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The coverage of regional ionosphere maps is determined by the
distribution of ground-based monitoring stations, e.g., GNSS receivers. Since
ionospheric delay has a high spatial correlation, ionosphere map coverage
can be extended using spatial extrapolation methods. This paper proposes a
support vector machine (SVM) to extrapolate the ionosphere ma...
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... flow chart of the SVM training process is shown in Fig. 1 region, and these inputs are identical for each extrapolation point. Targets include the true ionospheric delay in the j -th extrapolation point. After the input and output of the SVM is defined, a kernel matrix is generated for each input. Then, the training is performed to find the optimal coefficients and bias of the regression ...
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... implies that the ionospheric spatial gradient is the main factor of the extrapolation perfor- mances. Figure 10 compares the RMS errors of four 10 • extrapola- tion points (N10, S10, E10, and W10) on 28 October 2014. Unlike the 5 • results in Fig. 7, there is little difference be- tween the two models for the northern area. ...
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... means that the extrapolation per- formance of the SVM and the NN model is larger for the high ionospheric variation region. The extrapolation errors of the east and west region are not significantly different from those in Fig. 9. Figure 11 compares the RMS errors of four 15 • extrapola- tion points (N15, S15, E15, and W15). The overall error level increases from that of the 5 • points, but the SVM still out- performs the NN, particularly at the south and north points. ...
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... with the single-day ex- trapolation, the 1-year data from October 2013 to September 2014 are used for the training process. Figure 12 shows the daily extrapolation errors for the south 10 • extrapolation point (S10) in October 2014. The 1- month means of the daily RMS errors are 1.89 TECU for the SVM and 2.54 TECU for the NN. ...
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With the development of real-time precise clock and orbit products, high-precision real-time ionospheric products have become one of the most critical resources for real-time single-frequency precise point positioning. Fortunately, there are several international GNSS service (IGS) analysis centers, e.g., UPC, WHU, and CAS, that are providing real-...
Citations
... When evaluating on the training dataset, the performance of most models was either lower than or equivalent to SVR; however, even in the latter case, their accuracy on the evaluation dataset was worse. Experiments in other fields indicate that SVR has relatively better extrapolation potential on unseen data (Horn and Schulz, 2011;Kim and Kim, 2019), which may explain why it outperformed other algorithms. We have not examined neural network algorithms, since they require more computer resources during training, and evidence suggests that they tend to underperform relative to other machine learning (ML) techniques when applied to tabular data (Borisov et al., 2022;Shwartz-Ziv and Armon, 2022). ...
Snow modelling is often hampered by the availability of input and calibration data, which can affect the choice of models, their complexity, and transferability. To address the trade-off between model parsimony and trans-ferability, we present the Generalizable Empirical Model of Snow Accumulation and Melt (GEMS), a machine-learning-based model, which requires only daily precipitation, temperature or its daily diurnal cycle, and basic topographic features to simulate snow water equivalent (SWE). The model embeds a support vector regression pretrained on a large dataset of daily observations from a diverse set of the SNOw-pack TELemetry Network (SNOTEL) stations in the United States. GEMS does not require any user calibration, except for the option to adjust the temperature threshold for rain-snow partitioning, though the model achieves robust simulation results with the default value. We validated the model with long-term daily observations from numerous independent SNOTEL stations not included in the training and with data from reference stations of the Earth System Model-Snow Model Intercomparison Project. We demonstrate how the model advances large-scale SWE modelling in regions with complex terrain that lack in situ snow mass observations for calibration, such as the Pamir and Andes mountains, by assessing the model's ability to reproduce daily snow cover dynamics. Future model improvements should consider the effects of vegetation, improve simulation accuracy for shallow snow in warm locations at lower elevations, and possibly address wind-induced snow redistribution. Overall, GEMS provides a new approach for snow modelling that can be useful for hydroclimatic research and operational monitoring in regions where in situ snow observations are scarce.
... The wavelet neural network for VTEC modeling (El-Diasty, 2017) combines the inputs of the day of the year, the hour of the day, latitude, and longitude of the ionosphere pierce point (IPP) with the estimated Klobuchar model at the same IPP point and VTEC output data for the model training estimated from the CORS stations observations. Another application of support vector machines extrapolates VTEC in regions where GNSS observations are not available (Kim & Kim, 2019). The inputs include the hour of the day, the day of the year, F10.7 and Kp indices, sunspot number, and VTEC from areas where GNSS observations were available to provide estimates for VTEC for regions devoid of GNSS observations (Kim & Kim, 2019). ...
