Regional Ionospheric Model Research Articles

Comparison of PPP-RTK performance under different regional ionospheric models

Abstract Establishing a regional ionospheric model to provide precise ionospheric products is a prerequisite for rapid real-time kinematic precise point positioning (PPP-RTK). Thus, a stochastic model for these real-time ionospheric products is also crucial. In this study, we use a Wuhan regional network (average inter-station distance of about 30 km) to comparatively analyze four regional ionospheric modeling methods with commonly-used stochastic models: the inverse distance weighting model (IDW), the quasi-four-dimension ionospheric modeling (Q4DIM), the first-order polynomial function model with internal validation (POLY), and the first-order polynomial function model with external validation (POLY-EV). Our results show that, the POLY/POLY-EV model has the smallest ionospheric delay interpolation root mean square (RMS) error, regardless of whether for inside or peripheral stations of the regional network, during both quiet and active ionospheric conditions. For 4024 and 4314 one-hour samples, the PPP-RTK results show that at inside stations, all four models converge to a horizontal precision of 10 cm within two epochs, with the POLY-EV model having the highest horizontal positioning precision (a mean RMS of 0.83 cm). At the peripheral station, PPP-RTK with the POLY/POLY-EV model achieves a horizontal precision of 10 cm within two epochs, while the IDW and Q4DIM models need 4 and 43 epochs, respectively. The horizontal positioning precision of PPP-RTK using the POLY-EV model is the highest, with a mean RMS of 1.59 cm.

A Gaussian Variogram‐Based Model of Total Electron Content in the Regional Ionosphere of China

AbstractThis study utilizes ionospheric total electron contents (TECs) data from China and its surrounding areas to compute the regional ionospheric semi‐variance using the Gaussian variogram. The regional ionospheric model is then constructed by introducing an additional stochastic term, named adjusted Spherical Harmonics Adding KrigING method (SHAKING), in which the stochastic Vertical Total Electron Content estimated using Kriging interpolation based on Ionospheric Variogram Model Parameters (IVMP) predict model. In the IVMP prediction model, two notable periodic patterns, that is, diurnal and annual signals with periods of 365.25/i days and 24/j hours, are recognized as Fourier series decompositions. These patterns capture the regular daily and yearly periodic variations in variogram parameters, and the IVMP prediction model is established using harmonic estimation methods. IVMP‐SHAKING is employed to generate the regional ionospheric map in China using multi‐GNSS data from 27 reference stations during days of the year 150–250 in 2022, with 14 rover stations used for evaluation. Results indicate that the proposed model exhibits a standard deviation of 4.85 TECu compared to the difference of slant TEC extracted from rover stations. Compared to existing models, including BDS‐3 broadcast ionospheric model (BDGIM), GPS broadcast model (Klobuchar), Galileo broadcast model (NeQuickG) and post‐processing Global Ionospheric Map released by IGS (IGSG), the accuracy of IVMP‐SHAKING improves by 6%–52%. Additionally, the Standard Point Positioning performance with different ionospheric corrections is analyzed on test stations. Results demonstrate that the horizontal and vertical positioning accuracy of the IVMP‐SHAKING model improves by 31%–55% and 16%–33%, respectively, compared to other three solutions.

Assessment of Satellite Differential Code Biases and Regional Ionospheric Modeling Using Carrier-Smoothed Code of BDS GEO and IGSO Satellites

