Prediction Of Vertical Total Electron Content Research Articles

Modeling Ionospheric TEC Using Gradient Boosting Based and Stacking Machine Learning Techniques

AbstractAccurately predicting and modeling the ionospheric total electron content (TEC) can greatly improve the accuracy of satellite navigation and positioning and help to correct ionospheric delay. This study assesses the effectiveness of four different machine learning (ML) models in predicting hourly vertical TEC (VTEC) data for a single‐station study over Ethiopia. The models employed include gradient boosting machine (GBM), extreme gradient boosting (XGBoost), light gradient boosting machine (LightGBM) algorithms, and a stacked combination of these algorithms with a linear regression algorithm. The models relied on input variables that represent solar activity, geomagnetic activity, season, time of the day, interplanetary magnetic field, and solar wind. The models were trained using the VTEC data from January 2011 to December 2018, excluding the testing data. The testing data comprised the data for the year 2015 and the initial 6 months of 2017. The RandomizedSearchCV algorithm was used to determine the optimal hyperparameters of the models. The predicted VTEC values of the four ML models were strongly correlated with the GPS VTEC, with a correlation coefficient of ∼0.96, which is significantly higher than the corresponding value of the International Reference Ionosphere (IRI 2020) model, which is 0.87. Comparing the GPS VTEC values with the predicted VTEC values based on diurnal and seasonal characteristics showed that the predictions of the developed models were generally in good agreement and outperformed the IRI 2020 model. Overall, the ML models used in this study demonstrated promising potential for accurate single‐station VTEC prediction over Ethiopia.

Bi-LSTM based vertical total electron content prediction at low-latitude equatorial ionization anomaly region of South India

In this study, we consider Bi-directional Long Short Term Memory (Bi-LSTM) model based Vertical Total Electron Content (VTEC) prediction over Thanjavur (Geographic 10.72˚ N, 79.01˚ E, Geomagnetic 2.34˚ N, 152.19˚ E) Global Positioning System (GPS) station. This station is located at low latitude Equatorial Ionization Anomaly (EIA) region of 2˚ geomagnetic dip latitude and has unique ionospheric dynamics. In this region, the VTEC prediction is crucial and challenging for space weather and the Sixth Generation (6G) Internet of Space (IoS) application to support early warning systems and future spatial data transmissions. A Deep Learning (DL) model based on Bi-LSTM was developed and trained for F10.7 and Dst index for predicting the VTEC. This study highlights the prediction of VTEC for any day that includes solstice and equinox time frames. The Bi-LSTM has an improvement of 28 % in mean absolute error (MAE), 48% in mean square error (MSE) and 24% in root mean square error (RMSE) as compared to the conventional Long Short Term Memory (LSTM) network. Hence, this Bi-LSTM model can be helpful to predict the VTEC in the EIA region and may be helpful to extrapolate over the unmeasured grid region of ocean and land.

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.

Predicting global ionospheric TEC maps using Gaussian process regression

The integration of machine learning technology into ionospheric prediction has emerged as a burgeoning field of research. However, several challenges still exist, such as the disregard of delays in real-world data acquisition, variations in accuracy due to different input data and methods. In this study, we present an ionospheric Gaussian process regression (GPR) model with multiple input parameters to forecast global ionospheric total electron content (TEC). We assess two solutions based on GPR model that leverage different ionospheric data, namely the vertical TEC (VTEC) and spherical harmonic coefficients (SHC) prediction solutions. Our findings demonstrate that both GPR models exhibit strong accuracy and stability. Specifically, for 1-day-ahead-predicted global ionospheric maps (GIMs) in 2015 year and 2019 year, the root mean square error (RMSE) of the SHC prediction solution is 4.343 TECU and 1.702 TECU, respectively, while the VTEC prediction solution has RMSE values of 4.321 TECU and 1.673 TECU. Moreover, in high and low solar activity, over 29% and 68% of the absolute residuals are within 1.0 TECU, respectively. Furthermore, we compare the GPR model with conventional methods (such as Adaptive Autoregressive Model (AAR)) and observe that the RMSE of the GPR model is lower than that of the AAR model for GIMs predicted under different solar and geomagnetic activities, with a difference ranging from 0.2 to 0.4 TECU. In addition, the GPR model can provide prediction intervals for the predicted values. These intervals are typically represented using the mean and standard deviation, where the mean represents the predicted value and the standard deviation represents the uncertainty associated with the prediction. Prediction intervals can assist users in understanding the uncertainty of the model's predictions.

