Ionospheric Modeling by Using a Self-Organizing Map Under Disturbed Conditions

  • NAVIGATION: Journal of the Institute of Navigation
  • July 2026,
  • 73
  • navi.781;
  • DOI: https://doi.org/10.33012/navi.781

Abstract

As solar activity approaches the peak of the 25th solar cycle, the Earth’s upper atmospheric layer, known as the ionosphere, is strongly disturbed by solar activity. Ionospheric disturbances are the main error source of global navigation satellite systems. We propose a real-time ionospheric modeling system (RIMS) based on a self-organizing map (SOM) to accurately model ionospheric conditions. A SOM is an unsupervised machine-learning tool with origins in biological algorithms, having a topological self-organizing structure. The RIMS can model the ionosphere while automatically detecting and removing outliers. Results demonstrate that models generated by the RIMS exhibit high accuracy in quiet and disturbed ionospheric conditions compared with a current actual-use method. The median residual slant total electron content improved from 0.254 to 0.118 total electron content units as compared with the assumed actual-use method. Moreover, the RIMS flexibly and stably models the ionosphere in real time under disturbed conditions without large quantities of data from prior years.

Keywords

1 INTRODUCTION

Solar activity is reaching the peak of the 25th solar cycle, and high solar activity affects the performance of global navigation satellite systems (GNSSs) (Afraimovich et al., 2001; Hirokawa et al., 2023). High solar activity affects the behavior of the Earth’s upper atmospheric layer, known as the ionosphere. Part of the upper atmosphere, the ionospheric layer is ionized by the sun’s extreme ultraviolet rays at altitudes of 100–1000 km. GNSS signals passing through the ionosphere are delayed by free electrons in the ionosphere, representing the main error source of GNSSs. The ionospheric delay error is estimated from the total electron content (TEC), which corresponds to the total number of free electrons along the path between the receiver and satellite. To improve the accuracy of GNSS positioning, it is important to understand the spatial TEC distribution of the ionosphere and appropriately remove errors caused by the ionosphere, particularly during ionospheric disturbances.

At middle geomagnetic latitudes, medium-scale traveling ionospheric disturbances (MSTIDs) are frequently occurring ionospheric irregularity phenomena. MSTIDs have a wave-like structure with a wavelength of 100–200 km and a period of 10 min to 1 h. MSTIDs exhibit large fluctuations in temporal and spatial TEC values, leading to serious concerns regarding the reliability of GNSS positioning. An ionospheric model must be able to adapt to complex phenomena, such as MSTIDs, for stable positioning.

Many ionospheric models have been proposed for understanding ionospheric conditions. Ionospheric models can be divided into two main categories: physical and empirical. Physical models include methods for calculating ionospheric conditions based on physical laws or fundamental equations, such as coupling with a neutral atmosphere and magnetosphere. For example, the thermosphere–ionosphere–electrodynamics general circulation model is one of the physical ionospheric models provided by the National Center for Atmospheric Research (Richmond et al., 1992). These physical models are sophisticated and can respond to any ionospheric condition; therefore, running simulations is costly. In contrast, empirical modeling includes methods for determining the relation between input and output variables based on experimental or observational data. The International Reference Ionosphere (Bilitza et al., 2022) and NeQuick (Nava et al., 2008) models are well-known empirical ionospheric models. In general, empirical models do not incur operational running costs. However, irrespective of the ionospheric disturbance or the number of observatories in a region, the models may not adequately estimate the TEC variation for all cases (Kim & Kwak, 2025; Tariku, 2020). Robust real-time estimations under disturbed conditions are desirable.

With the development of machine-learning technology, machine learning has been increasingly used to model the ionosphere. Multilayer perceptron (MLP) (Natras et al., 2023), long short-term memory (LSTM) (Chen & Gao, 2023; Tang et al., 2024), and MLP-based recurrent neural network (RNN) (Priyadarshi et al., 2023) methods are representative examples of such approaches. Moreover, many hybrid models that combine machine-learning methods have been developed. These models include a method combining a convolutional neural network (CNN) with a gated recurrent unit (GRU), which is a variation of an RNN (Kaselimi et al., 2021), and a model combining an LSTM and a CNN (Mao et al., 2024; Ruwali et al., 2021). Model performance using these machine-learning methods achieves higher accuracy under disturbed ionospheric conditions than conventional methods such as classical broadcast, Klobuchar, or NeQuick models. Machine-learning methods can represent complex nonlinear behaviors with high ionospheric activity. Therefore, these machine-learning methods have been applied to the ionosphere in a wide range of fields, including ionospheric modeling for positioning systems, such as satellite-based augmentation systems (SBASs) (Wang et al., 2023), and ionospheric monitoring for natural hazard warning systems (Komjathy et al., 2016). Recently, the National Aeronautics and Space Administration Jet Propulsion Laboratory developed a near-real-time ionospheric monitoring system for natural hazard warnings using the machine-learning method GUARDIAN (Martire et al., 2023). The generation of accurate models via machine-learning methods usually requires a large amount of additional data, such as solar activity or the geomagnetic activity index over the past several years. Unfortunately, these machine-learning technologies are computationally expensive. From a practical perspective of GNSS positioning, an ionospheric modeling method should be as simple, responsive, robust, and accurate as possible.

To address this challenge, we propose ionospheric modeling using a self-organizing map (SOM), which is an unsupervised machine-learning method (Kohonen, 1982). A SOM maps from a high-dimensional space to a low-dimensional space while preserving topology and is highly suitable for modeling complex distributed data in space. Because the SOM has its origins in biological algorithms with topological representational self-organization through “competitive” and “cooperative” learning processes, even complex phenomena can be modeled with flexibility and stability. Over the past few years, these processes have made it possible to perform modeling in real time without a large amount of training data. In contrast to LSTM approaches, SOMs are generally incapable of learning time dependence in sequences; however, SOMs can capture the features of input data in real time owing to its simple algorithm. Thus, SOMs allow for high responsiveness to track temporal variability without time-series training data.

A few studies have explored ionospheric modeling using SOMs. For instance, a SOM was applied to the ionosphere estimation problem by adapting the triangular interpolation (TRIN) grid adopted by the European Geostationary Navigation Overlay Service (EGNOS), Europe’s regional SBAS (Désert et al., 2015). This model focuses on EGNOS and includes tuning constraints that preserve the global shape of the initial TRIN. However, for a wider range of applications for ionospheric models, including SBAS, positioning, and space weather applications, more general ionospheric modeling systems using SOMs are required.