The geostationary earth orbit (GEO) represents a distinctive geosynchronous orbit situated in the Earth’s equatorial plane, providing an excellent platform for long-term monitoring of ionospheric total electron content (TEC) at a quasi-invariant ionospheric pierce point (IPP). With GEO satellites having limited dual-frequency coverage, the inclined geosynchronous orbit (IGSO) emerges as a valuable resource for ionospheric modeling across a broad range of latitudes. This article evaluates satellite differential code biases (DCB) of BDS high-orbit satellites (GEO and IGSO) and assesses regional ionospheric modeling utilizing data from international GNSS services through a refined polynomial method. Results from a 48-day observation period show a stability of approximately 2.0 ns in BDS satellite DCBs across various frequency signals, correlating with the available GNSS stations and satellites. A comparative analysis between GEO and IGSO satellites in BDS2 and BDS3 reveals no significant systematic bias in satellite DCB estimations. Furthermore, high-orbit BDS satellites exhibit considerable potential for promptly detecting high-resolution fluctuations in vertical TECs compared to conventional geomagnetic activity indicators like Kp or Dst. This research also offers valuable insights into ionospheric responses over mid-latitude regions during the March 2024 geomagnetic storm, utilizing TEC estimates derived from BDS GEO and IGSO satellites.

Regional Real-Time between-Satellite Single-Differenced Ionospheric Model Establishing by Multi-GNSS Single-Frequency Observations: Performance Evaluation and PPP Augmentation

The multi-global navigation satellite system (GNSS) undifferenced and uncombined precise point positioning (UU-PPP), as a high-precision ionospheric observables extraction technology superior to the traditional carrier-to-code leveling (CCL) method, has received increasing attention. In previous research, only dual-frequency (DF) or multi-frequency (MF) observations are used to extract slant ionospheric delay with the UU-PPP. To reduce the cost of ionospheric modeling, the feasibility of extracting ionospheric observables from the multi-GNSS single-frequency (SF) UU-PPP was investigated in this study. Meanwhile, the between-satellite single-differenced (SD) method was applied to remove the effects of the receiver differential code bias (DCB) with short-term time-varying characteristics in regional ionospheric modeling. In the assessment of the regional real-time (RT) between-satellite SD ionospheric model, the internal accord accuracy of the SD ionospheric delay can be better than 0.5 TECU, and its external accord accuracy within 1.0 TECU is significantly superior to three global RT ionospheric models. With the introduction of the proposed SD ionospheric model into the multi-GNSS kinematic RT SF-PPP, the initialization speed of vertical positioning errors can be improved by 21.3% in comparison with the GRAPHIC (GRoup And PHase Ionospheric Correction) SF-PPP model. After reinitialization, both horizontal and vertical positioning errors of the SD ionospheric constrained (IC) SF-PPP can be maintained within 0.2 m. This proves that the proposed SDIC SF-PPP model can enhance the continuity and stability of kinematic positioning in the case of some GNSS signals missing or blocked. Compared with the GRAPHIC SF-PPP, the horizontal positioning accuracy of the SDIC SF-PPP in kinematic mode can be improved by 37.9%, but its vertical positioning accuracy may be decreased. Overall, the 3D positioning accuracy of the SD ionospheric-constrained RT SF-PPP can be better than 0.3 m.

A Two-Step Regional Ionospheric Modeling Approach for PPP-RTK.

In the precise point positioning/real-time kinematic (PPP-RTK) technique, high-precision ionospheric delay correction information is an important prerequisite for rapid PPP convergence. The commonly used ionospheric modeling approaches in the PPP-RTKs only take the trend term of the ionospheric total electron content (TEC) variations into account. As a result, the residual ionospheric delay still affects the positioning solutions. In this study, we propose a two-step regional ionospheric modeling approach that involves combining a polynomial fitting model (PFM) and a Kriging interpolation (KI) model. In the first step, a polynomial fitting method is used to model the trend term of the ionospheric TEC variations. In the second step, a KI method is used to compensate for the residual term of the ionospheric TEC variations. Datasets collected from continuously operating reference stations (CORSs) in Hunan Province, China, are used to validate the PFM/KI method by comparing with a single PFM method and a combined PFM and inverse distance weighting interpolation (IDWI) method. The experimental results show that the two-step PFM/KI modeled ionospheric delay achieves an average root mean square (RMS) error of 1.8 cm, which is improved by about 48% and 23% when compared with the PFM and PFM/IDWI methods, respectively. Regarding the positioning performance, the PPP-RTK with the PFM/KI method takes an average of 1.8 min or 4.0 min to converge to a positioning accuracy of 1.3 cm or 2.5 cm in the horizontal and vertical directions, respectively. The convergence times are decreased by about 18% and 14% in the horizontal direction and 9% and 5% in the vertical direction over the PFM and the PFM/IDWI methods, respectively.

