Evaluation of Ionospheric Delays Based on Orthogonal Dimensionality Reduction Approach

Abstract The effect of space weather on Global Positioning System (GPS) signals transmitted through the ionosphere is a significant cause of range errors and can be vulnerable to GPS users. Accurate evaluation of ionospheric delays plays an essential role in improving the navigation service in the position domain for Category I (CAT I) operations. In this paper, an attempt is made to estimate the ionospheric delays based on the Spherical Harmonic Function (SHF) model using the Singular Value Decomposition (SVD) approach. Total Electron Content (TEC) data from 17 GPS stations were considered in this analysis and operate under the GPS–Aided Geo Augmented Navigation (GAGAN) network in the Indian region. The results show that the SVD–SHF approach is more efficient in estimating ionospheric delays than the Weighted Least Square (WLS) method. Due to the rapid convergence of the SVD, the first five singular values of the geometric matrix (H) can be used to represent the total variance. The average Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) deviations of (WLS–SHF) are 0.75 m and 0.61 m, and the corresponding deviations of SVD–SHF are 0.71 m and 0.59 m were recorded during the storm period 26 to 28 July 2004 (Dst = −170 nT). The computational load for modeling the ionosphere delays with the WLS–SHF model is 15.48 s and the corresponding load for SVD–SHF is 3.81 s. The proposed solution is numerically stable, requires less computation time, reduces the data dimensions, and round–off errors in initial data. The proposed algorithm can be implemented in Global Navigation Satellite System (GNSS) and surveying applications.

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