasting timescales (from 1 to 24 hours). The process, based on eleven machine learning models, highlights that the most important external drivers are: the 10.7 cm Solar Flux (F10.7), the magnitude BT of the Interplanetary Magnetic Field (IMF), and the Auroral Electrojet (AE) index. The forecasting performance of the four models (MLP, CNN, ELM, STACKED) is then analysed. The analysis relies on three statistical metrics to compare actual and forecasted vTEC: the coefficient of determination (R2), the Mean Absolute Error (MAE), and the Root Mean Squared Error (RMSE). Additionally, descriptive statistics are presented using box and whisker plots. The four ANN models show a quite satisfactory capability to forecast vTEC when applied to the test dataset which represents 10% of the available data from 2006 to 2018. Furthermore, by conducting a Wilcoxon signed rank test, it is shown that statistically significant improvements are achieved by the STACKED model with regard to MLP, CNN and ELM. On average, by analysing the forecasted (from 1 to 24 hours in advance) vs the actual vTEC, the STACKED model achieves R2=0.816,RMSE=0.426 TECu, and MAE=0.296 TECu (1 TECunit =1016 electrons/m2) whilst MLP, CNN and ELM show respectively R2=0.808,0.812,0.803,RMSE=0.436 TECu, 0.431 TECu, 0.441 TECu and MAE=0.304 TECu, 0.299 TECu, 0.312 TECu.

Physics-informed loss functions for vertical total electron content forecast

We design physics-informed loss functions for training Artificial Neural Network (ANN) models to forecast the ionospheric vertical Total Electron Content (vTEC) from 1 to 24 hours in advance. The ANN models exploit our physics-informed loss functions, data provided by the Global Navigation Satellite Systems (GNSS) receiver installed at Tsukuba (36.06o\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{o}$$\\end{document} N, 140.05o\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{o}$$\\end{document} E), Japan, and external drivers (solar and geomagnetic indices). The time series used span from January 1, 2006, to December 31, 2018, i.e., a full solar cycle. A proper set of external drivers for the ANN models training are selected by ranking their importance in relation to the vTEC dynamics at different forecasting horizons. They result to be the 10.7 cm Solar Flux (F10.7), the magnitude of the Interplanetary Magnetic Field (IMF) BT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\boldsymbol{B}_{\\boldsymbol{T}}$$\\end{document}, and the Auroral Electrojet (AE) index. Moreover, a second set of indices among those available has been considered as constraints in the design of the physics-informed loss functions. They are the Disturbance Storm Time (Dst) index, the solar wind speed v,BT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\boldsymbol{v}, \\boldsymbol{B}_{\\boldsymbol{T}}$$\\end{document}, and the By and Bz components of the interplanetary magnetic field. To assess the performance of the resulting ANN models, we use the statistical parameter coefficient of determination (R2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\boldsymbol{R}^{{\ extbf {2}}}$$\\end{document}), the standard deviation (SD), and the Wilcoxon non-parametric signed ranked test. We show that, in the testing period analyzed (from 2017-09-13, at 04:40:00, to 2018-12-31, at 23:55:00), one of our physics-informed loss functions provides a better performance of the ANN with regard to the standard loss function commonly adopted. In particular, when the new loss function is used in the ANN model, the average SD is minimized across all forecasting horizons in the training, validation and test datasets. SD is 0.2560 TECU, 0.3183 TECU and 0.4240 TECU for the training, validation and test dataset respectively, where 1 TECU = 1016\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ extbf {10}}^{{\ extbf {16}}}$$\\end{document} electrons/m2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\boldsymbol{m}^{{\ extbf {2}}}$$\\end{document}. The ANN model, incorporating the new loss function and applied to the test dataset, shows a significant improvement according to the Wilcoxon signed ranked test. In fact by selecting a significance level α=0.05\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\boldsymbol{\\alpha }~ \\mathbf {= 0.05}$$\\end{document}, the probability to obtain results by chance with the new loss function as compared to the standard loss function is 0.01504 (i.e., <α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$<\\alpha $$\\end{document}), which implies that the new loss function gives a statistical improvement to the forecasting capability of the ANN model. To the best of our knowledge, this is the first time a physics-informed loss function has been designed for the task of forecasting the ionospheric vTEC.