A Multi-Parameter Empirical Fusion Model for Ionospheric TEC in China’s Region

This article takes the measured Total Electron Content (TEC) from the GPS points of the China Regional Crust Observation Network as the starting point to establish a regional ionospheric empirical model. The model’s performance is enhanced by considering solar flux and geomagnetic activity data. The refinement function model of the ionospheric TEC diurnal variation component, seasonal variation component, and geomagnetic component is studied. Using the nonlinear least squares method to fit undetermined coefficients, MEFM-ITCR (Multi-parameter Empirical Fusion Model–Ionospheric TEC China Regional Model) is proposed to forecast the regional ionosphere TEC in China. The results show that the standard deviation of MEFM-ITCR residuals is 3.74TECU, and MEFM-ITCR fits the modeling dataset well. Analyses of geographic location variation, seasonal variation, and geomagnetic disturbance were carried out for MEFM-ITCR performance. The results indicate that in the Chinese region, MEFM-ITCR outperforms IRI2020 and NeQuick2 models in terms of forecast accuracy, linear correlation, and model precision for TEC measured using GPS points under different latitudes and longitudes, different seasons, and different geomagnetic disturbances. The empirical TEC model built for the Chinese region in this paper provides a new ionospheric delay correction method for GNSS single frequency users and is of great significance for establishing other new and improving existing ionospheric empirical models.

Constructing a Regional Ionospheric TEC Model in China with Empirical Orthogonal Function and Dense GNSS Observation

Using Global Navigation Satellite Systems (GNSS) observation data for developing a high-precision ionospheric Total Electron Content (TEC) model is one of the essential subjects in ionospheric physics research and the application of satellite navigation correction. In this study, we integrate the Empirical Orthogonal Function (EOF) method with the TEC data provided by the Center for Orbit Determination in Europe (CODE), and observed by the dense GNSS receivers operated by the Crustal Movement Observation Network of China (CMONOC) to construct a regional ionospheric TEC model over China. The EOF analysis of CODE TEC in China from 1998 to 2010 shows that the first-order EOF component accounts for 90.3813% of the total variation of the ionospheric TEC in China. Meanwhile, the average value of CODE TEC is consistent with the spatial and temporal distribution characteristics of the first-order EOF base function, which mainly reflects the latitude and diurnal variations of TEC in China. The first-order coefficient after EOF decomposition shows an obvious 11-year period and semi-annual variations. The maximum amplitude of semi-annual variation mainly appears in March and October, which is closely associated with the variation in geographical longitude, the semi-annual change of the low-latitude electric field, and the ionospheric fountain effect. The second-order coefficient has an evident annual variation, the minimum amplitude mainly occurs in March, August, and September, and the amplitude values in the high solar activity years are more significant than those in the low solar activity years. The third-order coefficient mainly shows the characteristics of annual variation, and the fourth-order coefficient shows the noticeable semi-annual and annual variations. The third and fourth-order coefficients are both modulated by the solar activity index F10.7. The ionospheric TEC model in China, driven by CMONOC real-time GNSS observation data, can better reflect the latitude, local time and seasonal variation characteristics of ionospheric TEC over China. In particular, it can clearly show the spring and autumn asymmetry of ionospheric TEC in the low latitudes. The root mean square error of the absolute error between the model and the actual observation is mainly distributed around 2.45 TECU (1 TECU = 1016 electrons/m2). The values of the TEC model constructed in this study are closer to the actual observed values than those of the CODE TEC in China.

