Ionospheric Grid Points Research Articles

MLP-based user-applicable method for SBAS GIVD calibration: A comparative study based on CODE final GIM products

Satellite-Based Augmentation Systems (SBASs) are designed to enhance the performance of Global Navigation Satellite Systems (GNSSs) for civil aviation users. As SBAS Geostationary Earth Orbit (GEO) satellite signals are received in a wide area, far more non-aeronautical GNSS users utilize SBAS to improve navigation performance. Since ionospheric delay is the principal error source of GNSS and a leading correction aspect of SBAS, the GEO-broadcast ionospheric data quality of six SBASs over the past three years is assessed in this article. Results show that European Geostationary Navigation Overlay Service (EGNOS), System for Differential Correction and Monitoring (SDCM), and Wide-Area Augmentation System (WAAS) have the highest Grid Ionospheric Vertical Delay (GIVD) accuracy judged by the residual Standard Deviation (STD), then followed by BeiDou SBAS (BDSBAS) and Multi-functional Satellite Augmentation System (MSAS), while GPS-Aided GEO Augmented Navigation (GAGAN) is the worst. The 6 m Grid Ionospheric Vertical Error (GIVE) availability is over 90 percent of the time for most Ionospheric Grid Points (IGPs) of all tested SBASs. However, GAGAN and WAAS have a significant availability decline at 3 m GIVE. In addition, the integrity limits of MSAS and WAAS are fairly conservative. In contrast, the confidence bounds of BDSBAS and SDCM are excessively radical that fail to meet the integrity requirement. To improve the ionospheric data quality received from SBAS, a Multi-Layer Perceptron (MLP)-based user-applicable GIVD calibration method is proposed in the article. A well-trained MLP learned temporal and spatial correlations of the IGP delays and extracted transfer functions between broadcast and reference GIVDs to eliminate error. The SBAS processing errors in Differential Code Bias (DCB) compensation, GIVD estimation modeling, and GEO message quantization are rectified by the MLP trained by abundant historical data with Center for Orbit Determination in Europe (CODE) final Global Ionospheric Maps (GIMs) as reference. Test results on real-time data show that over 85 percent IGPs have STD decline after calibration. The STD declination rates of six SBASs except for SDCM are over 15 percent, and the Mean Absolute Error (MAE) and Root Mean Square Error (RMS) calibration effects are dramatic for all systems. Finally, the average GIVEs are reduced by more than 50 percent for EGNOS, GAGAN, MSAS, and WAAS with a 99.9 percent integrity level maintained. Despite no promotion on availability for BDSBAS and SDCM, the proposed method compensates for the integrity issues of the systems.

Maximum eigenvalue detection for local ionospheric anomaly - theory, cases, statistics, and potential application

At low latitudes in China, local ionospheric anomalies are frequent and difficult to capture, posing positioning errors and safety risks to GNSS users. This leads to conservative error bounds in GNSS augmentation systems. For example, in Satellite Based Augmentation System (SBAS), the presence of under-sampled regions and the ionospheric instability at low latitudes can result in an over-conservative error bound, i.e., Grid Ionospheric Vertical Error (GIVE) with reduced availability. Ionospheric irregularity detectors could be used to exclude anomalies from the grid model to share the integrity risk and tighten the GIVE. The detection method needs to have theoretical validity and sensitivity to small local anomalies. However, current irregularity detectors are designed for Ionospheric Grid Point (IGP), dealing with wide-area spatial anomalies. The problem of decreased availability resulting from the over-conservative error bound caused by the frequent local ionospheric anomalies is unsolved, especially at low latitudes and the equatorial region. To further enhance the GNSS performance, the applicability analysis of a maximum eigenvalue-based ionospheric irregularity detector, which is sensitive to local-scale spatial anomalies, is presented. The detection capability of MED for ionospheric anomalies is demonstrated by theory, cases, statistics, and simulation applications. This method can also be used for ionospheric monitoring in geodesy or geophysics.

