Research ArticleOriginal Article
Open Access

Regional Ionosphere Delay Models Based on CORS Data and Machine Learning

Randa Natras, Andreas Goss, Dzana Halilovic, Nina Magnet, Medzida Mulic, Michael Schmidt, and Robert Weber
NAVIGATION: Journal of the Institute of Navigation September 2023, 70 (3) navi.577; DOI: https://doi.org/10.33012/navi.577

Article Figures & Data

Figures

  • FIGURE 1
    FIGURE 1

    Locations of GNSS tracking ground stations used by CODE to produce GIMs (obtained from Jee et al. (2010)).

  • FIGURE 2
    FIGURE 2

    Map documenting the locations of the dual-frequency stations of the CORS (blue dots) and the EPN (red dots) networks whose observations were used for VTEC modeling. Stations used for the RIM validation are highlighted with an inner black dot with a white rim; their names are indicated on the map.

  • FIGURE 3
    FIGURE 3

    Representation of the architecture of the ANN5 model with one input, three hidden, and one output layer (right). An additional bias unit was added to the input and the hidden layers. ANN architectures were drawn using the web-based tool NN-SVG (LeNail, 2019).

  • FIGURE 4
    FIGURE 4

    Correlation heatmap of the input features and the output of the machine learning model.

  • FIGURE 5
    FIGURE 5

    The RMSE (left) and correlation coefficients (CCs, right) for training and validation of ANN and RF models.

  • FIGURE 6
    FIGURE 6

    Relative importance of input variables when training AI models with (left) and without coefficients (right) estimated using Random Forest (RF).

  • FIGURE 7
    FIGURE 7

    Flowchart leading to the development of RIMs. First, GPS data from local CORS and EPN observations were processed in the Bernese GNSS software to form geometry-free linear combinations of phase observations which were then used to estimate coefficients representing the regional ionosphere parameters that form the basis of the RIM IONOBH and the RIM IONOWB. Regional ionosphere parameters were then fed into the ANN along with the spatial and temporal parameters as well as solar and geomagnetic indices, resulting in the RIM IONOWB_AI model.

  • FIGURE 8
    FIGURE 8

    Overview of solar and geomagnetic indices for the three study periods. Left panel: March 20-26, 2014; middle panel: March 15-20, 2015; right panel: March 20-26, 2018. From top to bottom: R sunspot number (SN), solar radio flux F10.7 in sfu (solar flux units), Dst in nT, Kp (Quiet kp · 10 < 30, Moderate 30 ≤ kp · 10 < 40, Active 40 ≤ kp · 10<50, Storm kp · 10 ≥ 50).

  • FIGURE 9
    FIGURE 9

    VTEC time series and differences between VTEC from the RIM IONOBH and other models that were estimated based on the location of the EPN SRJV station. Top two panels: March 20–26, 2014 (solar maximum); bottom two panels: March 20–26, 2018 (solar minimum). Note the different scaling of the y-axes due to the effect of the solar cycle on VTEC.

  • FIGURE 10
    FIGURE 10

    VTEC time series and differences between VTECs from the RIM IONOWB and other ionosphere models estimated based on the location of the EPN SRJV station. Top two panels: March 20–26, 2014 (solar maximum); bottom two panels: March 15–20, 2015 (includes a severe geomagnetic storm). Note the different scaling of the y-axes due to the solar cycle and the effects of the geomagnetic storm on VTEC.

  • FIGURE 11
    FIGURE 11

    Top: RMSE values for study periods March 2014, March 2015, and March 2018 for the entire day (0:00 to 23:00 UTC, upper left) and daytime hours only (6:00 to 16:00 UTC, upper right). Bottom: Correlation coefficients for the entire day (00:00 to 23:00 UTC). Note that correlations from 0.7 to 1.0 are shown.

  • FIGURE 12
    FIGURE 12

    VTEC maps (from left to right) for RIM IONOWB_AI, RIM OTHR, and GIM CODE (top). Middle: VTEC differences (from left to right): VTECIONOWB_AI – VTECOTHR, VTECIONOWB_AI – VTECCODE, and VTECOTHR – VTECCODE. Bottom: VTEC map for the Klobuchar model (left) and VTEC difference VTECIONOWB_AI – VTECKlob (right). All maps were from 12 UTC on March 21, 2014.