Therefore, this study aims to develop a more general modeling system that can be applied under ionospheric disturbance conditions with higher accuracy while using fewer data sets by utilizing a SOM, with a focus on practical applications. Among the various possible applications of the proposed ionospheric modeling system using a SOM, precise point positioning (PPP) real-time kinematic (RTK) services, such as the Quasi-Zenith Satellite System (QZSS) Centimeter-Level Correction Service (CLAS), are considered as a strong candidate for application. In QZSS CLAS, the ionospheric delay is calculated as an ionospheric correction for the slant total electron content (STEC) at the receiver’s position, determined independently for each satellite, to improve the positioning accuracy (Cabinet Office Government of Japan, 2022). Therefore, we focus on STEC models in this study.

In this study, only the position and STEC data, which are calculated by ground receivers of continuously operating reference stations (CORSs), were used to conduct a feasibility study on ionospheric modeling using a SOM (batch version) under an MSTID (September 14, 2021) in Japan as a first step toward a practical application of the proposed SOM system.

2 SOM BATCH VERSION

A SOM is an unsupervised machine-learning technique introduced by Kohonen (Kohonen, 1982). A SOM is built using biological models of neural systems. A SOM consists of two layers: an input layer and an output layer. The “neurons” in the lattice are set as two-dimensional nodes on the output layer. Each neuron is associated with a synaptic-weight vector in the input layer while preserving the topological structure. SOM training processes include “competition,” “cooperation,” and “synaptic adaption,” as described below (Haykin, 2009; Furukawa, 2017).

Competition Process

In this process, x represents an input vector selected from the input space and m is the dimension of the input data space:

x=[x1,x2,⋯,xm]T1

Here, wjT represents a reference vector for each neuron, and its dimensions are the same as those of the input vector. The variable j denotes the index of the data, and l is the total number of neurons:

wj=[wj1,wj2,⋯,wjm]Tj=1,2,3…,l2

We apply the following to identify the neuron i(x) that best matches the input vector x:

i(x)=argminj‖x−wj‖3

i(x) is called the best-matching or winning neuron.

Cooperation Process

The identified winning neuron is located at the center of a topological neighborhood during the competition process. The typological neighborhood function hj,i is defined as follows:

hj,i(x)=exp⁡(−‖rj−ri‖22σ2)4

where ‖rj−ri‖2 is the Euclidean distance between rj, which defines the position of the excited neuron j, and ri, which defines the position of the winning neuron i in the output space.

At time t, σ is the “effective width” of the neighborhood, which is defined as follows:

σ(t)=max[σ0exp⁡(−tτ),σmin]5

where t is the number of iterations, τ is a time constant, σ0 is the initiation value, and σmin is the minimum effective width. From the initial value σ0 to σmin, σ(t) decreases exponentially as the number of iterations increases.

Synaptic Adaption Process

The synaptic-weight vectors wj of all neurons are adjusted using the following formula:

wj(t)=∑i=1mhj,i(x)(t)xi∑i′=1mhj,i′(x)(t)6

This process is iterated until convergence is achieved.

In this work, the ionospheric model was trained using the SOM, as shown above. An overview of the architecture of the ionospheric model is shown in Figure 1. The input vector x comprises three elements in the input space: latitude, longitude, and STEC. The synaptic-weight vector wj of each neuron (where j is the number of neurons or nodes) connects the input and latent spaces. The wj terms are initialized via principal component analysis. The Euclidean distance between vectors x and wj is calculated mathematically to minimize the identification of best matches for all neurons. Through this process, the input space of the activation patterns is mapped onto a discrete latent space of neurons. The synaptic-weight vectors are updated using the neighborhood function and are distributed similarly to the input vector. The synaptic-weight vector comprises the latitude, longitude, and STEC, similar to the input-space dimension, and is identified from the output layer to the input layer, as shown in Figure 1.

Overview of the architecture for the ionospheric model using a SOM
FIGURE 1

Overview of the architecture for the ionospheric model using a SOM

3 METHOD AND DATA

3.1 Real-Time Ionospheric Modeling System Based on a SOM

The goal of the real-time ionospheric modeling system (RIMS) developed here is to provide users with a highly accurate spatial STEC distribution in real time using an ionospheric model. The input data used for modeling were the STEC and the CORS position (longitude and latitude) at which the STEC was observed. The RIMS architecture consists of three modeling steps (see Figure 2), as described below:

Flowchart of the RIMS based on a SOM
FIGURE 2

Flowchart of the RIMS based on a SOM

(1) STEP 1: Standardize the input data.

The initial input data consist of three components: latitude, longitude, and STEC. In this study, the STEC was generated via the next-generation PPP-RTK service developed by the Mitsubishi Electric Corporation using GNSS measurements from the CORS network in Japan (Sato et al., 2022) for the initial input data. The STEC was calculated and provided independently for each satellite.

In STEP 1, the initial input data are standardized, and the SOM is implemented to capture the initial overall features drawn from the ionospheric conditions (SOM_0). SOM_0 is implemented under the conditions listed in Table 1.

View this table:
TABLE 1 SOM Parameters of the RIMS

(2) STEP 2: Perform modeling to remove outliers.

SOM_0 is applied in STEP 1 for all input data, including possible outliers for each sampling time. However, it is important to appropriately identify and remove outliers for ionospheric modeling. In STEP 2, anomaly detection is performed based on STEP 1. The input data that significantly deviate from the features of the models are determined as outliers. The initial input data are updated by removing the outliers, and the SOM is implemented again (SOM_0).

(3) STEP 3: Conduct more accurate modeling using the updated input data.

In STEP 3, outlier detection and removal are applied in more detail using the models from STEP 2, and the values correlated with variations in the ionospheric disturbance are also monitored. The details of this process are as follows.

First, outliers are detected and removed. The estimated STEC values are calculated using the SOM and a linear interpolation method, and the estimated and observed STEC are compared at the position of the CORS for modeling. If the difference between the estimated and observed values is abnormally large based on 99% prediction intervals, the point is considered an outlier. Outliers in the input data are removed.

Additionally, the magnitude of ionospheric disturbances is monitored by the variation in the 99% prediction intervals. Variations in the 99% prediction intervals are calculated before outliers are removed. As most outliers are removed in STEP 2, the outliers removed in STEP 3 have little impact on the overall trend of the STEC distributions.

Finally, using the updated input data consisting of the latitude, longitude, and STEC values without outliers, the ionosphere is modeled using the SOM.

The CORS and STEC data are available in real time without any postprocessing. Therefore, the user simply enters their position (longitude and latitude), and the STEC at that location is calculated almost instantaneously by the SOM model generated using the RIMS.