Regional ionospheric TEC modeling during geomagnetic storm in August 2021- data fusion using multi-instrument observations

Regional ionospheric Total Electron Content (TEC) models are most significant to investigate the variability of ionosphere during all-weather conditions. Since the ground-based TEC measurements are not available in oceanic and polar regions, space-based observations are incorporated to increase the positional accuracy and reliability of Global Ionospheric TEC Maps (GIMs). Therefore, data fusion techniques are necessary to enhance the prediction capability of regional ionospheric models by considering multi-source data. In view of this, an attempt is made to investigate Equatorial Ionization Anomaly (EIA) structures in low-latitudinal Indian region using multi-instrument data. Data observations from background model CODEGIM, available International GNSS Service (IGS) stations in India, GNSS receivers at KLEF and Tripura stations, FORMOSAT/COSMIC radio occultation and SWARM during geomagnetic storm period August 26–28, 2021 are used for the study. Spherical Harmonics Function (SHF) of order 4 is employed along with Weighted Least Squares analysis (WLS), where separate weight constraint is computed for each data source. TEC maps of spatial resolution 5° x 5° and temporal resolution of 1 h are generated to illustrate the dynamic behavior of ionosphere. The standard deviation for 3 days is obtained as 0.42, 0.61 and 1.43 TECU respectively. TEC depletions and enhancements are observed on August 27 and 28, with mean values of 12.74 and 15.27 TECU respectively, demonstrating negative and positive storm effects.

Method of Development of a New Regional Ionosphere Model (RIM) to Improve Static Single-Frequency Precise Point Positioning (SF-PPP) for Egypt Using Bernese GNSS Software

Due to the lack of coverage of IGS in Africa, especially over North Africa, and the construction revolution of infrastructure in Egypt, a geodetic CORS stations network was established in 2012. These CORS stations are operated by the Egyptian Surveying Authority (Egy. SA) and cover the whole of Egypt. The paper presents a fully developed regional ionosphere model (RIM) depending on the Egyptian CORS stations. The new model and the PPP solution were obtained using Bernese GNSS V. 5.2 software. An observation data series of eight days (DOY 201–208)/2019 was used in this study. Eighteen stations were used to develop the RIM model for each day; fifteen stations were used to validate the new RIM model. A static SF-PPP solution was obtained using the CODE-GIM and RIM models. Comparing the outcomes to the reference network solution, based on the recently developed RIM model, the solution showed a mean error of 0.06 m in the East direction, 0.13 m in the North direction, and 0.21 m in the height direction. In the East, North, and height directions, this solution improves the SF-PPP result achieved by the Global Ionosphere Maps (CODE-GIM) model by 60%, 68%, and 77%, respectively.

Regional ionospheric electron density modeling by assimilation of GPS-derived TEC into IRI-provided grids on May 8, 2016

Retrieved vertical total electron content (VTEC) via dual-frequency GPS measurements is a valuable observation for regional VTEC modeling of the ionosphere (3D), and also ionospheric electron density (IED) modeling (4D). In the case of 4D modeling, spatial and temporal changes in IED are imaged. 4D reconstruction of IED in different ionosphere layers is not possible only by retrieved VTECs. In all IED modeling methods, in addition to VTEC observations, a priori knowledge of how electron density is distributed in different layers is required, which is often taken from global empirical models. One of these methods is data assimilation, in which the information of a global model is considered as background and both observations and background are used optimally for IED modeling. Data assimilation has more prominent importance in regions where the observations are sparse. In this study, a grid-based data assimilation method is proposed for IED modeling. The optimum interpolation method (OI) is presented with a modification to find the optimal variance factor related to the background covariance matrix. The covariance matrix of the background during the data assimilation interval is estimated by an optimization process. The method is utilized for regional assimilative IED modeling over Iran with sparse VTEC data from a low number of permanent GPS stations on May 8, 2016 which is the most active ionospheric day in that year. International reference ionosphere (IRI) is considered as background, and although it has a significant bias in the study region, the proposed method resulted in an accurate regional IED model. The model is evaluated in two ways. First, by measuring RMS of the differences between parts of VTECs that are excluded from observations as test data and the obtained VTECs from the model. Second, by examining the accuracy of ionospheric delay estimation via single-frequency positioning at a control station in Tehran. Despite the use of sparse data on an active ionospheric day and poor background accuracy in the study region, the constructed regional assimilative model is accurate both in RMS with test data and ionospheric delay estimation.