... Another application of support vector machines extrapolates VTEC in regions where GNSS observations are not available (Kim & Kim, 2019). The inputs include the hour of the day, the day of the year, F10.7 and Kp indices, sunspot number, and VTEC from areas where GNSS observations were available to provide estimates for VTEC for regions devoid of GNSS observations (Kim & Kim, 2019). Also, an ensemble of tree-based meta-estimators has been developed by combining random forest, adaptive boosting (AdaBoost), and extreme gradient boosting (XGBoost) methods for VTEC forecasting during both calm and stormy geomagnetic conditions (Natras et al., 2022a) and estimating forecast uncertainties as an ensemble spread (Natras et al., 2022b). ...
... Most previous studies employed a fully-connected feed-forward neural network. Regarding the size of the training dataset, different lengths of time were used in previous studies, including one day Zhao et al., 2021), four days (El-Diasty, 2017;Kaselimi et al., 2020), ten days (Leandro & Santos, 2007), one to two years (Kim & Kim, 2019;Liu et al., 2020;Natras et al., 2022a), and four years (Habarulema et al., 2009;Okoh et al., 2016;Orus Perez, 2019) among others. Results from previous studies demonstrated the feasibility of machine learning for VTEC estimation, with a focus on artificial neural networks and also when applied to a limited dataset of several days. ...
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.
... Center for Orbit Determination in Europe (CODE) final GIMs are picked as the reference IGP vertical delay, which was 11 days' delay calculated with a Spherical Harmonic (SH) model. It is considered precise and used as a reference for many studies with 1-hour temporal resolution [13,30,32]. ...
Ionospheric delay is a critical error source in Global Navigation Satellite Systems (GNSSs) and a principal aspect of Satellite Based Augmentation System (SBAS) corrections. Grid Ionospheric Vertical Delays (GIVDs) are derived from the delays on Ionosphere Pierce Points (IPPs), which are observed by SBAS reference stations. SBAS master stations calculate ionospheric delay corrections by several methods, such as planar fit or Kriging. However, when there are not enough IPPs around an Ionosphere Grid Point (IGP) or the IPPs are unevenly distributed, the fitting accuracy of planar fit or Kriging is unsatisfactory. Moreover, the integrity bounds of Grid Ionospheric Vertical Errors (GIVEs) are overly conservative. Since Artificial Neural Networks (ANNs) are widely used in ionospheric research due to their self-adaptation, parallelism, non-linearity, robustness, and learnability, the ANN method for GIVD and GIVE derivation is proposed in this article. Networks are separately trained for IGPs, and five years of historical data are applied on network training. Principal Component Analysis (PCA) is applied for dimensionality reduction of geomagnetic and solar indices, which is employed as a network input feature. Furthermore, the GIVE algorithm of the ANN method is derived based on the distribution of the residual random variable. Finally, experiments are conducted on 12 IGPs over the East China region. Under normal ionospheric conditions, compared with the planar fit and Kriging methods, the residual reduction of the ANN method is approximately 15%. The ANN method fits the ionospheric delay residual error better. The percentage of GIVE availability under 2.7 m increases at least 25 points in comparison to Kriging. Under disturbed conditions, due to a lack of training samples, the ANN method is incompetent compared with planar fit or Kriging.
... Ionospheric delay observations were used as the input parameters, and the ionospheric delay outside the coverage area was extrapolated. In addition to these environmental parameters, Kim and Kim [16,17] used machine learning methods, NN, and a support vector machine (SVM), for the spatial extrapolation of the inner ionosphere data. They found that those machine learning methods are more efficient than the biharmonic spline method and the SVM model is more efficient than the NN model. ...
... The original WAAS service area was extended to 15 • in the east/west direction. The southern region, where the ionospheric variation is large, has a relatively worse extrapolation performance than the east/west direction, so it was only expanded up to 10 • [16,17]. Section 3.1. ...