3.2 Setting Parameters

The output layer of a SOM is a two-dimensional lattice space, and the neurons are placed at the nodes in lattice space. In this paper, the neurons are called “SOM_0 nodes” or “SOM nodes.” For example, a SOM node (5 × 5) is expressed in five rows and five columns for a total of 25 SOM nodes in the lattice space. More SOM nodes allow a more detailed description of ionospheric conditions. However, there has been little research on general ionospheric modeling using SOMs under disturbed ionospheric conditions, and there is no clear method for determining the optimal number of SOM nodes. Therefore, in this study, the following SOM node conditions were used to investigate the effect of the number of SOM nodes on modeling accuracy, as shown in Table 1. The SOM_0 processing objective in STEP 1 and STEP 2 is to capture the features of the ionosphere and to detect and remove outliers; therefore, it is not necessary to explore many SOM_0 node conditions. However, the ionospheric model derived from STEP 3 directly affects the calculations of the STEC distribution; thus, STEP 3 must investigate a wide range of SOM node conditions.

Regarding the parameters of the neighborhood function h, assuming that the length of one side of the output two-dimensional layer is 1, smin of Equation (5) is usually set to 1/10 and s0 is set to 1/2 (Furukawa, 2017). In this paper, the parameters of the neighborhood function were determined by following the work of Furukawa (2017). The number of iterations was determined by the effective width σ, as shown in Equation (5). The effective width decreases exponentially to smin with the number of training iterations t, where τ is a time constant, which is a selectable parameter. In this study, τ was set as 30 to avoid a local solution. Figure 3 shows the relationship between the effective width and the number of iterations. Here, the σ0 and σmin values of the neighborhood function were set to 0.5 and 0.1, respectively, to capture the features of the ionospheric conditions with an accurate depiction of the local behavior. The optimal values of σ0 and σmin were determined through preliminary investigation. A σmin value of 0.1 was confirmed to be sufficiently small to accurately evaluate the performance of the models in this study. Regarding the iteration number, we found that when the iteration number exceeded 50, the effective width reached smin, as shown in Figure 3. Therefore, for this study, 100 was selected as the number of iterations, including the margin, as listed in Table 1.

Relationship between the effective width and number of iterations (τ = 30)
FIGURE 3

Relationship between the effective width and number of iterations (τ = 30)

3.3 Building the Data Set

The initial input data were calculated using observational data from a maximum of approximately 416 CORSs in the region of Japan, with the latitude ranging from 33.0° to 39.0° and longitude ranging from 137.0° to 142.0°. The CORS-observed input data used were recorded on September 14, 2021, between 08:56 Universal Time (UT) (205200 Global Positioning System [GPS] time) and 13:40 UT (222000 GPS time). This day was selected because it corresponded to an MSTID observed in Japan. The sampling interval was 60 s from G25 (GPS).

The initial input position data were the longitude and latitude of the CORSs. Outliers in the initial input data were removed in STEP 2 and STEP 3. The removed outliers were divided into two categories for modeling and validation in STEP 3. Input data for final modeling (SOM) in STEP 3 were randomly selected from the categorized modeling data. The number of input data points for modeling was set to 10, 20, 50, 100, and 200. These parameters are referred to as CORS_10, CORS_20, CORS_50, CORS_100, and CORS_200, respectively. If there was an epoch in which the minimum quantity of initial input data was not reached, that epoch was skipped. Figure 4 shows the distribution of the CORSs for the input data at 11:21 UT / 213660 GPS time.

CORS locations of the input data for modeling and validation at 11:21 UT: (a) CORS_10, (b) CORS_20, (c) CORS_50, (d) CORS_100, and (e) CORS_200
FIGURE 4

CORS locations of the input data for modeling and validation at 11:21 UT: (a) CORS_10, (b) CORS_20, (c) CORS_50, (d) CORS_100, and (e) CORS_200

4 RESULTS AND DISCUSSION

4.1 Feasibility Study of Ionospheric Modeling by a SOM

4.1.1 Detecting and Removing Outliers

The initial STEC input data were generated by the Next-Generation PPP-RTK Service developed by Mitsubishi Electric Corporation (Sato et al., 2022). This service is still a prototype; therefore, the initial STEC input data include outliers in some cases. Figure 5(a) shows the generated raw STEC data for September 14, 2021, which contain outliers, as shown by a yellow line in the figure.

(a) Initial STEC data during all observation times and (b, c) the results of removing outliers with (b) (5 × 5) or (c) (16 × 16) SOM_0 nodes in STEP 2
FIGURE 5

(a) Initial STEC data during all observation times and (b, c) the results of removing outliers with (b) (5 × 5) or (c) (16 × 16) SOM_0 nodes in STEP 2

To detect and remove outliers in STEP 2 and STEP 3, the SOM_0 models generated in the previous step were used as input data for each time interval. In STEP 2, the distance between the SOM_0 models and the input data was used as a threshold. In STEP 3, the magnification of the 99% prediction interval was used as a threshold. A preliminary investigation on the sensitivity to outlier removal determined thresholds of 0.5 for STEP 2 and 1.1 for STEP 3.

Figure 5(b) shows the results of removing outliers in STEP 2. The red data points in the figure show the outliers removed in STEP 2, and the green data points represent the remaining data. In STEP 2, the SOM was applied under two conditions, where the SOM_0 nodes were (5 × 5) (Figure 5(b)) and (16 × 16) (Figure 5(c)). Both results showed that the outliers were appropriately removed in most cases.

Figure 6 shows that the STEC distributions at 11:50 UT / 215400 GPS time under SOM_0 nodes were (5 × 5) and (16 × 16), respectively. Figures 6(a-1) and 6(c-1) show the STEC distributions before outlier removal with (5 × 5) and (16 × 16) SOM_0 nodes, respectively. Figures 6(a-2) and 6(c-2) show that the abnormal points displayed in the red circle were correctly removed in STEP 2. Regarding the results of STEP 3, when the estimated and observed STEC data were compared, as shown in Figures 6(b-1) and 6(d-1), there were no plots that deviated significantly from the 99% prediction interval. Therefore, the process of removing outliers was omitted, as shown in Figures 6(b-2) and 6(d-2).

Results of removing outliers at 11:50 UT with (5 × 5) SOM_0 nodes during (a-1, a-2) STEP 2 and (b-1, b-2) STEP 3 and with (16 × 16) SOM_0 nodes during (c-1, c-2) STEP 2 and (d-1, d-2) STEP 3
FIGURE 6

Results of removing outliers at 11:50 UT with (5 × 5) SOM_0 nodes during (a-1, a-2) STEP 2 and (b-1, b-2) STEP 3 and with (16 × 16) SOM_0 nodes during (c-1, c-2) STEP 2 and (d-1, d-2) STEP 3

The effect of the condition of SOM nodes on outlier removal is discussed below. Both SOM_0 node conditions, (5 × 5) and (16 × 16), resulted in appropriate outlier removal, with no significant difference in the STEC distribution. The results of the confusion matrix under both SOM_0 node conditions, (5 × 5) and (16 × 16), are shown in Table 2. The results show that no significant qualitative differences. Meanwhile, the number of false positives was larger than that of false negatives, indicating that normal data were mistakenly identified as outliers. In this study, some false positive outliers were allowed if they did not significantly impact the overall trend of the STEC distributions. Consequently, the condition of the SOM_0 nodes for outlier removal was set to (5 × 5) in this study, because it is desirable to remove outliers as quickly as possible with the minimum required accuracy.