Characteristics of ionospheric disturbances during the 2021 Typhoon Chanthu based on GPS and GLONASS

Severe typhoons often result in substantial economic and human losses. Therefore, near-real-time monitoring and forecasting of severe typhoons have a significant importance. In this paper, characteristics of ionospheric disturbances during the 2021 Typhoon Chanthu are estimated and investigated from GPS and GLONASS measurements. We calculate high-precision de-trended and filtered ionospheric vertical total electron content (VTEC) data based on GPS and GLONASS data from intensive Global Navigation Satellite System (GNSS) observations at 30-second intervals in Taiwan. Based on the VTEC values, we analyze the characteristics of ionospheric disturbances caused by Typhoon Chanthu, such as the time of appearance of ionospheric disturbances, changes in the magnitude of these disturbances, alterations in two-dimensional disturbances, fluctuations in the speed of disturbance propagation, and shifts in the frequency spectrum. The results reveal that both GPS-TEC and GLONASS-TEC exhibit noticeable disturbances during the specified timeframe. These disturbances are accompanied by the occurrence of “N”-type anomalies in TEC. Notably, at the occurrence of the disturbance, the elevation angle of GPS PRN32 and GLONASS PRN1 satellites is approximately 50°-55°, and their respective distances from the typhoon eye are roughly 350 km and 150 km. The propagation velocity and center frequency of the ionospheric disturbances are located in the range of gravity waves. Specifically, the disturbances propagation speeds of GPS PRN32 and GLONASS PRN1 are approximately 129.36 m/s and 128.33 m/s, respectively, while the center frequencies are about 1.17 mHz and 1.43 mHz. The ionospheric perturbations observed by GPS and GLONASS exhibit certain similarities, which provide valuable insights into the relationship between typhoons and ionospheric disturbances.

GNSS/AQUA Fusion Study of Atmospheric Response Characteristics and Interaction Mechanisms during the 2022 Tonga Volcanic Eruption

A large-scale underwater volcanic eruption occurred at the volcano of Hunga Tonga-Hunga Ha’apai (HTHH) on 15 January 2022. At present, there is no consensus on the ionospheric response characteristics and interaction mechanism during volcanic eruptions. Based on the Global Navigation Satellite System (GNSS), AQUA satellite’s Atmospheric Infrared Sounder (AIRS), the experiment studies the response characteristics of the ionosphere and gravity waves during the eruption of the volcano and their interaction mechanisms and the International Real-Time Geomagnetic Observation Network (INTERMAGNET). First, a geomagnetic anomaly was detected before the eruption, which caused variations in the ionospheric VTEC (Vertical Total Electron Content) by about 15 TECU. Based on the IGS (International GNSS Service) observations, the VTEC distribution between 60° north and south latitudes was retrieved. The results show that before and after the eruption of Tonga Volcano, significant ionospheric anomalies were observed to the south, northwest and southwest of the volcano, with a maximum anomaly of 15 TECU. The study indicates that the geomagnetic anomaly disturbance is one of the precursors of volcanic eruption and has a certain degree of impact on the ionosphere. A correlation between geomagnetic anomalies and ionospheric anomalies was found to exist. The vast impact from the volcanic eruption excites gravity waves over the surface, which then propagate longitudinally, further perturbing the ionosphere. It is also detected that the ionospheric anomaly perturbation has a high coincidence effect with the gravity wave anomaly. Therefore, the gravity waves generated by atmospheric variations are used to explain the ionospheric perturbation phenomenon caused by volcanic eruptions.