Deep Learning for Global Ionospheric TEC Forecasting: Different Approaches and Validation

AbstractThe application of deep learning technology to ionospheric prediction has become a new research hotspot. However, there are still some gaps, such as the prediction effect with different input solar and geomagnetic activity parameters, and the forecast accuracy with different prediction methods as well as the validation of long period data results, to be filled. We developed an ionospheric long short‐term memory network (Ion‐LSTM) with multiple input parameters to predict the global ionospheric total electron content (TEC). Two solutions with different ionospheric data based on Ion‐LSTM were assessed, namely spherical harmonic coefficients (SHC) and vertical TEC (VTEC) prediction solution. The results show two solutions, both perform well in accuracy and stability. The input of the geomagnetic activity index improves the prediction effect of the model in the storm period. For the 1‐ and 2‐day‐predicted global ionospheric maps (GIMs) from 2015 to 2020, the root mean square error (RMSE) of SHC prediction solution is 1.69 TECU and 1.84 TECU while that of the VTEC prediction solution is 1.70 TECU and 1.84 TECU, respectively. Over 70% of the absolute residuals are within 3 TECU in high solar activity and over 96% in low solar activity. Further, by comparing the predicted results between Ion‐LSTM and conventional methods (e.g., Center for Orbit Determination in Europe (CODE) predicted GIMs), the evaluation results show that the RMSE of Ion‐LSTM is 0.7 TECU lower than that of CODE predicted GIMs under different solar and geomagnetic activities. Additionally, the accuracy of the Ion‐LSTM prediction results decreases slightly as the input time span increases.

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.

Ordinary kriging - and cokriging - based surrogate model for ionospheric TEC prediction using NavIC/GPS data

The ionospheric total electron content (TEC) plays a major role in the estimation of positional accuracy of satellite-based navigation systems. TEC disturbs the transmission of the signal transmitted from the satellite to receiver, which leads to range error. Hence, the prediction of VTEC can rectify the range errors in advance. Navigation with Indian Constellation (NavIC) is a navigational satellite system that gives position of a user and time information in India. NavIC receiver is installed at ACSCE, Bangalore, and it is utilized to estimate vertical total electron content (VTEC). In this paper, VTEC estimated from ACSCE station and VTEC obtained from IISC station, Bangalore, are compared and also ordinary kriging-based surrogate model (OKSM) and cokriging-based surrogate model (COKSM) are developed for forecasting NavIC/GPS VTEC. In these models, input parameters comprise the time, Bt, SSN, Ap and F10.7. NavIC and GPS VTEC are predicted for quiet days, i.e. from 16/1/2018 to 26/1/2018 and from 7/8/2018 to 13/8/2018, by using previous one week of VTEC data, and input parameters belong to ACSCE (12.8914° N, 77.4657° E) and IISC (13.0219° N, 77.5671° E) stations, Bangalore. The VTEC prediction results from OKSM and COKSM are compared. It shows that OKSM results are comparatively better than COKSM. In order to validate our developed models, OKSM and COKSM prediction results are compared with the SWIF model during storm days. Based on the comparison, it is observed that RMSE of OKSM is 3.5202 TECU, COKSM gives RMSE as 4.7126 TECU, and the SWIF model’s RMSE is 4.6804. From the comparison results, it is evident that OKSM yields better prediction results than COKSM and SWIF. These results indicate that the proposed model will be useful for correcting range measurement data in advance.

Forecasting of ionospheric TEC for different latitudes, seasons and solar activity conditions based on OKSM