View this table:
TABLE 2 Confusion Matrix of Outlier Removal

Figure 7(a) shows the variations in the normalized prediction intervals between 8:56 UT and 13:48 UT, and Figure 7(b) shows the detrended TEC map (30-min window) from DRAWING-TEC (National Institute of Information and Communications Technology in Japan, n.d.) between 10:00 UT and 13:00 UT. The prediction interval was normalized by the maximum absolute scaling during the observation period, and the values refer to the normalized prediction interval on the y-axis in Figure 7(a). Figure 7(b) shows the MSTID that occurred in Japan on September 14, 2021; the peak MSTID occurred at approximately 12:00 UT. A comparison of Figures 7(a) and 7(b) shows that the normalized prediction interval decreased when the ionosphere was quiet; moreover, as the ionospheric disturbance increased, the normalized prediction interval also increased. Because the behavior of the ionospheric disturbance coincided with variations in the prediction intervals, the RIMS uses variations in prediction intervals as indicators of ionospheric disturbances, such as MSTIDs. For practical applications, one must examine the possibility of using the RIMS under other ionospheric disturbances, such as plasma bubbles, and set the appropriate SOM parameters for the neighborhood function based on the ionospheric condition. The RIMS can identify the type and magnitude of ionospheric disturbances. In the next section, we discuss the SOM models for STEP 3.

(a) Result of variations of the prediction interval with (5 × 5) SOM nodes and (b) detrended TEC maps (30-min window) (September 14, 2021) from DRAWING-TEC (National Institute of Information and Communications Technology in Japan [NICT], n.d.)
FIGURE 7

(a) Result of variations of the prediction interval with (5 × 5) SOM nodes and (b) detrended TEC maps (30-min window) (September 14, 2021) from DRAWING-TEC (National Institute of Information and Communications Technology in Japan [NICT], n.d.)

4.1.2 Fitting Process of SOM Models

Figure 8 shows the fitting process of the SOM models in STEP 3 at 11:20 UT / 213660 GPS time under disturbed ionospheric conditions, where the number of input data points for modeling was 100 (CORS_100), and the iteration numbers were 0, 50, and 100. The red points represent the input data, and the black line represents the SOM model. As the number of training iteration cycles increases, the SOM model, shown by the black line, gradually fits the observed STEC data, plotted in red. When the number of training cycles reached 100 iterations, the SOM model became saturated. Thus, this number of iterations was appropriate for modeling the ionosphere. Moreover, higher SOM nodes could provide a more detailed description of the STEC distribution than lower SOM nodes, indicating that, even if the input data are sparse, a SOM model with higher SOM node conditions can implement finer spatial interpolation than a SOM model with fewer SOM nodes.

The modeling process at 11:20 UT for (a) (10 × 10), (b) (20 × 20), and (c) (50 × 50) SOM nodes, with (a1, b-1, c-1) n= 0, (a-2, b-2, c-2) n=50, and (a-3, b-3, c-3) n=100 iterations
FIGURE 8

The modeling process at 11:20 UT for (a) (10 × 10), (b) (20 × 20), and (c) (50 × 50) SOM nodes, with (a1, b-1, c-1) n= 0, (a-2, b-2, c-2) n=50, and (a-3, b-3, c-3) n=100 iterations

4.1.3 Performance of SOM Model Fitting in STEP 3

The model fitting performance was confirmed by monitoring the correlation between the observed input data and the estimated STEC data from the SOM model at the modeling position (triangle plots in Figure 4). The results for the (20 × 20) SOM nodes with CORS_10, CORS_20, CORS_50, CORS_100, and CORS_200 are shown in Figure 9. These results show that as the number of SOM nodes increases, the correlation coefficient between the observed data and the estimated value becomes closer to 1.0. From these results, it was confirmed that by selecting the appropriate SOM nodes and number of CORSs (input data), one can model ionospheric conditions using a SOM with only longitude, latitude, and STEC data.

Performance of model fitting for the proposed ionosphere modeling system with (20 × 20) SOM nodes for (a) CORS_10, (b) CORS_20, (c) CORS_50, (d) CORS_100, and (e) CORS_200
FIGURE 9

Performance of model fitting for the proposed ionosphere modeling system with (20 × 20) SOM nodes for (a) CORS_10, (b) CORS_20, (c) CORS_50, (d) CORS_100, and (e) CORS_200

The accuracy of the ionospheric models varies depending on the shape of the input-data distribution. When the aspect ratios of the input-data distribution (input layer) differ from those of the latent space (output layer), the model accuracy decreases (Furukawa, 2017). To enable applications to other regions, one must flexibly change the aspect ratio of the SOM nodes based on the distribution shape of the observed CORSs. Furthermore, different regions exhibit different ionospheric conditions. The SOM parameter values may not be suitable for other ionospheric conditions such as plasma bubbles. In future studies, the optimal SOM parameter values must be considered based on the ionospheric conditions for application to other regions.

4.2 Effect of SOM Parameters on Ionospheric Model Accuracy

The SOM nodes and number of CORSs (input data) are important SOM parameters to consider when creating an ionospheric model. To investigate the effects of these SOM parameters on the accuracy of the ionospheric model based on the proposed SOM system, the residual STEC, which is the difference between the observed and estimated STEC data, was calculated. The estimated STEC values were calculated using the SOM at the validation point. In particular, two points in the SOM close to the validation position were selected and linearly interpolated at the validation point. The median of the absolute value of the difference between the estimated and observed data at each validation position is taken as the residual STEC data.

The residual STEC results are shown in Figure 10, and Table 3 lists the statistical results with the median (Mdn.) and the median absolute deviation (MAD) for all cases. As the number of CORSs increased, the residual STEC decreased. In particular, the values of the residual STEC in these figures show large fluctuations and turbulence from approximately 11:00 UT to approximately 12:15 UT, as shown in Figure 10. During this period, a strong MSTID occurred at 11:00 UT in Japan (Hirokawa et al., 2023), and the time of the large fluctuations coincided with that of the MSTID. The large fluctuations were considered to be due to the MSTID. When the number of input data points was large, as in the cases of CORS_100 and CORS_200, the fluctuations in the residual STEC under the MSTID decreased compared with cases involving a small number of input data points, such as the cases of CORS_10 and CORS_20. Similarly, as the number of SOM nodes increased, the fluctuations decreased further. The ionospheric model based on the RIMS with more input data (CORSs) and SOM nodes was robust, even when a strong MSTID occurred.