A Novel Technique for High-Precision Ionospheric VTEC Estimation and Prediction at the Equatorial Ionization Anomaly Region: A Case Study over Haikou Station

This paper introduces a novel technique that uses observation data from GNSS to estimate the ionospheric vertical total electron content (VTEC) using the Kriging–Kalman method. The technique provides a method to validate the accuracy of the Ionospheric VTEC analysis within the Equatorial Ionization anomaly region. The technique developed uses GNSS VTEC alongside solar parameters, such as solar radio flux (F10.7 cm), Disturbance Storm Time (Dst) and other data, and Long Short Term Memory (LSTM) Networks to predict the occurrence time of the ionospheric equatorial anomaly and ionospheric VTEC changes. The LSTM method was applied to GNSS data from Haikou Station. A comparison of this technique with the neural network (NN) model and International Reference Ionosphere model shows that the LSTM outperforms all of them at VTEC estimation and prediction. The results, which are based on the root mean square error (RMSE) between GNSS VTEC and GIM VTEC outside the equatorial anomaly region, was 1.42 TECU, and the results of GNSS VTEC and VTEC from Beidou geostationary orbit satellite, which lies inside the equatorial ionization anomaly region, was 1.92 TECU. The method developed can be used in VTEC prediction and estimation in real time space operations.

Toward Real-Time GNSS Single-Frequency Precise Point Positioning Using Ionospheric Corrections

Real−time single−frequency precise point positioning (PPP) is a promising low−cost technique for achieving high−precision navigation with sub−meter or centimeter−level accuracy. However, its effectiveness depends heavily on the availability and quality of the real−time ionospheric state estimations required for correcting the delay in global navigation satellite system (GNSS) signals. In this study, the dynamic mode decomposition (DMD) model is used with global ionospheric vertical total electron content (vTEC) RMS maps to construct 24 h global ionospheric vTEC RMS map forecasts. These forecasts are assimilated with C1P forecast products, and L1 single−frequency positioning solutions are compared with different ionospheric correction models. The study examines the impact of assimilating predicted RMS data and evaluates the presented approach’s practicality in utilizing the IGRG product. The results show that the IGSG RMS prediction−based model improves positioning accuracy up to five hours ahead and achieves comparable results to other models, making it a promising technique for obtaining high−precision navigation.

Variability of Vertical Total Electron Content Gradients in the Brazilian Sector

Ground Based Augmentation Systems are designed to meet demanding requirements during airport approach and landing sections of aircraft routes. It computes corrected and smoothed differential corrections and other information. These messages are transmitted to aircraft, which may use the corrections to improve their position estimation. However, residual correction errors remain, due to ionospheric spatial and temporal gradients between Ground Based Augmentation System reference receivers and approaching aircrafts. Large vertical ionospheric delay gradients detected during combinations of extreme geophysical environments indicate that there are problematic conditions for Ground Based Augmentation System operation over the Brazilian region. Motivated by the above conditions, data from Rede Brasileira de Monitoramento Contínuo, the Brazilian public network of dual-frequency Global Navigation Satellite System receivers operated by Instituto Brasileiro de Geografia e Estatística were analyzed to estimate ionospheric vertical Total Electron Content gradients. The effects from different locations (represented by the dip latitude) and geophysical conditions (represented by solar activity, season, and local time) on variations of ionospheric vertical Total Electron Content gradients have been statistically quantified. The results from the present work provide information to more detailed performance assessments of Ground Based Augmentation System procedures under equatorial and low-latitude ionospheric regions, aimed at flexibly delimiting the conditions for feasible operation in such regions.