Ensemble Machine Learning of Random Forest, AdaBoost and XGBoost for Vertical Total Electron Content Forecasting

Space weather describes varying conditions between the Sun and Earth that can degrade Global Navigation Satellite Systems (GNSS) operations. Thus, these effects should be precisely and timely corrected for accurate and reliable GNSS applications. That can be modeled with the Vertical Total Electron Content (VTEC) in the Earth’s ionosphere. This study investigates different learning algorithms to approximate nonlinear space weather processes and forecast VTEC for 1 h and 24 h in the future for low-, mid- and high-latitude ionospheric grid points along the same longitude. VTEC models are developed using learning algorithms of Decision Tree and ensemble learning of Random Forest, Adaptive Boosting (AdaBoost), and eXtreme Gradient Boosting (XGBoost). Furthermore, ensemble models are combined into a single meta-model Voting Regressor. Models were trained, optimized, and validated with the time series cross-validation technique. Moreover, the relative importance of input variables to the VTEC forecast is estimated. The results show that the developed models perform well in both quiet and storm conditions, where multi-tree ensemble learning outperforms the single Decision Tree. In particular, the meta-estimator Voting Regressor provides mostly the lowest RMSE and the highest correlation coefficients as it averages predictions from different well-performing models. Furthermore, expanding the input dataset with time derivatives, moving averages, and daily differences, as well as modifying data, such as differencing, enhances the learning of space weather features, especially over a longer forecast horizon.

Undersampled Ionospheric Irregularity Threat Parameterization Using a Three-Dimensional Model for Satellite-Based Augmentation Systems

Single-frequency Satellite-based Augmentation Systems (SBASs) compute and broadcast estimates of vertical ionospheric delays and integrity bounds on the estimates called the Grid Ionospheric Vertical Errors (GIVEs) at Ionospheric Grid Points (IGPs). The dominant contribution of the GIVE comes from the undersampled ionospheric irregularity threat model. This paper presents a methodology for the undersampled ionospheric threat parameterization to reduce the magnitude of the GIVE. A threat model metric that measures the uniformity of angular separation of measurements was designed and incorporated into the current metric set, the fit radius and the relative centroid metric (RCM), such that threat geometries were parameterized rigorously based on the extended metric set. An undersampled threat model was constructed with the proposed three-dimensional metric set and historical ionospheric storm data from the global navigation satellite system stations in South Korea. We also simulated SBAS availability in the Korean region to demonstrate the benefit of the presented threat model methodology. In our preliminary assessment, the implementation of the proposed method was found to improve the 99.9% availability of the approach procedure with vertical guidance I by up to 12% when the approach was applied to the GIVE monitor algorithm.

An Improved Ionospheric Delay Correction Method for SBAS

The existing ionospheric delay correction methods in Satellite based augmentation system (SBAS) were just for single constellation and over conservative. In this paper, we propose a new method to make more accurate ionospheric delay correction and tighter error bound orienting towards GPS and GLONASS. Considering that some Ionospheric pierce points (IPPs) are almost motionless, we make a filtering process to estimate the ionospheric delays at Ionospheric grid points (IGPs) to better reflect the ionospheric temporal variation. Then we conduct a simulation on ionospheric delay estimation at IGPs in dual constellations through planar fit method and filtering method. It can be concluded that the filtering method can bound the ionospheric delay correction error more tightly, simultaneously the ionospheric delay correction accuracy is improved a bit.

A Vector Ionospheric Delay Correction Method for GNSS Positioning and Navigation Wide Area Augmentation Service

A new ionospheric delay correction method is proposed to improve the ionospheric correction accuracy of single frequency GNSS users. In the new method, the ionospheric grid point information is expanded from a single scalar vertical correction parameter to a vector of triple elements (the triple): vertical correction parameter, north correction parameter and east correction parameter. The new parameters are used to describe the variation of ionospheric delay correction caused by satellite azimuth. Using the observation data of the ground monitoring stations to fit the triple, and then broadcast the triple to the user. GNSS single frequency users can use the triple data to correct their own ionospheric delay. The testing results show that the correction error of the method is around 0.3 m lower than that of the scalar method.

Ionospheric correlation analysis and spatial threat model for SBAS in China region

Satellite Based Augmentation Systems (SBAS) broadcasts to users Grid Ionospheric Vertical Delays (GIVDs) and associated confidence bounds called Grid Ionospheric Vertical Errors (GIVEs) at Ionospheric Grid Points (IGPs). The correlation structure of ionosphere and undersampled threat should be taken into account in the generation of GIVE to meet the integrity requirement. In this contribution, the correlation structure of ionosphere over China was investigated and a primary undersampled threat model was built for the development of BDSBAS. Planar fit algorithm was used to estimate the GIVDs, the correlation structure was yielded from the differences and residuals of the vertical delays at Ionospheric Pierce Points (IPPs). Then undersampled threat model was created with data deprivation method. Five days’ data collected by 24 stations spread over China was selected to perform the correlation analysis and develop the threat model. Based on the correlation analysis, a maximum fit radius of 1500 km and a decorrelation value of 0.5 m were recommended for China area. Due to the ionospheric irregularity which could affect the region under the latitude of 30°N, a fit radius of 1300 km was suggested to improve the system availability. With the spatial threat model, it was found high latitude region owned a smaller threat value due to the relative quiet ionospheric condition. Relative Centroid Metric (RCM) less than 0.5 was proposed for determining the locations of BDSBAS’ sites. Threat models derived with different cut-off elevation angle were investigated and 5° elevation mask was proposed to generate the threat model.