Ionosphere is the upper atmosphere region that contains sufficient number of electrons which disturb the propagation of radio signal travel from navigational satellite to ground/user receiver. Ionospheric delay in range measurement is related to its Total Electron Content (TEC). Ionospheric delay results in range error and degrades the user position accuracy of navigational satellite systems such as Global Positioning System (GPS) and Indian Regional Navigational Satellite System (IRNSS). Hence a suitable TEC prediction model to correct the range delay in single frequency range measurement is necessary. In dual frequency receiver, ionospheric delay is estimated and eliminated using the two range measurements performed at the same time. This paper describes the TEC prediction methodology using Ordinary Kriging based Surrogate Model (OKSM). OKSM is evaluated using the data received and collected from the IRNSS receiver station installed at ACS College of Engineering (ACSCE), Bengaluru (12.8913 °N, 77.4658 °E), India and other International GNSS Service (IGS) network stations. IRNSS TEC data (January 2018) is calculated by using dual frequency (L5 & S) pseudo range method and TEC is smoothed by normal cubic smoothing spline method. IRNSS Vertical TEC (VTEC) is predicted from 16 January 2018 to 26 January 2018 by using previous six days of estimated VTEC values. Similarly, GPS VTEC for IGS station at IISC, Bengaluru is also predicted for same duration to validate the developed OKSM. In order to evaluate the performance of the developed forecasting model for different geographic locations, solar activity conditions and seasons, the VTEC is predicted and analyzed for different latitude regions such as low-latitude PHON station (6.9599 °N, 158.2101 °E), mid-latitude ALGO station (45.9588 °N, −78.0714 °E) and high-latitude NRIL station (69.3618 °N, 88.3597 °E) during different solar activity conditions (Low-2008, Medium-2011 and High-2013 solar activity) and during different seasons (spring, summer, rainy and winter) in the year 2017. From the analysis of OKSM prediction results, it is observed that, RMSE of predicted TEC varies from 0.79 to 3.6 TECU, MAE is 0.4 to 3 TECU and MAPE is within 40% for ionospheric quiet days. VTEC is also predicted during storm days (26 October 2003 to 31 October 2003). To study the performance of the model, VTEC prediction results of OKSM are compared with prediction results from Standard Persistence Model (SPM) and VTEC derived from International Reference Ionosphere (IRI-2016) model. The RMSE of OKSM is 1.9679 TECU, MAE is 1.245 TECU and MAPE is 9%, whereas for SPM, RMSE is 4.8372 TECU, MAE is 3.7496 TECU and MAPE is 36%. Similarly, for IRI-2016 model, RMSE is 7.9 TECU, MAE is 7.1976 TECU and MAPE is 66%. Therefore, TEC predictions by OKSM are better than SPM and IRI-2016. The results show that the OKSM is useful for applications in ionospheric studies.

Cokriging based statistical approximation model for forecasting ionospheric VTEC during high solar activity and storm days

The ionospheric storm is a space climate based event that takes place as a function of time, season and location. In spite of that, it is not yet possible to state how the ionosphere will react to a given space climate event since the measurements of the location, time of observation, amount of disturbances, and type of storm vary from event to event. Nevertheless, statistical analysis of observations in terms of Total Electron Content (TEC) enables one to calculate and forecast a most likely upcoming disturbed TEC, based on predictions of geomagnetic activity. The forecast of disturbed TEC is important and it helps users to know how much it affects the satellite communication systems. In this paper, GPS Vertical TEC (VTEC) data during ionospheric storm has been analyzed and storm-influenced features in the VTEC have been studied. Input parameters such as, location (Latitude & Longitude), Time, F10.7, Ap and Dst indices are collected from NASA website and its corresponding TEC values are used for construction of Cokriging (COK) based statistical approximation model. Prediction of VTEC is performed during storm and high solar activity days and for this purpose previous one-week data of different regions are used. The VTEC prediction is performed using COK model during high solar activity (2015) for IISC station. From the prediction, it is found that, our proposed COK model gives good prediction with RMSE of 6.5325 TECU, Correlation Coefficient as 0.9643 and Mean accuracy of 5.1752 TECU. Also VTEC prediction is performed over three different latitude regions during storm days (2003) and from the predicted results it is noted that, in high latitude region RMSE is 6.1848 TECU, correlation coefficient is 0.3958 and mean accuracy is 4.8105 TECU, in mid latitude RMSE is 12.7957 TECU, correlation coefficient is 0.9249 and mean accuracy is 9.2674 TECU and in low latitude RMSE is 11.5348 TECU, correlation coefficient is 0.9299 and mean accuracy is 9.2116 TECU. The results show that COK model provides good forecasting at low and mid latitude regions. Finally, prediction results of COK model is compared with the Empirical Orthogonal Function (EOF) and IRI-Plas-2017 models over Sutherland (−32.21°N, 20.81°E) station in South Africa during storm conditions. It is found that the average RMSE of EOF model is 5.91 TECU, average RMSE of the IRI-Plas-2017 model is 8.2079 TECU and average RMSE of COK model is 5.5971 TECU. Hence the prediction results show that COK model performs 5.6% better than the EOF model and 46.64% better than the IRI-Plas-2017 model. These results of the proposed COK model is encouraging and useful for indicating storm and high solar activity.