Statistical analysis of the regional and global ionosphere model on intense geomagnetic storm

Statistical analysis of the regional and global ionosphere model on intense geomagnetic storm

A consistent and grid-based regional slant ionospheric model with an increasing number of satellite corrections for PPP-RTK

A consistent and grid-based regional slant ionospheric model with an increasing number of satellite corrections for PPP-RTK

An Ionospheric Total Electron Content Model with a Storm Option over Japan Based on a Multi-Layer Perceptron Neural Network

Ionospheric delay has a severe effect on reducing the accuracy of positioning and navigation of single-frequency receivers. Therefore, it is necessary to construct a precise regional ionospheric model for real-time Global Navigation Satellite System (GNSS) applications. The total electron contents (TECs) of 839 GNSS stations affiliated with the GPS Earth Observation Network were used to build a Japanese ionospheric model (JIM) based on a multi-layer perceptron neural network. During quiet space conditions, the correlation coefficient between the targets and the predictions of the JIM was about 0.98, and the root-mean square error (RMSE) of TEC residuals was ~1.5TECU, while under severe space events, the correlation coefficient increased to 0.99, and the corresponding RMSE dropped to 0.96 TECU. Moreover, the JIM model successfully reconstructed the two-dimensional (time vs latitude) TEC maps, and the TEC maps had evident hourly and seasonal variations. Most of TEC residuals accumulated between universal time 01–06 with an averaged magnitude of 1-2TECU. Furthermore, the JIM model had a perfect prediction performance under various kinds of complex space environments. In the quiet days, the prediction accuracy of the JIM was nearly equal to the global ionosphere map (GIM), and in some moments, the JIM was more competitive than the GIM. In the disturbed days, the RMSEs of TEC residuals were proportional to the solar wind speed and were inversely proportional to the geomagnetic Dst value. The maximum RMSE of the JIM was lower than 2TECU, while the corresponding RMSEs for the IRI and TIE-GCM exceeded 5TECU.

MODELING OF SPATIAL-TEMPORAL VARIATIONS OF DYNAMIC AND THERMAL PROCESS PARAMETERS IN GEOSPACE OVER UKRAINE DURING THE MINIMUM OF 24-TH CYCLE OF SOLAR ACTIVITY (2009, 2019)

We have performed the modelling of spatiotemporal variations of parameters of dynamic and thermal processes in ionospheric plasma at the phases of the minimum of the 24-th cycle of solar activity according to the Kharkiv radar of incoherent scattering. The diurnal dependences of parameters of the processes in the ionospheric plasma at altitudes from 210 to 450 km are constructed for typical geophysical periods (vernal and autumn equinoxes, summer and winter solstices). In the paper, the analysis of spatial and temporal variations of parameters of dynamic and thermal processes in the ionosphere is presented. We determined the value of the plasma transfer velocity due to ambipolar diffusion, the density of the full plasma flux, and the flux of charged particles due to ambipolar diffusion, the value of the energy supplied to the electron gas, the density of the heat flux transferred by electrons from the plasmasphere to the ionosphere, as well as the velocity of the equivalent neutral wind, and the meridional component of the neutral wind velocity. We found that weak variations in space weather do not lead to significant changes in spatiotemporal variations of the parameters of dynamic and thermal processes in the ionosphere for most of the studied periods. Quantitative and qualitative characteristics of most of these parameters and their diurnal variations were typical for the considered seasons. On the contrary, the velocity of the equivalent neutral wind changed significantly (up to 2—2.5 times) even with a weak increase in geomagnetic activity. The reasons for such changes may be the strengthening of horizontal thermospheric winds and the penetration of zonal magnetospheric electric fields into midlatitudes during the equinoxes. The obtained results of calculations can be used in basic studies of solar-terrestrial relations and geospace, for the solution of applied problems related to the ability to predict the state of space weather, as well as for further development of the regional ionosphere model CERIM IION. The object of research: physical processes in the ionospheric plasma. The subject of research: spatiotemporal dependences of the main parameters of ionospheric plasma, which were obtained using incoherent scattering radar. Research methods — terrestrial radiophysical method of incoherent scatter of radio waves, statistical analysis of observation results, semi-empirical modelling of parameters of dynamic and thermal processes.