Ionosphere modeling in the context of Algerian Satellite-based Augmentation System

To guarantee safety-critical implementation of Algerian Satellite-based Augmentation Systems (SBAS), a comprehensive study of the impact of space weather on Global Navigation Satellite Systems (GNSS) over this region is necessary. In this work, three typical ionospheric algorithms: inverse distance weighting (IDW), kriging, and planar-fit were applied on GPS dual-frequency data from seven GPS stations spread over Algerian territory during three major geomagnetic storms of different intensity in addition to a quiet geomagnetic period. The performance of these ionospheric algorithms was investigated based on the broadcast ionospheric vertical delay (Grid Ionospheric Vertical Delay, GIVD) and its corresponding confidence bound error (Grid Ionospheric Vertical Error, GIVE) at two Ionospheric Grid Points (IGPs): (35°N, 5°E) and (30°N, 5°E), located in the Algerian mid-latitudes. The obtained GIVDs were compared to their corresponding delays estimated at nearby user stations as a first reference and to EGNOS messages as a second reference. In addition, the Global Ionospheric Maps (GIMs) from the International GNSS Service (IGS) was incorporated in the analysis. Our results indicate that the studied models provided equivalent accuracy even though kriging slightly outperformed the other models in most of the cases of study. The EGNOS model showed less agreement with the ground truth data during 2013 and 2015, while in 2017 became more accurate after the upgrade. The analysis of estimated GIVEs shows the ability of the three ionospheric models to protect and to safely bound GIVD errors while kriging is intended to provide better availability of Algerian SBAS. In addition, EGNOS GIVEs exhibit effective protection of users at the edge of its service area.

Performance Evaluation Method for Ionospheric Grid Information of BDS via Dual-frequency Observations

As one of the principal error sources in satellite navigation system, it is ionospheric delay whose correction accuracy directly affects single-frequency positioning accuracy. There are Klobuchar ionospheric model and ionospheric grid information for single-frequency users, provided by basic navigation service and enhancement service respectively in BeiDou Navigation Satellite System. Ionospheric grid information is broadcast as vertical delay estimates at specified ionospheric grid points (IGPs) with a resolution of 5°and 2.5° in longitude and latitude. To evaluate its performance, it proposed a performance evaluation method via dual-frequency observations. And the feasibility of this method was verified by the ionospheric grid information data from November 2017 to October 2018. Performance evaluation results showed that the effective coverage area of ionospheric grid information basically covers China, with a correction deviation of 1.55 TECU and a correction rate of 86.1%.And it is in winter that the correction accuracy of ionospheric grid information is lower and more fluctuating with a correction bias of 1.95 TECU and a correction rate of 81.5% and, but less than 1.47 TECU of bias and more than 86.5% of rate in other seasons. It is higher in both correction bias and correction percentage during the day than at night.

Comparison of observed ionospheric vertical TEC over the sea in Indian region with IRI-2016 model

The vertical ionospheric TEC values obtained from GAGAN grid based ionospheric delay correction values over the sea in the Indian equatorial region have been compared with the corresponding values derived from the International Reference Ionosphere model, IRI-2016. The objective of this work is to study the deviation of the vertical TEC derived from the IRI model from ground truths over the sea for different conditions. This will serve the basic intention of assessing the candidature of the IRI model as an alternative ionospheric correction model in navigation receivers in terms of accuracy. We have chosen different solar activity periods, seasons, geomagnetic conditions, locations etc. for our comparison and analysis. The TEC values by the IRI-2016 were compared with the actual measured values for the given conditions and errors were obtained. The measured vertical TEC values at the ionospheric grid points were derived from the GAGAN broadcast ionospheric delay data and used as reference. The IRI model with standard internal functions was used in estimating the TEC at the same ionospheric grid points. The errors in the model derived values are statistically analysed. Broadly, the results show that, for the Indian sector over the sea, the IRI model performs better on quiet days in off equatorial regions, particularly in the northern region. The overall performance degrades for other conditions with the model generally underestimating the true TEC values and most severely in the equatorial region. The performance is worst in this region for the disturbed days of the equinoctial period. The comparison study is also done with the TEC data measured directly by dual frequency GPS receivers. The results were found to be in general agreement with those obtained by comparing the model with GAGAN broadcast data as reference. This study will be useful in considering the IRI-2016 model for real time estimates of TEC as an alternative to the current parametric model in a satellite navigation receiver in absence of other options.