  • FIGURE 13
    FIGURE 13

    VTEC maps (from left to right) for RIM IONOWB_AI, RIM OTHR, and GIM CODE (top). Mid: VTEC differences (from left to right): VTECIONOWB_AI – VTECOTHR, VTECIONOWB_AI – VTECCODE, VTECOTHR – VTECCODE. Bottom: VTEC map for Klobuchar (left) and the VTEC difference VTECIONOWB_AI – VTECKlob (right). All maps relate to 12 UTC on March 17, 2015.

  • FIGURE 14
    FIGURE 14

    VTEC maps (from left to right) for RIM IONOWB_AI, RIM OTHR, and GIM CODE (top). Middle: VTEC differences (from left to right): VTECIONOWB_AI – VTECOTHR, VTECIONOWB_AI – VTECCODE, and VTECOTHR – VTECCODE. Bottom: VTEC map for the Klobuchar model (left) and the VTEC difference VTECIONOWB_AI – VTECKlob (right). All maps relate to 12 UTC on March 18, 2015.

  • FIGURE 15
    FIGURE 15

    RMS errors of single-frequency positioning solutions without ionospheric corrections compared to the GIM CODE and the RIM IONO_BH. Shown are vertical position errors on March 20–26, 2014 (top left), horizontal position errors on March 20–26, 2014 (top right), vertical position errors on March 20–26, 2018 (bottom left), horizontal position errors on March 20–26, 2018 (bottom right).

  • FIGURE 16
    FIGURE 16

    RMS errors of single-frequency positioning solutions without ionospheric corrections compared to the GIM CODE and the RIM IONO_WB. Shown are vertical position errors on March 20–26, 2014 (top left), horizontal position errors on March 20–26, 2014 (top right), vertical position errors on March 15–20, 2015 (bottom left), and horizontal position errors on March 15–20, 2015 (bottom right).

Tables

  • TABLE 1

    Processing Steps in the Bernese GNSS Software

    StepsBernese software routine
    Cutting 24-hour RINEX observations into 1-hour filesCCRINEXO
    Orbit and Earth’s orientation information preparationPOLUPD, PRETAB, ORBGEN
    Satellite clock correction files preparationRNXCLK, CCRNXC
    Import of RINEX observation data into the Bernese formatRXOBV3
    Receiver clock synchronizationCODSPP
    Ionosphere model estimationIONEST
  • TABLE 2

    The Specific Options for the VTEC Modeling (IONEST Routine)

    Pre-processing and processing options
    Linear combination for break detection (data cleaning)L4
    A priori sigma of a single observation0.01 m
    Elevation cut-off angle15°
    Height of the single layer450 km
    Degree of Taylor series expansion in latitude (nmax)1
    Degree of Taylor series expansion in hour angle (mmax)2
  • TABLE 3

    AI Models with Input data, Architecture, and Training Quantities. A bias unit is added to the input and the hidden layers in the ANN. ReLu, Rectified Linear Unit, SGD, Stochastic Gradient Descent.