Residual STEC between observed STEC and estimated STEC, obtained by using the SOM model at validation positions for (a) CORS_10, (b) CORS_20, (c) CORS_50, (d) CORS_100, and (e) CORS_200 SOM nodes
FIGURE 10

Residual STEC between observed STEC and estimated STEC, obtained by using the SOM model at validation positions for (a) CORS_10, (b) CORS_20, (c) CORS_50, (d) CORS_100, and (e) CORS_200 SOM nodes

View this table:
TABLE 3 Median (Mdn.) and MAD of the Residual STEC (TECU) at Validation Positions

Moreover, the optimal SOMs were investigated, with results shown in Figure 11. Normal and disturbed ionospheric conditions were examined. The black lines in the figures represent the results under normal ionospheric conditions at 9:58 UT and 13:04 UT. The red lines present the results under disturbed ionospheric conditions at 11:12 UT and 11:21 UT, respectively. As a result, with regard to normal ionosphere conditions, the black lines in the figures show that the residual STEC values did not significantly change, with almost the same values observed for every SOM node condition. For the disturbed conditions, the red lines in the figures indicate that the residual STEC values tended to saturate to a lower value when the SOM nodes exceeded (20 × 20). However, CORS_10 (Figure 11(a)) exhibits unstable behavior regardless of the condition of the SOM nodes.

Relationship between the SOM nodes and residual STEC for (a) CORS_10, (b) CORS_20, (c) CORS_50, (d) CORS_100, and (e) CORS_200
FIGURE 11

Relationship between the SOM nodes and residual STEC for (a) CORS_10, (b) CORS_20, (c) CORS_50, (d) CORS_100, and (e) CORS_200

In addition, the optimal amount of input data (CORSs) was determined, as shown in Figure 12. The black lines in the figures show that the amount of input data (CORSs) did not significantly affect the residual STEC under normal conditions. In contrast, for disturbed conditions, the red lines in the figures indicate that the residual STEC values tend to saturate to a lower value when the number of input data points (CORSs) exceeds 100. As a result, the condition of the SOM nodes and the amount of input data (CORSs) should be varied in response to the ionospheric conditions and the amount of input data. These results revealed that at least (20 × 20) SOM nodes and CORS_100 are required to generate an accurate ionospheric model based on the SOM within the scope of these conditions.

Relationship between the number of input data points (CORSs) and residual STEC for (a) (5 × 5), (b) (10 × 10), (c) (16 × 16), (d) (20 × 20), (e) (32 × 32), (f) (50 × 50), and (g) (64 × 64) SOM nodes
FIGURE 12

Relationship between the number of input data points (CORSs) and residual STEC for (a) (5 × 5), (b) (10 × 10), (c) (16 × 16), (d) (20 × 20), (e) (32 × 32), (f) (50 × 50), and (g) (64 × 64) SOM nodes

In addition, the computational time of the proposed SOM system was investigated. The programs were written in Python, and the computational resource was a 13th Generation Intel(R) Core (TM) i7-13700, 32 GB. The computational time was calculated for CORS_200 at 11:21 UT, considering the traveling time of the MSTIDs. The results are summarized in Table 4. The minimum total computational time was 1.594 s for the (5 × 5) SOM nodes. The maximum time, that of the (64 × 64) SOM nodes, was 2.609 s. This result indicates that it is possible to model the ionosphere using the proposed SOM system in real time. The proposed SOM system achieved real-time performance for two reasons: (1) the SOM algorithm is extremely simple, as shown in Section 2, and (2) fewer types of input data were used (only latitude, longitude, and STEC information) compared with other machine-learning methods.

View this table:
TABLE 4 Computational Time (s) of the Proposed SOM System for CORS_200 at 11:21 UT

4.3 Comparison with Other Machine-Learning Methods

In the previous sections, the results showed that the proposed SOM system can model the spatial distribution of STEC accuracy in real time. In this section, the performance of the proposed SOM system is compared with that of other machine-learning methods. In this study, CNNs were selected for comparison because CNNs are a strong tool for capturing spatial variability to adjust the weight in a manner similar to that of a SOM.

The conditions of the CNN were set to be as simple as possible. The CNN was trained by using the input data, which is the same instantaneous data used above (latitude, longitude, and STEC, after outlier removal as described in Section 3.3). Because the CNN is a supervised learning method, the input data for modeling were further split into training and test groups at a 9:1 ratio. The input data conditions were selected as CORS_20 and CORS_200 and then normalized. The CNN layer was composed of two 1d_convolution layers with a maximum pooling layer, and the units of the neurons were fully connected. The CNN utilized a rectified linear unit activation function, a learning rate of 0.01, an Adam optimizer, a mean squared error loss function, a channel size of 400, a kernel size of five, and a total parameter count of 803,201, with the network trained for 150 epochs. The validation accuracy was monitored as a metric for early stopping, and the patience parameter was 2.

Figures 13(a) and (b) show the results of the SOM and CNN models, respectively. The condition of the SOM was (20 × 20) nodes under both CORS_20 and CORS_200. As shown in the figures, the residual STEC calculated by the CNN was larger than the residual STEC calculated by the proposed SOM system; that is, the ionospheric model based on the CNN was less accurate.

Comparison of the performance of a CNN and the proposed SOM system for (a) CORS_20 and (b) CORS200
FIGURE 13

Comparison of the performance of a CNN and the proposed SOM system for (a) CORS_20 and (b) CORS200

Moreover, the computational time of the CNN at 11:21 UT was approximately 4.4 s for CORS_20 and approximately 9.4 s for CORS_200. In contrast, the computational time of the proposed SOM system was 1.664 s, as shown in the “(20 × 20) SOM nodes“ column of Table 4. Although the conditions of the CNN were set to be as simple as possible in this study, the convolution calculations were time-consuming because of their heavy processing.

Based on these results, the performance of the ionospheric model using the proposed SOM system was much better than that of the CNN model in this study. One of the most likely reasons for this result is the difference in training algorithms for the input data. The SOM uses a competitive learning method for training. In this process, the neurons are selectively tuned to various patterns of input data; that is, the error correction is updated during the training process. Therefore, it is not necessary to implement back-propagation to compute the required network parameter updates, as in CNNs or other neural networks. Therefore, a SOM model can be built with high accuracy and less computational time.

5 VALIDATION FOR ACTUAL USE

5.1 Method

The scope of application of the proposed SOM system is wide and includes GNSS positioning, space weather, and disaster prevention. One of the most useful applications of the proposed SOM system lies in highly precise satellite positioning systems such as the PPP-RTK service. QZSS CLAS is a representative open-satellite-based PPP-RTK service in Japan (Cabinet Office Government of Japan, 2022). QZSS CLAS generates correction messages, including ionosphere delays, using measurement data from the CORSs and broadcasts these messages to users via QZSS. In this study, the actual usage was assumed to be the QZSS CLAS.