Distributed processing of a GPS receiver network for a regional ionosphere map

This paper proposes a distributed processing method applicable to GPS receivers in a network to generate a regional ionosphere map accurately and reliably. For accuracy, the proposed method is operated by multiple local Kalman filters and Kriging estimators. Each local Kalman filter is applied to a dual-frequency receiver to estimate the receiver’s differential code bias and vertical ionospheric delays (VIDs) at different ionospheric pierce points. The Kriging estimator selects and combines several VID estimates provided by the local Kalman filters to generate the VID estimate at each ionospheric grid point. For reliability, the proposed method uses receiver fault detectors and satellite fault detectors. Each receiver fault detector compares the VID estimates of the same local area provided by different local Kalman filters. Each satellite fault detector compares the VID estimate of each local area with that projected from the other local areas. Compared with the traditional centralized processing method, the proposed method is advantageous in that it considerably reduces the computational burden of each single Kalman filter and enables flexible fault detection, isolation, and reconfiguration capability. To evaluate the performance of the proposed method, several experiments with field collected measurements were performed.

Southern European ionospheric TEC maps based on Kriging technique to monitor ionosphere behavior

Global or regional Maps of the ionospheric Total Electron Content (TEC) are an efficient tool to monitor the delay introduced by the ionosphere in the satellite signals. Ionospheric disturbance periods are of particular interest because these conditions can strongly affect satellite navigation range measurements. This work presents post-processing regional vertical TEC maps over Southern Europe ([35°N–50°N] latitude) obtained by applying Kriging interpolation to GPS derived TEC over more than 100 Global Navigation Satellite System (GNSS) stations. These maps are used to study the behavior of the ionosphere during space weather events and their effects. To validate these maps, hereafter called Southern European Ionospheric Maps (SEIMs), their TEC values have been compared with those obtained from EGNOS Message Server (EMS) and with direct experimental TEC data from GNSS stations. Ionospheric space weather events related to geomagnetic storms of March 17th, 2013, February 19th, 2014 and March 17th, 2015 have been selected. To test the methodology, one period of quiet days has been also analyzed. TEC values obtained by SEIMs in the Ionospheric Grid Points (IGPs) defined by EGNOS are very close to those given by EMS and in the period of major geomagnetic storms the difference does not exceed 6 TEC units. These results confirm the good performance of the technique used for obtaining the SEIMs that can be a useful tool to study the ionosphere behavior during geomagnetic storms and their effects in the region of interest.

Kriging with Unknown Variance Components for Regional Ionospheric Reconstruction.

Ionospheric delay effect is a critical issue that limits the accuracy of precise Global Navigation Satellite System (GNSS) positioning and navigation for single-frequency users, especially in mid- and low-latitude regions where variations in the ionosphere are larger. Kriging spatial interpolation techniques have been recently introduced to model the spatial correlation and variability of ionosphere, which intrinsically assume that the ionosphere field is stochastically stationary but does not take the random observational errors into account. In this paper, by treating the spatial statistical information on ionosphere as prior knowledge and based on Total Electron Content (TEC) semivariogram analysis, we use Kriging techniques to spatially interpolate TEC values. By assuming that the stochastic models of both the ionospheric signals and measurement errors are only known up to some unknown factors, we propose a new Kriging spatial interpolation method with unknown variance components for both the signals of ionosphere and TEC measurements. Variance component estimation has been integrated with Kriging to reconstruct regional ionospheric delays. The method has been applied to data from the Crustal Movement Observation Network of China (CMONOC) and compared with the ordinary Kriging and polynomial interpolations with spherical cap harmonic functions, polynomial functions and low-degree spherical harmonic functions. The statistics of results indicate that the daily ionospheric variations during the experimental period characterized by the proposed approach have good agreement with the other methods, ranging from 10 to 80 TEC Unit (TECU, 1 TECU = 1 × 1016 electrons/m2) with an overall mean of 28.2 TECU. The proposed method can produce more appropriate estimations whose general TEC level is as smooth as the ordinary Kriging but with a smaller standard deviation around 3 TECU than others. The residual results show that the interpolation precision of the new proposed method is better than the ordinary Kriging and polynomial interpolation by about 1.2 TECU and 0.7 TECU, respectively. The root mean squared error of the proposed new Kriging with variance components is within 1.5 TECU and is smaller than those from other methods under comparison by about 1 TECU. When compared with ionospheric grid points, the mean squared error of the proposed method is within 6 TECU and smaller than Kriging, indicating that the proposed method can produce more accurate ionospheric delays and better estimation accuracy over China regional area.

