A New Algorithm for Ill-Posed Problem of GNSS-Based Ionospheric Tomography

Abstract

Ill-posedness of GNSS-based ionospheric tomography affects the stability and the accuracy of the inversion results. Truncated singular value decomposition (TSVD) is a common algorithm of ionospheric tomography reconstruction. However, the TSVD method usually has low inversion accuracy and reconstruction efficiency. To resolve the above problem, a truncated mapping singular value decomposition (TMSVD) algorithm is presented to improve the reconstructed accuracy and computational efficiency. To authenticate the effectiveness and the advantages of the TMSVD algorithm, a numerical test scheme is devised. Finally, ionospheric temporal–spatial variations of the selected reconstructed region are studied using the GNSS observations under different geomagnetic conditions. The reconstructed results of TMSVD can accurately reflect semiannual anomalies, diurnal variations, and geomagnetic storm effects. In contrast with the ionosonde data, it is found that the reconstructed profiles of the TMSVD method are more consistent with than those of the IRI 2016. The study suggests that TMSVD is an efficient algorithm for the tomographic reconstruction of ionospheric electron density (IED).

Three-Dimensional Computerized Ionospheric Tomography over Maritime Areas Based on Simulated Slant Total Electron Content along Small-Satellite Constellation–Automatic Identification System Signal Rays

“…where λ k is the relaxation factor, often set to be a fixed value in the MART reconstruction, and it ranges from 0 to 1; in this paper, it is set to be 0.5 in the MART process. λ k determines the accuracy and the smoothness of the reconstructed electron density [24].…”

“…Considering the advantage of the truncated singular value decomposition (TSVD) method for CIT-that no prior values are needed and whose result is an approximation of the real electron density-D. Wen combined TSVD and MART to solve the ill-posed problem in 3D CIT. They utilized the TSVD result as the initial value for the ART iteration [23,24]. C. Wang used the total electron content (TEC) obtained by the spaceborne full-polarization synthetic aperture radar (PolSAR) to correct the Empirical Canadian High Arctic Ionospheric Model (E-CHAIM), to improve the authenticity of the initial n e for MART [25].…”

A Novel Method of Ionospheric Inversion Based on Horizontal Constraint and Empirical Orthogonal Function

“…The ionosphere is an important component of the atmosphere above the Earth's surface. The aggregation of free electrons impacts the propagation speed of satellite signals [1,2]. This leads to an extension of the transmission time of radio waves, which is referred to as ionospheric delay.…”