Statistical analysis of ionospheric vertical total electron content anomalies before global Mw≥6.0 shallow earthquakes during 2000–2020

To quantitatively investigate the relationship between earthquakes and ionospheric anomalies, this paper presents a statistical study of pre-earthquake vertical total electron content (VTEC) variations. A total of 1522 shallow (≤60 km) strong (Mw≥6.0) earthquakes in the global area during 2000-2020 are selected, and classified according to different magnitudes, latitudes and focal depths. A quartile-based process with different lengths of sliding windows, equaling 10 days, 15 days and 27 days, respectively, has been utilized to detect VTEC anomalies. The abnormal level is first defined, and then VTEC anomalies occurrence probabilities (Po) and occurrence rates (PE) within 1-10 days before 1522 earthquakes have been calculated. Besides, VTEC anomalies occurrence rates of the background days (PN) are also calculated. The results show that the significant correlation between Po and epicentral latitudinal locations could be observed within 1-10 days before earthquakes. The values of Po increase with larger magnitudes in the equatorial and low-latitude regions, but decrease with greater magnitudes in the mid- and high-latitude regions to some degree. Within 1-5 days before earthquakes, the overall trend of PE shows an increase with larger magnitudes, but the correlation between the values of PE and magnitudes is relatively weak in the southern mid- and high-latitude regions. There is no evident causality between PN and the magnitude, and most of the values of PE/PN are larger than 1, indicating that VTEC anomalies within a few days before earthquakes are probably related with the forthcoming earthquakes. Moreover, when the abnormal level exceeds 60%, different sliding window lengths have a significant impact on the values of Po and PE in the mid- and high-latitude regions. In particular, there are obvious systematic deviations between the values of Po obtained from different sliding windows in the southern mid- and high-latitude regions. However, the selection of the optimal sliding window needs to be further studied.

Assessment of Dynamic Mode Decomposition (DMD) Model for Ionospheric TEC Map Predictions

In this study, we assess the Dynamic Mode Decomposition (DMD) model applied with global ionospheric vertical Total Electron Content (vTEC) maps to construct 24-h global ionospheric vTEC map forecasts using the available International GNSS Service (IGS) 2-h cadence vTEC maps. In addition, we examine the impact of a EUV 121.6 nm time series data source with the DMD control (DMDc) framework, which shows an improvement in the vTEC Root Mean Square Error (RMSE) values compared with the IGS final solution vTEC maps. Both the DMD and DMDc predictions present close RMSE scores compared with the available CODE 1-day predicted ionospheric maps, both for quiet and disturbed solar activity. Finally, we evaluate the predicted global ionospheric vTEC maps with the East-North-Up (ENU) coordinate system errors metric, as an ionospheric correction source for L1 single-frequency GPS/GNSS Single Point Positioning (SPP) solutions. Based on these findings, we argue that the commonly adopted vTEC map comparison RMSE metric fails to correctly reflect an informative impact with L1 single-frequency positioning solutions using dual-frequency ionospheric corrections.

A Survey for GNSS Application of Ionospheric Information Extraction, Modeling, and Forecasting Techniques

lonospheric information plays a signifcant role in modern communication and navigation systems, This article provides a comprehensive survey of the application, modelingmethods,and results related to ionospheric infor-mation, The article frst introduces prerequisiteknowledge of the ionosphere,and then describesthe methods and techniques used in the extrac-tion of ionospheric information, the generationof ionospheric Vertical Total Electron Content(VTEC) maps, the modeling and interpolation ofthe ionosphere, and the forecasting of ionosphericinformation, The article also provides illustrativeexamples and fgures to demonstrate the effectiveness of the presented methods. Our surveyprovides insights and guidance for researchers andpractitioners interested in developing ionosphericmodeling and forecasting methods for GNSS applications.