... The original WAAS service area was extended to 15° in the east/west direction. The southern region, where the ionospheric variation is large, has a relatively worse extrapolation performance than the east/west direction, so it was only expanded up to 10° [16,17]. The ionospheric delay covariance, GIVE, was also extrapolated by using the biharmonic spline. ...
Space-based augmentation system (SBAS) provides correction information for improving the global navigation satellite system (GNSS) positioning accuracy in real-time, which includes satellite orbit/clock and ionospheric delay corrections. At SBAS service area boundaries, the correction is not fully available to GNSS users and only a partial correction is available, mostly satellite orbit/clock information. By using the geospatial correlation property of the ionosphere delay information, the ionosphere correction coverage can be extended by a spatial extrapolation algorithm. This paper proposes extending SBAS ionosphere correction coverage by using a biharmonic spline extrapolation algorithm. The wide area augmentation system (WAAS) ionosphere map is extended and its ionospheric delay error is compared with the GPS Klobuchar model. The mean ionosphere error reduction at low latitude is 52.3%. The positioning accuracy of the extended ionosphere correction method is compared with the accuracy of the conventional SBAS positioning method when only a partial set of SBAS corrections are available. The mean positioning error reduction is 44.8%, and the positioning accuracy improvement is significant at low latitude.
... SVM provides a method to construct a mapping into a higher-dimensional feature space by using a kernel function, such as linear, polynomial, sigmoid, and radial basis function(RBF). At present, in the ionosphere field, the SVM algorithm is mostly used to solve the ionosphere prediction problem [20,21]. Ban [22] used the SVM algorithm to establish the low-latitude storm ionosphere foF2 model, which can detect the ionospheric disturbance better and has improved compared with the empirical model. ...
The distribution of total electron content (TEC) in the ionosphere is irregular and complex, and it is hard to model accurately. The polynomial (POLY) model is used extensively for regional ionosphere modeling in two-dimensional space. However, in the active period of the ionosphere, the POLY model is difficult to reflect the distribution and variation of TEC. Aiming at the limitation of the regional POLY model, this paper proposes a new ionosphere modeling method with combining the support vector machine (SVM) regression model and the POLY model. Firstly, the POLY model is established using observations of regional continuously operating reference stations (CORS). Then the SVM regression model is trained to compensate the model error of POLY, and the TEC SVM-P model is obtained by the combination of the POLY and the SVM. The fitting accuracies of the models are verified with the root mean square errors (RMSEs) and static single-frequency precise point positioning (PPP) experiments. The results show that the RMSE of the SVM-P is 0.980 TECU (TEC unit), which produces an improvement of 17.3% compared with the POLY model (1.185 TECU). Using SVM-P models, the positioning accuracies of single-frequency PPP are improved over 40% compared with those using POLY models. The SVM-P is also compared with the back-propagation neural network combined with POLY (BPNN-P), and its performance is also better than BPNN-P (1.070 TECU).
Ionospheric Total Electron Content (TEC) predominantly affects the radio wave communication and navigation links of Global Navigation Satellite Systems (GNSS). The ionospheric TEC exhibits a complex spatial–temporal pattern over equatorial and low latitude regions, which are difficult to predict for providing early warning alerts to GNSS users. Machine Learning (ML) techniques are proven better for ionospheric space weather predictions due to their ability of processing and learning from the available datasets of solar-geophysical data. Hence, a supervised ML algorithm such as the Support Vector Regression (SVR) model is proposed to predict TEC over northern equatorial and low latitudinal GNSS stations. The vertical TEC data estimated from GPS measurements for the entire 24th solar cycle period, 11 years (2009–2019), is considered over Bengaluru and Hyderabad International GNSS Service (IGS) stations. The performance of the proposed SVR model with kernel Gaussian or Radial Basis Function (RBF) is evaluated over the two selected testing periods during the High Solar Activity (HSA) year, 2014 and the Low Solar Activity (LSA) year, 2019. The proposed model performance is compared with Neural Networks (NN) model, and International Reference Ionosphere (IRI-2016) model during both LSA and HSA periods. It is noticed that the proposed SVR model has well predicted the VTEC values better than NN and IRI-2016 models. The experimental results of the SVR model evidenced that it could be an effective tool for predicting TEC over low-latitude and equatorial regions.