As shown in Figure 14, QZSS CLAS generates a gridded STEC correction of the ionosphere based on observed data using the GNSS network, and each gridded STEC correction is computed depending on the distance between the CORS position and the grid position. Figure 4 shows the validation point as the user’s position and grid position, after which the ionospheric information is broadcast to the users. Users calculate the ionosphere delay, which is computed via interpolating methods, such as bilinear methods (Cabinet Office, Government of Japan, 2022), using the gridded STEC information. Four cases were included in this study, and the accuracy of the ionospheric model was assessed for the four cases.

Flow diagram of validation cases for actual use
FIGURE 14

Flow diagram of validation cases for actual use

Case 1: “CORS_Grid” (Assumed case based on actual method; the calculated process was not exactly the same as the actual process; the interpolation at the validation position is referred to in the specification of QZSS CLAS)

First, the gridded STEC data were calculated using the input data for modeling using inverse distance weighting (IDW), as shown in Equation (7):

STEC=∑i=1NwiSTECi∑j=1Nwj7

where N is the number of input data points within 150 km of each grid point and w is the weight, which is the reciprocal of the square of the distance from the grid point. The grid positions are shown in Figure 4. Then, the estimated STEC at the validation position was calculated for validation from the gridded STEC data. A bilinear interpolation method was used to estimate the STEC. The four gridded points nearest to the validation point were selected, and the estimated STEC was calculated.

Case 2: “SOMnode_Grid”

The SOM model was generated using the input data, and the calculated STEC data were stored at each SOM node. The gridded STEC data were calculated using the STEC data at each SOM node using IDW. The STEC data at the validation position were then calculated using the gridded STEC data in the same way as in Case 1 (CORS_Grid).

Case 3: “SOMnode_direct”

The STEC data at the validation position were calculated directly using the bilinear interpolation method based on the STEC data stored in each SOM node. The four SOM node points nearest to the validation point were selected, and the estimated STEC was calculated.

Case 4: “CORS_direct”

The STEC data at the validation position were calculated directly using the bilinear interpolation method with the four nearest inputs.

The processes for validation of all cases are summarized in Figure 14.

5.2 Test Results and Evaluation of Performance with Actual Usage Assumed

Four cases were implemented to validate the proposed SOM system under conditions CORS_20 and CORS_200 with (5 × 5), (10 × 10), (20 × 20), (32 × 32), (50 × 50), and (64 × 64) SOM nodes. The results under CORS_20 are shown in Figures 15(a-1) to 15(d-1), and those under CORS_200 are shown in Figures 15(a-2) to 15(d-2). The “CORS_Grid” result, shown by a black line, represents a case similar to the current actual use to estimate the STEC at the validation position by referring to the specification of QZSS CLAS (Cabinet Office, Government of Japan, 2022). The “SOMnode_Grid” results are shown as a green line, displaying the case where the STEC values were estimated by SOM models with reference to the specifications. “SOMnode_direct” (red) and “CORS_direct” (blue) represent cases in which the STEC values were directly estimated at the validation position.

Validation results for the condition of CORS_50 (number of input data points) for (a-1) (5 × 5), (b-1) (20 × 20), (c-1) (32 × 32), and (d-1) (64 × 64) SOM nodes and for the condition of CORS_200 for (a-2) (5 × 5), (b-2) (20 × 20), (c-2) (32 × 32), and (d-2) (64 × 64) SOM nodes
FIGURE 15

Validation results for the condition of CORS_50 (number of input data points) for (a-1) (5 × 5), (b-1) (20 × 20), (c-1) (32 × 32), and (d-1) (64 × 64) SOM nodes and for the condition of CORS_200 for (a-2) (5 × 5), (b-2) (20 × 20), (c-2) (32 × 32), and (d-2) (64 × 64) SOM nodes

The results for CORS_Grid (black) and SOMnode_Grid (green) in Figure 15 are almost identical; the lines in the figure appear to overlap. Even if an accurate ionosphere model can be generated using the proposed SOM system, transforming the model information into gridded information would degrade the accuracy of the user position estimation.

For CORS_50 with fewer SOM nodes, CORS_Grid, SOMnode_Grid, CORS_direct, and SOMnode_direct exhibited similar behavior, as shown in Figures 15(a-1) to 15(d-1). In contrast, when the SOM nodes were greater than (20 × 20), SOMnode_direct provided the smallest residual STEC for assumed actual use, as shown in Figures 15(a-1) to 15(d-1). The residual STEC of SOMnode_direct remained below 0.5 total electron content units (TECU), without significant fluctuations throughout the experiment. With regard to CORS_200 in Figures 15(a-2) to 15(d-2), the residual STEC of SOMnode_direct was the smallest; that is, the error was the lowest compared with all cases except the case of (5 × 5) SOM nodes. When the SOM nodes were greater than (20 × 20), the residual STEC of SOMnode_direct remained stably below approximately 0.25 TECU throughout the experiment, regardless of whether there was an ionospheric disturbance, as shown in Figures 15(a-2) to 15(d-2). These results show that SOMnode_direct, the SOM model, has excellent interpolation performance for directly estimating the STEC at the user position. This high performance is a result of the improved model accuracy caused by the increase in the amount of input data used as training data. These results indicate that the SOM model is robust and stable against ionospheric disturbances. An advantage of the proposed SOM system is that it is possible to estimate the STEC of the user’s position with high interpolation accuracy, even for locations where the input data are sparse, regardless of whether there is an ionospheric disturbance.

Additionally, the results of CORS_direct were similar to those of SOMnode_direct, as shown in Figures 15(a-2) to 15(d-2). The amount of input data increased, and the distance between the neighbors of the input data was almost the same as the distance of interpolation using the SOM nodes. Therefore, the SOM nodes become sufficiently large for (64 × 64), and SOMnode_direct exhibited the best performance.

Table 5 shows a comparison of the basic statistics of the validation results for all cases with regard to the median and MAD. This comparison indicates that SOMnode_direct had the best performance for estimating the STEC for the user’s position under disturbed ionospheric conditions, such as an MSTID. The median residual STEC for assumed actual use of SOMnode_direct was 0.118 for the (64 × 64) SOM nodes and CORS_200. However, the median of the assumed CORS_Grid based on actual use was 0.254 at CORS_200. This result shows that if the STEC at the user’s position can be directly estimated using the SOM model, the estimation accuracy is significantly improved compared with a method that assumes the current actual use, such as the CORS_Grid case.

View this table:
TABLE 5 Error Statistics for All Cases (Median and MAD)

5.3 Validation for Different Ionosphere Conditions

Four additional days (Tests 1, 2, 3, and 4) were investigated, with details shown in Table 6. If both quiet and disturbed conditions occurred during the test period, the test period was divided based on the ionosphere conditions. Ionosphere conditions were verified by the detrended TEC map (National Institute of Information and Communications Technology in Japan, n.d.).