Single-station quad-constellation GNSS regional ionospheric modelling for navigation

Conventionally, regional ionospheric models (RIMs) are established using GNSS at multiple stations. However, this will severely rely on the availability of the local GNSS observation network. In this study, a single-station quad-constellation GNSS regional ionospheric modelling (SQG-RIM) approach is proposed by establishing the RIM with the GPS/GLONASS/BDS/Galileo observations at a single station. To facilitate its application, an algorithm is further proposed to divide the entire modelling region into the core area and the non-core area. Compared with the global ionospheric map (GIM), the SQG-RIM in the core area can increase the ionospheric error correction rate by about 9%. Further, the SQG-RIM is applied to single point positioning (SPP) using a differentiated weighting scheme for different signal-passing areas. Test results indicate that the three-dimensional quad-constellation SPP accuracies are improved by 57% and 52% after applying the SQG-RIM as compared to the Klobuchar and GIM models, respectively.

3‐D Regional Imaging of Ionosphere Over Africa Through Assimilating Satellite and Ground‐Based Data

AbstractIn this study, the first high‐resolution regional ionospheric model over Africa and adjacent areas (−40–40°N latitude, 30°W–60°E longitude, and 80–1,400 km in altitude) is constructed by assimilating ground‐based slant total electron content (STEC) from 40 GPS (Global Positioning System) receiver stations and space‐based NmF2 (ionospheric F2 peak density) data from C2 (Constellation Observing System for Meteorology, Ionosphere, and Climate‐2) into the International Reference Ionosphere (IRI‐2016) model. An Ionospheric Data Assimilation Four‐Dimensional (IDA4D) technique was used to estimate electron densities as high as 1.5° 3° in latitude and longitude, 10 km in altitude in the E and F regions, and 15 min in universal time. Two experiments were run for the following data sets: (a) GPS‐STECs only and (b) GPS‐STECs and NmF2s from C2 during geomagnetically quiet (6–11 May 2021) and storm periods (12–14 May 2021). The IDA4D assimilation results are validated using independent C2 control group, ionosonde, and JASON‐3 observations. Results for the storm period show that experiment 2 reduces the average root‐mean‐square error (RMSE) of NmF2, foF2, and VTEC by 34%, 31%, and 34%, respectively, and increases the associated correlations by 10%, 14%, and 2% over IRI, respectively. Using IDA4D, we observed enhancement of the northern crest equatorial ionization anomaly in the late evening that was caused by upward and northward plasma transport.

Regional Ionosphere Delay Models Based on CORS Data and Machine Learning

<h3>Abstract</h3> The ionospheric refraction of GNSS signals can have an impact on positioning accuracy, especially in cases of single-frequency observations. Ionosphere models that are broadcasted by the satellite systems (e.g., Klobuchar, NeQuick-G) do not include enough details to permit them to correct single-frequency observations with sufficient accuracy. To address this issue, regional ionosphere models (RIMs) have been developed in several countries in the western Balkans based on dense Continuous Operating Reference Stations (CORS) observations. Subsequently, a RIM for the western Balkans was built using an artificial neural network that combined regional ionosphere parameters estimated from the CORS data with spatiotemporal (latitude, longitude, hour of day), solar (F10.7) and geomagnetic (Kp, Dst) parameters. The RIMs were tested at the solar maximum (March 2014), a geomagnetic storm (March 2015), and the solar minimum (March 2018). The new RIMs mimic the integrated electron density much more effectively than the Klobuchar model. Furthermore, RIMs significantly reduce the ionospheric effects on single-frequency positioning, indicating their necessity for use in positioning applications.