Analysis of a grid ionospheric vertical delay and its bounding errors over West African sub-Saharan region

Investigating the effects of the Equatorial Ionization Anomaly (EIA) ionosphere and space weather on Global Navigation Satellite Systems (GNSS) is very crucial, and a key to successful implementation of a GNSS augmentation system (SBAS) over the equatorial and low-latitude regions. A possible ionospheric vertical delay (GIVD, Grid Ionospheric Vertical Delay) broadcast at a Ionospheric Grid Point (IGP) and its confidence bounds errors (GIVE, Grid Ionospheric Vertical Error) are analyzed and compared with the ionospheric vertical delay estimated at a nearby user location over the West African Sub-Saharan region. Since African sub-Saharan ionosphere falls within the EIA region, which is always characterized by a disturbance in form of irregularities after sunset, and the disturbance is even more during the geomagnetically quiet conditions unlike middle latitudes, the need to have a reliable ionospheric threat model to cater for the nighttime ionospheric plasma irregularities for the future SBAS user is essential. The study was done during the most quiet and disturbed geomagnetic conditions on October 2013. A specific low latitude EGNOS-like algorithm, based on single thin layer model, was engaged to simulate SBAS message in the study. Our preliminary results indicate that, the estimated GIVE detects and protects a potential SBAS user against sampled ionospheric plasma irregularities over the region with a steep increment in GIVE to non-monitored after local sunset to post midnight. This corresponds to the onset of the usual ionospheric plasma irregularities in the region. The results further confirm that the effects of the geomagnetic storms on the ionosphere are not consistent in affecting GNSS applications over the region. Finally, this paper suggests further work to be investigated in order to improve the threat integrity model activity, and thereby enhance the availability of the future SBAS over African sub-Saharan region.

Preliminary availability assessment to support single-frequency SBAS development in the Korean region

Satellite-Based Augmentation Systems (SBASs) enhance the global navigation satellite system (GNSS) to support all phases of flight by providing required accuracy, integrity, continuity, and availability. The Korean SBAS program was recently initiated to develop a single-frequency SBAS aiming to provide Approach Procedure with Vertical guidance (APV)-I Safety-of-Life (SoL) service to aviation users by 2022 within the Korean region. We assess the preliminary availability of the single-frequency SBAS which will be deployed in the Korean peninsula. The resulting system performance shall be used as a baseline to design system components and specifications. The fundamental components of SBAS architecture, SBAS monitor network, geostationary earth orbiting satellite parameters, and ionospheric grid point mask, are defined and their effects on system performance are investigated. Ionospheric correction and integrity algorithm parameters including an ionospheric irregularity threat model are determined using data collected from the Korean GNSS network. The coverage of 99.9 % availability for APV-I service increases from approximately 70 % for the baseline case to 100 % when SBAS monitor stations are expanded to overseas. Even with the expanded monitor network, however, 90 % and less than 95 % availability for LPV-200 service can be achieved only in a very limited region.

Evaluation of COMPASS ionospheric grid

As an important component of the augmentation service, the ionospheric grid contributes to improving single-frequency positioning accuracy. The ionospheric delay corrections are broadcast as vertical delay estimates at specified ionospheric grid points (IGPs) for most satellite-based augmentation system, where the IGPs are predefined with a resolution of 5° and 5° in latitude and longitude. Different from the general strategy, the COMPASS IGPs are predefined with a resolution of 2.5° and 5° in latitude and longitude. The need for this special IGPs distribution is investigated with experiments using real data. The performance of the COMPASS ionospheric grid is analyzed in terms of accuracy and availability. Comparing the performance of the special IGPs distribution with that of 5° × 5° IGPs, the results show that the ionospheric correction improves by 0.2 m and the 3D positioning accuracy improves by 1 m in middle-low latitude regions. The RMS of the COMPASS grid ionospheric correction accuracy is better than 0.5 m in most regions of the China mainland, and the availability is better than 95 % except in the northeast, northwest and outside China. In addition, we investigated the performance of the method that combined the inverse distance weighted and spherical harmonics grid modeling algorithm. Simulations show that the new method clearly improves grid availability. The mean availability in the mainland is better than 99 %.