View this table:
TABLE 6 Ionospheric Conditions

Table 7 shows the percentage of outliers removed (sum of false positives and false negatives in the confusion matrix). In all tests, the percentage of removed outliers was low. The results show that outlier removal was limited, and the overall shape of the ionosphere was maintained without significant changes.

View this table:
TABLE 7 Rate of Outlier Removal (Sum of False Positives [FP] and False Negatives [FN] in the Confusion Matrix)

Cases 1 to 4, shown in Figure 14, were implemented to validate the accuracy of the proposed method. The cases are based on the process for calculating the estimated accuracy at the user’s (validation) position. SOM models were generated under the condition CORS_50 with (20 × 20) SOM nodes. Additionally, the same SOM parameter values were used in all tests. The median and MAD of the residual STEC for assumed actual use were analyzed to evaluate the accuracy of the four cases.

Table 8 shows the statistical results of the residual STEC for all cases; residual STEC values under disturbed ionosphere conditions were larger than those under quiet conditions. Under both quiet and disturbed conditions, SOMnode_direct (Case 3) had the smallest residual STEC among all cases; the values were smaller by approximately half, as compared with the results of CORS_Grid (Case 1). This finding indicates that the SOM model can estimate the STEC with high accuracy in any ionospheric condition. Meanwhile, there was a slight difference in the residual STEC values between Tests 2 and 4, where an MSTID occurred, and Test 1, where a plasma bubble occurred. The same SOM parameter values were used regardless of the ionospheric conditions. Clearly, further work is needed to reveal whether the optimal SOM parameter values may differ depending on storm morphologies.

View this table:
TABLE 8 Residual STEC for Actual Use Assumed for Different Ionosphere Conditions

5.4 Consideration for Application

Augmentation information utilized for high accuracy, such as ionospheric slant delay correction, is transmitted by satellites such as QZSS satellites. These SOM models are also required to transmit augmentation information. From a practical perspective, it is important to maintain the model data transmission size within the satellite data capacity. Figure 16 shows the relationship between the SOM nodes and the data size of the model based on the accuracy of the SOM model. With an increase in the number of SOM nodes used to improve the model accuracy, the data size also increased. The data size of the model under the condition of (20 × 20) SOM nodes was 9600 bytes. In practice, it is difficult to send all SOM model information simultaneously. Therefore, future studies should consider a transmission method that does not deteriorate the SOM model information. In particular, the discrete wavelet transform (DWT) is a useful method for data compression. The DWT is applicable to local fluctuations and is suitable for the non-stationarity of complex signals, such as ionospheric disturbances, as it decomposes the input signal into both frequency and location information. The input-data size can be reduced via frequency selection. Therefore, the RIMS could integrate a compression method such as DWT to transmit the SOM model information via satellites.

Relationship between SOM nodes and data size of the SOM model based on accuracy
FIGURE 16

Relationship between SOM nodes and data size of the SOM model based on accuracy

Furthermore, we consider SBASs as a potential application of the proposed SOM model. Further work is needed to consider the applicability of the SOM model to integrity algorithms such as those used in SBASs and wide-area augmentation systems (WAASs).

6 CONCLUSION

In this paper, we proposed a RIMS approach using a SOM, an unsupervised machine-learning method. Ionospheric models were generated using the proposed RIMS based on a SOM. Our results can be summarized into three points as follows.

First, the results clearly demonstrate that it is possible to model disturbed ionospheric conditions using the proposed RIMS in real time, with better accuracy and stability under both quiet and disturbed ionospheric conditions compared with conventional approaches.

Second, the RIMS can significantly reduce the amount of input data needed compared with other machine-learning methods such as CNNs. This system does not need to input additional data sets, such as solar activity information or the Earth’s magnetic field, for modeling.

Third, in terms of practical application, the SOM model had the best performance for estimating the STEC for the user’s position under disturbed ionospheric conditions, such as an MSTID, compared with a method assuming current actual use. The RIMS achieved an improvement of 0.254 to 0.118 TECU in the median residual STEC compared with the assumed actual method. The results confirmed that the RIMS can model the robustness of ionospheric conditions in real time across any disturbance. Moreover, the ionospheric model using the proposed SOM system can be understood in more detail in terms of the ionospheric behavior, even if the input data are sparse in a given area.

However, the output-data size of the ionospheric SOM model using the proposed SOM system grew with an increasing number of SOM parameters for modeling resolution. Future work should consider a transmission method without the deterioration of SOM model information from a practical perspective. For example, the RIMS could integrate a compression method using a DWT to transmit SOM model information via satellites.

Additionally, the accuracy of the ionospheric models from the RIMS varies depending on the distribution of the input data (CORSs). To enable applications of the RIMS in other regions, the aspect ratio of SOM nodes can be flexibly changed based on the distribution shape of the observed CORSs. Furthermore, different regions exhibit different ionospheric conditions. The values of the SOM parameters in this study were suitable for an MSTID. In future studies, the optimal SOM parameter values must be considered based on the ionospheric conditions involved.

We consider SBASs as a potential candidate for application of the SOM model. Further work is needed to consider the applicability of the SOM model to integrity algorithms such as those used in SBASs and WAASs.

HOW TO CITE THIS ARTICLE:

Murai, K., Sato, Y., Hirokawa, R., & Nakasuka, S. (2026). Ionospheric modeling by using a self-organizing map under disturbed conditions. NAVIGATION, 73. https://doi.org/10.33012/navi.781

ACKNOWLEDGEMENTS

Funding from Mitsubishi Electric Corporation is gratefully acknowledged. The authors would like to thank the members of the Mitsubishi Electric Corporation, Dr. Seigo Fujita, and Mr. Yuichiro Tsukamoto. DRAWING-TEC from the National Institute of Information and Communications Technology in Japan is gratefully acknowledged for providing products. We likewise appreciate the Geospatial Information Authority of Japan CORSs for providing GNSS observation data.