    AI modelsInput dataArchitectureTraining
    ANN1Regional ionosphere coefficients
    Latitude, Longitude    		Input layer: 27 neurons
    Output layer: 1 neuron
    Linear mapping    		Optimizer: SGD
    Learning rate: 2e-1
    Momentum: 0.9
    Epochs: 400
    Batch size: 300
    ANN2Regional ionosphere coefficients
    Latitude, Longitude    		Input layer: 27 neurons
    Hidden layer 1: 10 neurons
    Hidden layer 2: 10 neurons
    Hidden layer 3: 10 neurons
    Output layer: 1 neuron
    Activation function: ReLU    		Optimizer: SGD
    Learning rate: 1e-3
    Momentum: 0.9
    Epochs: 400
    Batch size: 300
    ANN3Regional ionosphere coefficients
    Latitude, Longitude
    HoDsin, HoDcos    		Input layer: 29 neurons
    Hidden layer 1: 10 neurons
    Hidden layer 2: 10 neurons
    Hidden layer 3: 10 neurons
    Output layer: 1 neuron
    Activation function: ReLU    		Optimizer: SGD
    Learning rate: 1e-3
    Momentum: 0.9
    Epochs: 400
    Batch size: 300
    ANN4Regional ionosphere coefficients
    Latitude, Longitude
    HoDsin, HoDcos
    F10.7    		Input layer: 30 neurons
    Hidden layer 1: 10 neurons
    Hidden layer 2: 10 neurons
    Hidden layer 3: 10 neurons
    Output layer: 1 neuron
    Activation function: ReLU    		Optimizer: SGD
    Learning rate: 1e-3
    Momentum: 0.9
    Epochs: 400
    Batch size: 300
    ANN5
    IONOWB_AI    		Regional ionosphere coefficients
    Latitude, Longitude
    HoDsin, HoDcos
    F10.7
    Kp, Dst    		Input layer: 32 neurons
    Hidden layer 1: 10 neurons
    Hidden layer 2: 10 neurons
    Hidden layer 3: 10 neurons
    Output layer: 1 neuron
    Activation function: ReLU    		Optimizer: SGD
    Learning rate: 1e-3
    Momentum: 0.9
    Epochs: 400
    Batch size: 300
    ANN6Latitude, Longitude
    HoDsin, HoDcos
    F10.7
    Kp, Dst    		Input layer: 7 neurons
    Hidden layer 1: 10 neurons
    Hidden layer 2: 10 neurons
    Hidden layer 3: 10 neurons
    Output layer: 1 neuron
    Activation function: ReLU    		Optimizer: SGD
    Learning rate: 1e-4
    Momentum: 0.9
    Epochs: 200
    Batch size: 50
    RF1Regional ionosphere coefficients
    Latitude, Longitude
    HoD
    F10.7, Kp, Dst    		Number of trees= 300
    Min_samples_split=5
    Min_samples_leaf=3    		Criterion: Mean
    squared error
    RF2Latitude, Longitude
    HoD
    F10.7, Kp, Dst    		Number of trees= 300
    Min_samples_split=5
    Min_samples_leaf=5    		Criterion: Mean
    squared error
  • TABLE 4

    RMSE and CCs for Training and Validation Datasets for Different AI Models.

    DatasetANN1ANN2ANN3ANN4ANN5ANN6RF1RF2
    RMSE
    (TECU)    		Train7.313.993.002.862.608.342.678.51
    Validation7.154.013.112.862.738.732.838.75
    CCTrain0.9060.9740.9850.9860.9890.8760.9880.870
    Validation0.9100.9730.9840.9860.9870.8690.9860.868
  • TABLE 5

    Overview of the Mean Differences for the Solar Maximum (March 21, 2014) and the Geomagnetic Storm (March 17–18, 2015) for the Region from 13°E to 23°E Longitude and from 40°N to 47°N Latitude. Mean values from both periods (final column) were calculated based on the mean differences from March 21, 2014, and the mean differences averaged over March 17–18, 2015.

    Differences between modelsAbsolute mean differences (TECU)
    March 21, 2014March 17, 2015March 18, 2015Mean values
    IONOWB_AI – OTHR0.941.361.031.07
    IONOWB_AI – CODE1.481.401.051.35
    OTHR – CODE1.510.550.491.02
    IONOWB_AI – Klob.23.2425.1613.2421.22
  • TABLE 6

    RMS errors for Vertical (ID), Horizontal (2D), and 3D Position Solutions from Static 24-hour Positioning Data. Data were averaged over all stations examined. Improvement of the RMS 3D error was observed compared to the solutions generated without ionosphere corrections.

    Study periodsRMS Vertical errorRMS Horizontal errorRMS 3D errorImprovement In 3D error
    March 2014NO IONO5.461.255.49
    GIM CODE0.910.601.1079.96%
    IONOBH0.560.500.7586.34%
    IONOWB0.660.500.8384.88%
    IONOWB_AI0.650.510.8384.88%
    March 2015NO IONO3.300.963.43
    GIM CODE0.380.380.5484.26%
    IONOWB0.370.400.5484.26%
    IONOWB_AI0.350.390.5583.97%
    March 2018NO IONO1.340.511.45
    GIM CODE0.250.240.3873.79%
    IONOBH0.110.260.3675.17%

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Regional Ionosphere Delay Models Based on CORS Data and Machine Learning
Randa Natras, Andreas Goss, Dzana Halilovic, Nina Magnet, Medzida Mulic, Michael Schmidt,, Robert Weber
NAVIGATION: Journal of the Institute of Navigation Sep 2023, 70 (3) navi.577; DOI: 10.33012/navi.577
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