Enhanced neural network model for regional ionospheric modeling and evaluation under different solar-geomagnetic conditions

Monitoring spatiotemporal variations of ionospheric vertical total electron content (VTEC) is crucial for space weather and satellite positioning. In the present study, an enhanced neural network (ENN) model is proposed to capture the changing characteristics of ionospheric VTEC and compared with the traditional mathematical models, i.e. the POLYnomial (POLY) model, generalized trigonometric series function and spherical harmonic function (SHF) model. The ionospheric VTEC data obtained from 31 permanent global positioning system stations in the southwest region of China on 26 August and 8 September, 2017, were used to test the performance of the mentioned models under different Solar-geomagnetic conditions. The ENN model is derived from the ensemble learning method, and the disadvantage that simple backpropagation neural network learners that are not robust enough is weakened by the ENN model. After statistical analysis and single-frequency precise point positioning (SF-PPP) experiments, it is demonstrated that the ENN model is superior to the above three mathematical models, regardless of the solar-geomagnetic conditions. In terms of mean absolute error, root mean square error, standard deviation, and mean absolute percentage error, the ENN model outperforms the SHF model, which is the best mathematical model in the analysis, by 40.7%, 30.20%, 29.88%, 38.04% under quiet solar-geomagnetic conditions, and by 37.66%, 29.93%, 30.96%, 32.01% under active solar-geomagnetic conditions. In addition, the accuracy of the SF-PPP is greatly affected by the error caused by ionosphere. In the static SF-PPP experiment of this study, the ENN model can better correct ionospheric error. Under quiet and active solar-geomagnetic conditions, the SF-PPP accuracy can be improved by 85.1% and 85.2% with the ionosphere delay correction from the ENN model.

SHAKING: Adjusted spherical harmonics adding KrigING method for near real-time ionospheric modeling with multi-GNSS observations

Precise positioning based on Global Navigation Satellite System (GNSS) technique requires high accuracy ionospheric total electron content (TEC) correction models to account for the ionospheric path delay errors. We present an adjusted Spherical Harmonics Adding KrigING method (SHAKING) approach for regional ionospheric vertical TEC (VTEC) modeling in real time. In the proposed SHAKING method, the VTEC information over the sparse observation data area is extrapolated by the Adjusted Spherical Harmonic (ASH) function, and the boundary distortion in regional VTEC modeling is corrected by the stochastic VTEC estimated using Kriging interpolation. Using real-time GPS, GLONASS and BDS-2/3 data streams of the Crust Movement Observation Network of China (CMONOC), the SHAKING-based regional ionospheric VTEC maps are re-constructed over China and its boundary regions. Compared to GNSS VTECs derived from the independent stations, the quality of SHAKING solution improves by 13–31% and 6–33% with respect to the ASH-only solution during high and low geomagnetic periods, respectively. Compared to the inverse distance weighting (IDW) generated result, significant quality improved of SHAKING-based VTEC maps is also observed, especially over the edge areas with an improvement of 60–80%. Overall, the proposed SHAKING method exhibits notable advantage over the existing regional VTEC modeling techniques, which can be used for regional TEC modeling and associated high-precision positioning applications.

Long short-term memory and gated recurrent neural networks to predict the ionospheric vertical total electron content

This paper provides the application of deep learning models such as Long Short-Term Memory (LSTM) and a recently proposed Gated Recurrent Unit (GRU) in forecasting the ionospheric GPS_VTEC, and compare the performance of the results with that of Multilayer Perceptron (MLP) neural networks, GIM_TEC and the IRI-Plas 2017 models. GPS_VTEC time series data estimated from GPS measurement over low latitude equatorial station MAL2 with (geo.lat -2.70NandLong40.190E) located in Kenya is used in this study. The data span from January 1, 2010 to December 31, 2018 which covers 9 years of solar cycle 24. The data from the year 2010 to 2016 is used for the training, while the year 2017 data is used for validation and finally the data in the year 2018 is used to examine the performance of the models during the testing period. The performance of the models is based on statistical parameters such as root-mean-square error (RMSE) and correlation coefficient (R). The GRU unit shows a correlation coefficient of 0.971 with GPS_VTEC and a prediction error of 2.004 TECU while that of LSTM, MLP, GIM_TEC, and IRI-Plas 2017 models are 0.967, 0.951, 0.832 and 0.774 with a prediction error of 2.055 TECU, 2.336 TECU, 5.913 and 16.183 TECU, respectively. This shows that the predictions of the gated system models are better than the MLP, GIM_TEC and IRI-Plas models. Considering the prediction ability of these models to forecast the GPS-VTEC values under an intense Geomagnetic Storm event, it is observed that the GRU unit can achieve the best prediction accuracy and shows a strong performance for the trend prediction of this event more than the LSTM, MLP, GIM_TEC, and IRI-Plas models. In all, the three deep learning models perform better than the GIM_TEC and the IRI-Plas 2017 model.