Real-Time Ionosphere Prediction Based on IGS Rapid Products Using Long Short-Term Memory Deep Learning

<h3>Abstract</h3> High-precision ionospheric corrections are essential for precise positioning using low-cost single-frequency GNSS receivers. Although Real-Time Global Ionosphere Maps (RT-GIMs) are available from the International GNSS Service (IGS), their ionospheric predictions continue to rely on networks of globally-distributed GNSS stations and real-time data links. In this paper, we develop a regional real-time ionospheric prediction model based on a long short-term memory (LSTM) deep learning method. Because the GIMs from the IGS are used as prediction bases, the requirement for real-time GNSS data-links is eliminated. A comparison of the ionospheric predictions generated over 24 hours by the proposed method and the IGS GIM revealed a prediction accuracy root mean square error of 0.8 TECU. These results suggest that the proposed model may be suitable for use in real-time applications.

A Consistent Regional Vertical Ionospheric Model and Application in PPP-RTK Under Sparse Networks

<h3>Abstract</h3> Ionospheric augmentation is one of the most important dependences of PPP-RTK. Because of the dispersive features of the ionosphere, the ionospheric information is usually coupled with satellite- and receiver-related biases. This will pose a hidden trouble of inconsistent ionospheric corrections if different numbers of reference stations are involved in calculation. In this paper, we aimed at introducing a consistent regional vertical ionospheric model (RVIM) by estimating receiver biases. We first presented the inconsistent ionospheric corrections under sparse networks. Then the RVIM is compared with the International GNSS Service (IGS) final global ionospheric map (GIM) product, and the average of differences between them is 1.13 TECU. Furthermore, the slant ionospheric corrections were employed as a reference to evaluate both RVIM and GIM. The mean RMS values are 1.48 and 2.23 TECU for the RVIM and GIM, respectively. Finally, we applied the RVIM into PPP-RTK. Results indicate that the PPP-RTK with RVIM constraints achieves improvements in horizontal errors, vertical errors, and convergence time by 43.45, 29.3, and 22.6% under the 68% confidence level, compared with the conventional PPP-AR.

Spatiotemporal Analysis of Regional Ionospheric TEC Prediction Using Multi-Factor NeuralProphet Model under Disturbed Conditions

The ionospheric total electron content (TEC) is susceptible to factors, such as solar and geomagnetic activities, resulting in the enhancement of its non-stationarity and nonlinear characteristics, which aggravate the impact on radio communications. In this study, based on the NeuralProphet hybrid prediction framework, a regional ionospheric TEC prediction model (multi-factor NeuralProphet model, MF-NPM) considering multiple factors was constructed by taking solar activity index, geomagnetic activity index, geographic coordinates, and IGS GIM data as input parameters. Data from 2009 to 2013 were used to train the model to achieve forecasts of regional ionospheric TEC at different latitudes during the solar maximum phase (2014) and geomagnetic storms by sliding 1 day. In order to verify the prediction performance of the MF-NPM, the multi-factor long short-term memory neural network (LSTMNN) model was also constructed for comparative analysis. At the same time, the TEC prediction results of the two models were compared with the IGS GIM and CODE 1-day predicted GIM products (COPG_P1). The results show that the MF-NPM achieves good prediction performance effectively. The RMSE and relative accuracy (RA) of MF-NPM are 2.33 TECU and 93.75%, respectively, which are 0.77 and 1.87 TECU and 1.91% and 6.68% better than LSTMNN and COPG_P1 in the solar maximum phase (2014). During the geomagnetic storm, the RMSE and RA of TEC prediction results based on the MF-NPM are 3.12 TECU and 92.86%, respectively, which are improved by 1.25 and 2.30 TECU and 2.38% and 7.24% compared with LSTMNN and COPG_P1. Furthermore, the MF-NPM also achieves better performance in low–mid latitudes.