Modeling the global ionospheric variations based on complex network

The modern science of networks has brought significant advances to our understanding of complex systems. We employ the probabilistic graphical model to build complex networks to model the global ionospheric variations. The global ionospheric maps (GIMs) of vertical total electron content (VTEC) for the 12 months in 2012 have been selected analyze the ionospheric variations from the perspective of complex network. The information flow in the networks represents the causal interactions between the ionospheric variations at different locations. The distributions of the edges' geospatial distances in the ionospheric networks show that the information flow in the ionosphere is mainly transmitted locally, almost obeying the geospatial proximity principle. The asymmetric distribution of the edges' distances probably elucidates the more efficient transmission of ionospheric variations in the westward and southward directions. The community topologies within the ionospheric networks indicate the effect of the geomagnetic field and geographical distance on the information flow in the ionosphere. The geomagnetic field has shown an enhanced effect on the meridional interaction in the ionosphere, causing the vertical community topologies within the ionospheric networks at middle and low latitudes. For the ionospheric cells located at high latitudes in GIM, the geographical distances result in the horizontal community topologies. The fractal analysis reveals the existence of self-similar structure in the ionospheric networks on the global scale. The fractality in the ionospheric information flow may indicate the reasonability of the VTEC's prediction at a certain location by spatial prediction based on the data obtained in known regions.

Appraisal of ANN and ANFIS for Predicting Vertical Total Electron Content (VTEC) in the Ionosphere for GPS Observations

Positional accuracy in the usage of GPS receiver is one of the major challenges in GPS observations. The propagation of the GPS signals are interfered by free electrons which are the massive particles in the ionosphere region and results in delays in the transmission of signals to the Earth. Therefore, the total electron content is a key parameter in mitigating ionospheric effects on GPS receivers. Many researchers have therefore proposed various models and methods for predicting the total electron content along the signal path. This paper focuses on the use of two different models for predicting the Vertical Total Electron Content (VTEC). Artificial Neural Network (ANN) and Adaptive Neuro Fuzzy Inference System (ANFIS) algorithms have been developed for the prediction of VTEC in the ionosphere. The developed ANN and ANFIS model gave Root Mean Square Error (RMSE) of 1.953 and 1.190 respectively. From the results it can be stated that the ANFIS is more suitable tool for the prediction of VTEC. Keywords: Artificial Neural Network, Adaptive Neuro Fuzzy Inference System, Vertical Total Electron

Global prediction of the vertical total electron content of the ionosphere based on GPS data

Although vertical total electron content (VTEC) forecasting is still an open subject of research, the use of predictions of the ionospheric state at a scale of several days is an area of increased interest. A global VTEC forecast product for two days ahead, which is based exclusively on actual Global Positioning System (GPS) data, has been developed in the frame of the International Global Navigation Satellite Systems (GNSS) Service (IGS) Ionospheric Working Group (IGS Iono‐WG). The UPC ionospheric VTEC prediction model is based on the Discrete Cosine Transform (DCT), which is widely used in image compression (for instance, in JPEG format). Additionally, a linear regression module is used to forecast the time evolution of each of the DCT coefficients. The use of the DCT coefficients is justified because they represent global features of the whole two‐dimensional VTEC map/image. Also, one can therefore introduce prior information affecting the VTEC, for instance, smoothness or the distribution of relevant features in different directions. For this purpose, the use of a long time series of final/rapid UPC VTEC maps is required. Currently, the UPC Predicted product is being automatically generated in test mode and is made available through the main IGS server for public access. This product is also used to generate two days ahead preliminary combined IGS Predicted product. Finally, the results presented in this work suggest that the two days ahead UPC Predicted product could become an official IGS product in the near future.

An experiment of predicting Total Electron Content (TEC) by fuzzy inference systems

Abstract The Total Electron Content (TEC) is predicted by fuzzy inference systems for various station-satellite pairs. GPS data from the GRAZ, HFLK, LINZ, MOPI and UZHL permanent stations are processed in order to obtain the vertical total electron content (VTEC) using differenced carrier-smoothed code observations. The quality of the VTEC prediction was studied on 9 and 11 September 2005 (DOY 252 and 254). The predictions were computed for 5, 10 and 15 min intervals. The mean accuracies of predictions are about 0.1, 0.2 and 0.3 TECU for these time intervals. More than 98% of the VTEC is successfully recovered with the proposed prediction method.