Design of Ionospheric TEC Gradient Anomaly Detection Platform Based on GNSS

Abstract Ionospheric anomalies can seriously threaten important flight phases such as approach and landing, so accurate real-time monitoring is necessary. In this paper, an ionospheric anomaly gradient detection platform is designed for satellite navigation receiver. Based on GNSS observation data, the spatial gradient of ionospheric vertical total electron content is calculated, and anomaly ionospheric gradient is detected using generalized likelihood ratio test method. To verify the correctness of detection results, rate of TEC change index is also calculated for comparison. Simulation results show that the platform can detect ionospheric anomaly gradient state fast and accurately, and the proposed approach can used by GNSS receivers to detect ionospheric anomaly.

A study of vTEC above Nepal exploring different calibration techniques, including a comparison with the NeQuick-2 model

In this paper, we investigate the performance of the NeQuick 2 (NeQ-2) model with respect to Ciraolo’s and Gopi’s derived ionospheric vertical Total Electron Content (vTEC) during the years 2014 and 2015. GPS observables derived from dual-frequency receivers over western Nepal (Simikot, Bhimchula, and Nepalganj) are processed to obtain the experimental vTEC utilizing Gopi’s and Ciraolo’s calibration procedures. The monthly and seasonal behavior of vTEC obtained from each calibration technique is compared with the vTEC obtained from the NeQ-2 model during a quiet period. It is observed that the vTEC value obtained from all studied approaches started to increase from 00:00 Universal Time (UT = Local Time(LT) +5:45), reached a maximum around 08:00 UT (13:45 LT), followed by a decrease, attaining a minimum value around 23:00 UT (4:45 LT). Moreover, a comparative study showed that vTEC computed using the Ciraolo calibration technique overestimates GPS vTEC, calculated in all hours and months by Gopi’s approach. In the Spring and Summer, vTEC derived using Ciraolo’s TEC calibration overestimates NeQ-2 and underestimates it in the Autumn and Winter. It is found that NeQ-2 model vTEC is favorably associated with GPS vTEC obtained using the Gopi procedure in Spring and correlates with the Ciraolo technique in Autumn. Two GPS vTEC estimations demonstrate superior consistency in the Summer and Winter seasons over the region of Nepal. It is found that the mean absolute difference between NeQ-2 prediction and GPS vTEC procured through the Gopi approach is less on the storm event day. By contrast, it is discovered less by the Ciraolo technique when the storm is recovering (except for a few cases).

High‐Resolution and Accurate Low‐Latitude Gridded Electron Density Generation and Evaluation

AbstractThe accurate specification of three‐dimensional (3‐D) ionosphere states is crucial to positioning, navigation, and communication systems, especially in low‐latitude and equatorial regions. In this work, the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC‐2) radio occultation total electron content was assimilated around a whole year from October 2020 to September 2021 via the Kalman filter (KF) data assimilation system. This system includes an empirical ionosphere background model and the KF data assimilation algorithm. Accurate 3‐D ionosphere data assimilation results were produced hourly with spatial resolutions of 2° latitude, 5° longitude, and 20 km height in low‐latitude and equatorial regions. First, the results were validated by Massachusetts Institute of Technology vertical total electron content and global ionosonde data. The ionosphere vertical total electron content and the critical frequency at the F2 layer agree well with the independent observations. Then, a general ionosphere climatological pattern is found in the reconstructed 3D ionosphere results, including seasonal variation, annual asymmetry, and December anomaly. In addition, the results can well capture the daily spatial and temporal ionospheric variations in the day‐to‐day variability, the longitudinal wave 4 structures, and the interhemispheric asymmetry transition of the equatorial ionization anomaly crests. The current results demonstrate that assimilating COSMIC‐2 TEC observations can further improve the 3D ionosphere specification in low‐latitude and equatorial regions and can also contribute to physical research on ionosphere variability characteristics.

