Kriging with Unknown Variance Components for Regional Ionospheric Reconstruction.

Area of Science:

• Geodesy and Geophysics
• Satellite Navigation Systems
• Atmospheric Physics

Background:

• Ionospheric delay significantly impacts Global Navigation Satellite System (GNSS) accuracy, especially at mid- and low-latitudes.
• Existing Kriging interpolation methods for ionospheric modeling do not fully account for random observational errors.
• Accurate ionospheric modeling is vital for precise single-frequency GNSS positioning.

Purpose of the Study:

• To develop a novel Kriging spatial interpolation method for Total Electron Content (TEC) that incorporates variance components for both ionospheric signals and measurement errors.
• To enhance the accuracy of regional ionospheric delay estimations for GNSS applications.
• To improve the reliability of GNSS positioning and navigation for single-frequency users.

Main Methods:

• Developed a Kriging spatial interpolation technique integrating variance component estimation for ionospheric TEC.
• Applied Total Electron Content (TEC) semivariogram analysis to model spatial correlations.
• Compared the proposed method with ordinary Kriging and polynomial interpolation using data from the Crustal Movement Observation Network of China (CMONOC).

Main Results:

• The proposed method demonstrated good agreement with existing methods for daily ionospheric variations (10-80 TECU).
• Achieved a smaller standard deviation (around 3 TECU) compared to other methods, indicating smoother TEC level estimations.
• Showed improved interpolation precision over ordinary Kriging (1.2 TECU) and polynomial interpolation (0.7 TECU).
• The root mean squared error was within 1.5 TECU, outperforming other methods by approximately 1 TECU.
• Mean squared error against ionospheric grid points was within 6 TECU, outperforming Kriging.

Conclusions:

• The new Kriging method with variance components provides more accurate regional ionospheric delay estimations over China.
• This approach enhances GNSS positioning accuracy by better modeling ionospheric variability and measurement errors.
• The method offers a more robust solution for precise single-frequency GNSS navigation in regions with significant ionospheric disturbances.