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

REFERENCES

  1. ↵
    Afraimovich, E. L., Altynsev, A. T., Grechnev, V. V., & Leonovich, L. A. (2001). Ionospheric effects of the solar flares as deduced from global GPS network data. Advances in Space Research, 27(6–7), 1333–1338. https://doi.org/10.1016/S0273-1177(01)00172-7
    Google ScholarOpenURL
  2. ↵
    Bilitza, D., Pezzopane, M., Truhlik, V., Altadill, D., Reinisch, B. W., & Pignalberi, A. (2022). The International Reference Ionosphere model: A review and description of an ionospheric benchmark. Reviews of Geophysics, 60, e2022RG000792. https://doi.org/10.1029/2022RG000792
    Google Scholar
  3. ↵
    Cabinet Office, Government of Japan. (2022). Quasi-Zenith Satellite System Interface Specification Centimeter Level Augmentation Service (IS-QZSS-L6 005). https://qzss.go.jp/en/technical/ps-is-qzss/ps-is-qzss.html
    Google Scholar
  4. ↵
    Chen, J., & Gao, Y. (2023). Real-time ionosphere prediction based on IGS rapid products using long short-term memory deep learning. NAVIGATION, 70(2). https://doi.org/10.33012/navi.581
    Google Scholar
  5. ↵
    Désert, T., Authié, T., & Trilles, S. (2015, September). Modelling of the ionosphere by neural network for equatorial SBAS. In Proceedings of the 28th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS+) (pp. 3542–3549). https://www.ion.org/publications/abstract.cfm?articleID=12884
    Google Scholar
  6. ↵
    Furukawa, T. (2017). Introduction of self-organizing map. https://www.brain.kyutech.ac.jp/~furukawa/wp/data/SOMtext.pdf
    Google Scholar
  7. ↵
    Haykin, S. (2009). Neural networks and learning machines (3rd ed.). Pearson Education, Inc.
    Google Scholar
  8. ↵
    Hirokawa, R., Fujita, S., & Hayase, N. (2023, September). The first satellite-based open PPP-RTK service: Operational experiences and improvements. In Proceedings of the 36th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS+) (pp. 469–482). https://doi.org/10.33012/2023.19213
    Google Scholar
  9. ↵
    Kaselimi, M., Doulamis, N., Voulodimos, A., Doulamis, A., & Delikaraoglou, D. (2021, July). Spatio-temporal ionospheric TEC prediction using a deep CNN-GRU model on GNSS measurements. In 2021 IEEE International Geoscience and Remote Sensing Symposium (IGARSS) (pp. 8317–8320). https://doi.org/10.1109/IGARSS47720.2021.9554258
    Google Scholar
  10. ↵
    Kim, J. H., & Kwak, Y. S. (2025). Validating the IRI-2020 model for ionospheric storms over the north-east Asian sector induced by extreme geomagnetic storms. Advances in Space Research, 75(5), 4347–4369. https://doi.org/10.1016/j.asr.2024.07.032
    Google ScholarOpenURL
  11. ↵
    Kohonen, T. (1982). Self-organized formation of topologically correct feature maps. Biological Cybernetics, 43, 59–69.
    Google ScholarOpenURLCrossRefWeb of Science
  12. ↵
    Komjathy, A., Yang, Y. M., Meng, X., Verkhoglyadova, O., Mannucci, A. J., & Langley, R. B. (2016). Review and perspectives: Understanding natural-hazards-generated ionospheric perturbations using GPS measurements and coupled modeling. Radio Science, 51(7), 951–961. https://doi.org/10.1002/2015RS005910
    Google ScholarOpenURL
  13. ↵
    Mao, S., Li, H., Zhang, Y., & Shi, Y. (2024). Prediction of ionospheric electron density distribution based on CNN-LSTM model. IEEE Geoscience and Remote Sensing Letters, 21, 1–5. https://doi.org/10.1109/LGRS.2024.3437650
    Google ScholarOpenURL
  14. ↵
    Martire, L., Krishnamoorthy, S., Vergados, P., Romans, L.-J., Szilágyi, B., Meng, X., Anderson, J.-L., Komjathy, A., & Bar-Sever, Y.-E. (2023). The GUARDIAN system - a GNSS upper atmospheric real-time disaster information and alert network. GPS Solutions, 27(32). https://doi.org/10.1007/s10291-022-01365-6
    Google Scholar
  15. ↵
    National Institute of Information and Communications Technology in Japan. (n.d.). DRAWING-TEC. https://aer-nc-web.nict.go.jp/GPS/DRAWING-TEC/
    Google Scholar
  16. ↵
    Natras, R., Goss, A., Halilovic, D., Magnet, N., Mulic, M., Schmidt, M., & Weber, R. (2023). Regional ionosphere delay models based on CORS data and machine learning. Journal of the Institute of Navigation, 70(3), navi.577. https://doi.org/10.33012/navi.577
    Google Scholar
  17. ↵
    Nava, B., Coïsson, P., & Radicella, S.-M. (2008). A new version of the NeQuick ionosphere electron density model. Journal of Atmospheric and Solar-Terrestrial Physics, 70(15), 1856–1862. https://doi.org/10.1016/j.jastp.2008.01.015
    Google ScholarOpenURL
  18. ↵
    Priyadarshi, S., Syam, W. P., Roqué, A. A. G., Conesa, A. P., Buscarlet, G., Pérez, R. O., & Orso, D. M. (2003, September). High-solar activity ionospheric modelling using machine learning: A comparison against classical models. In Proceedings of the 36th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS+) (pp. 121–135). https://doi.org/10.33012/2023.19291
    Google Scholar
  19. ↵
    Richmond, A. D., Ridley, E. C., & Roble, R. G. (1992). A thermosphere/ionosphere general circulation model with coupled electrodynamics. Geophysical Research Letters, 19(6), 601–604. https://doi.org/10.1029/92GL00401
    Google ScholarOpenURL
  20. ↵
    Ruwali, A., Kumar, A. J. S., Prakash, K. B., Sivavaraprasad G., & Ratnam, D. V. (2021). Implementation of hybrid deep learning model (LSTM-CNN) for ionospheric TEC forecasting using GPS data. IEEE Geoscience and Remote Sensing Letters, 18(6), 1004–1008. https://doi.org/10.1109/LGRS.2020.2992633
    Google ScholarOpenURL
  21. ↵
    Sato, Y., Motooka, N., Fujita, S., Hirokawa, R., Nakakuki, K., Keshin, M., Ikari, S., & Nakasuka, S. (2022, September). Emergency warning utilizing next-generation PPP-RTK service. In Proceedings of the 35th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS+) (pp. 3720–3730). https://doi.org/10.33012/2022.18486
    Google Scholar
  22. ↵
    Tang, J., Xu, L., Wu, X., & Chen, K. (2024). A short-term forecasting method for ionospheric TEC combining local attention mechanism and LSTM model. IEEE Geoscience and Remote Sensing Letters, 21, 1–5. https://doi.org/10.1109/LGRS.2024.3373457
    Google ScholarOpenURL
  23. ↵
    Tariku, Y. A. (2020). Comparison of performance of the IRI 2016, IRI-Plas 2017, and NeQuick 2 models during different solar activity (2013–2018) years over South American sector. Radio Science, 55, e2019RS007047. https://doi.org/10.1029/2019RS007047
    Google Scholar
  24. ↵
    Wang, D., Wang, S., Zhu, B., & Wang, Z. (2023). MLP-based user-applicable method for SBAS GIVD calibration: A comparative study based on CODE final GIM products. Advances in Space Research, 72(11), 5013–5029. https://doi.org/10.1016/j.asr.2023.09.031
    Google ScholarOpenURL
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