A Novel GNSS Single-Frequency PPP Approach to Estimate the Ionospheric TEC and Satellite Pseudorange Observable-Specific Signal Bias

As the significant error sources influencing the Global Navigation Satellite System (GNSS) positioning, navigation, and timing (PNT) services, ionospheric delay and satellite hardware delay should be properly calibrated. Particularly, the pseudorange observable-specific signal bias (OSB) is convenient and can be directly corrected in the raw pseudorange measurement. In this work, we present a novel single-frequency ionospheric-free-half precise point positioning (PPP) (SFPPP2) approach for ionospheric studies, in which the ionospheric vertical total electron content (VTEC) and satellite OSB are isolated from the slant ionospheric observables by means of the ionospheric multilayer mapping function (MF). The computation and parameterization methods of the ionospheric VTEC and satellite pseudorange OSB are present. To validate the effectiveness and reliability of the novel method, we investigate and compare the performance of the single-frequency ionospheric-float PPP (SFPPP1), SFPPP2, and dual-frequency ionospheric-float PPP (DFPPP1) solutions for ionosphere sensing. The analytical results indicate that the novel approach can extract the slant ionospheric observables with the accuracy of submeters. The accuracy of the estimated ionospheric VTEC by the single-frequency PPP approaches is in the submeter level, which exhibits a slightly worse accuracy than that from the dual-frequency PPP solution. The estimated ionospheric VTEC accuracy is improved with the multilayer MF compared with the single-layer MF. The estimated BeiDou Navigation Satellite System (BDS) pseudorange OSB with the proposed SFPPP2 approach is stable, reliable, and of the high accuracy, and the rms’s with respect to Chinese Academy of Sciences (CAS) product for C2I and C6I signals with single-layer and multilayer MFs are 0.40, 0.41, 0.60, and 0.63 ns, respectively. The proposed PPP approach can retrieve the VTEC and satellite pseudorange OSB by mass-market receivers for the GNSS users.

Ionospheric vertical total electron content prediction model in low-latitude regions based on long short-term memory neural network

Ionosphere delay is one of the main sources of noise affecting global navigation satellite systems, operation of radio detection and ranging systems and very-long-baseline-interferometry. One of the most important and common methods to reduce this phase delay is to establish accurate nowcasting and forecasting ionospheric total electron content models. For forecasting models, compared to mid-to-high latitudes, at low latitudes, an active ionosphere leads to extreme differences between long-term prediction models and the actual state of the ionosphere. To solve the problem of low accuracy for long-term prediction models at low latitudes, this article provides a low-latitude, long-term ionospheric prediction model based on a multi-input-multi-output, long-short-term memory neural network. To verify the feasibility of the model, we first made predictions of the vertical total electron content data 24 and 48 hours in advance for each day of July 2020 and then compared both the predictions corresponding to a given day, for all days. Furthermore, in the model modification part, we selected historical data from June 2020 for the validation set, determined a large offset from the results that were predicted to be active, and used the ratio of the mean absolute error of the detected results to that of the predicted results as a correction coefficient to modify our multi-input-multi-output long short-term memory model. The average root mean square error of the 24-hour-advance predictions of our modified model was 4.4 TECU, which was lower and better than 5.1 TECU of the multi-input-multi-output, long short-term memory model and 5.9 TECU of the IRI-2016 model.