Considerations on Ionospheric Correction and Integrity Algorithm for Korean SBAS

Satellite Based Augmentation Systems (SBAS) provide ionospheric corrections at geographically five degree-spaced Ionospheric Grid Points (IGPs) and confidence bounds, called Grid Ionospheric Vertical Errors (GIVEs), on the error of those corrections. Since the ionosphere is one of the largest error sources which may threaten the safety of a single frequency Global Navigation Satellite System (GNSS) user, the ionospheric correction and integrity bound algorithm is essential for the development of SBAS. The current single frequency based SBAS, already deployed or being developed, implement the ionospheric correction and error bounding algorithm of the Wide Area Augmentation System (WAAS) developed for use in the United States. However, the ionospheric condition is different for each region and it could greatly degrade the performance of SBAS if its regional characteristics are not properly treated. Therefore, this paper discusses key factors that should be taken into consideration in the development of the ionospheric correction and integrity bound algorithm optimized for the Korean SBAS. The main elements of the conventional GIVE monitor algorithm are firstly reviewed. Then, this paper suggests several areas which should be investigated to improve the availability of the Korean SBAS by decreasing the GIVE value.

Estimating ionospheric delay using kriging: 1. Methodology

The Wide Area Augmentation System (WAAS) is an augmentation of the Global Positioning System (GPS) that provides safe and reliable use of GPS signals for airline navigation over much of North America. Ever since WAAS was first commissioned in July of 2003, the vertical delay estimate at each node in the WAAS ionospheric grid has been determined from a planar fit of slant delay measurements, projected to vertical using an obliquity factor specified by the standard thin shell model of the ionosphere. In a future WAAS upgrade (WAAS Follow‐On Release 3), however, the vertical delay will be estimated by an established, geo‐statistical technique known as kriging. When compared to the planar fit model, the kriging model is generally found to match better the observed random structure of the vertical delay. This paper presents the kriging methodology to be used to estimate the vertical delay and its uncertainty at each ionospheric grid point. In addition, it provides examples of the improvement in delay accuracy achieved. Under disturbed conditions, the implementation of kriging reduces the magnitude of the root mean square fit residual by up to 15%.

A different approach to the analysis of GPS scintillation data

Amplitude scintillation data from GPS were analyzed. The objective is to estimate the impact of ionospheric scintillations at Satellite Based Augmentation Systems Ranging and Integrity Monitoring Station (SBAS RIMS) level and at GPS user level. For this purpose, a new approach to the problem was considered. Data were studied from the point of view of the impact of scintillations on the calculation of VTEC at pierce points and ionospheric grid points. An ionospheric grid of 5° 5° surface squares was assumed. From geometrical considerations and taking into account the basic principle to compute VTEC at grid points, with the data analyzed it is shown that scintillations very seldom affect the calculation of a grid point VTEC. Data from all the RIMS and for the entire GPS satellites network must be analyzed simultaneously to describe a realistic scenario for the impact of scintillations on SBAS. Finally, GPS scintillation data were analyzed at user level: service availability problems were encountered.

The Direct and Indirect Methods of Ionospheric TEC Predictions and Their Comparison

The direct and indirect methods for predicting the ionospheric total electron content (TEC) by using the ARIMA ( p, d, q) model in the theory of time-series analysis are proposed. The direct method predicts directly the time series composed of the TECs at the every grid point. The indirect method is: at first, to fit the ionospheric TECs with the spherical harmonics and obtain the time series of the fitting coefficients; then, to predict forward the fitting coefficients with the ARIMA ( p, d, q) model in the theory of time-series analysis; and finally, to calculate the TEC for the specific time and grid point. Using the ionospheric data of the International GPS Service (IGS) in the period from 1 January 2004 to 31 January 2005, the testing and comparisons on the proposed methods are performed, the results indicate that within 12 days, the results of the two methods are basically consistent, and that for the predictions longer than 12 days, the accuracy of the indirect method is higher than the direct method. In the duration of 20 days, relative to the total ionospheric grid points, the percentage of the grid points with a prediction error less than 3 TECUs is about 80%; as the duration becomes longer, compared with the indirect method, the decline of this percentage is not apparent for the direct method. Obviously, the direct method suits the prediction of regional TECs, and the indirect method suits the prediction of global TECs.