A Review of Voxel-Based Computerized Ionospheric Tomography with GNSS Ground Receivers

Abstract

Ionized by solar radiation, the ionosphere causes a phase rotation or time delay to trans-ionospheric radio waves. Reconstruction of ionospheric electron density profiles with global navigation satellite system (GNSS) observations has become an indispensable technique for various purposes ranging from space physics studies to radio applications. This paper conducts a comprehensive review on the development of voxel-based computerized ionospheric tomography (CIT) in the last 30 years. A brief introduction is given in chronological order starting from the first report of CIT with simulation to the newly proposed voxel-based algorithms for ionospheric event analysis. The statement of the tomographic geometry and voxel models are outlined with the ill-posed and ill-conditioned nature of CIT addressed. With the additional information from other instrumental observations or initial models supplemented to make the coefficient matrix less ill-conditioned, equation constructions are categorized into constraints, virtual data assimilation and multi-source observation fusion. Then, the paper classifies and assesses the voxel-based CIT algorithms of the algebraic method, statistical approach and artificial neural networks for equation solving or electron density estimation. The advantages and limitations of the algorithms are also pointed out. Moreover, the paper illustrates the representative height profiles and two-dimensional images of ionospheric electron densities from CIT. Ionospheric disturbances studied with CIT are presented. It also demonstrates how the CIT benefits ionospheric correction and ionospheric monitoring. Finally, some suggestions are provided for further research about voxel-based CIT.

High‐Resolution 3‐D Imaging of Daytime Sporadic‐E Over Japan by Using GNSS TEC and Ionosondes

“…The CIT approach in our analysis follows the voxel‐based model, the details of which can be found in a review by Lu et al. (2021) and references therein. The 3‐D regional volume to be imaged is divided into n voxels and each voxel ( j ) is assumed to have an unknown uniform distribution of electron densities x j .…”

IONOLAB-Fusion: Fusion of Radio Occultation into Computerized Ionospheric Tomography

“…In 3-D applications of tomographic reconstruction methods, one of the limiting factors is the scarcity of measurement data, resulting in ill-conditioned and sparse matrices in inversion [15][16][17][18]. Additionally, the inherent vertical bias of TEC measurements coupled with the uneven distribution of GPS receivers complicates the inversion process, leading to scenarios where some regions are oversampled while others lack sufficient data.…”

Regional Mapping of Small‐Scale Equatorial Ionospheric Irregularities Using Swarm Echo Satellite Measurements

“…Therefore, there are non‐illuminated and poorly sampled voxels in the model, which makes inversion of the system an ill‐posed problem. It is also an ill‐conditioned problem, since ionospheric electron density maps obtained from tomographic techniques are highly prone to errors in TEC estimates (Lu et al., 2021). Despite the recent progress made in the development of various ionospheric tomography techniques, it is still a challenge to the community to solve this ill‐conditioned and ill‐posed inverse problem to determine vertical profiles of ionospheric structures.…”

“…(1988) applied the ART algorithm to estimate the first 2‐D (latitude‐altitude) ionospheric electron density images using synthetic TEC data. Since then, ionospheric tomographic techniques have been developed and optimized significantly (e.g., see Bust & Mitchell, 2008; Lu et al., 2021, and references within). In general, tomography requires a large number of ray paths to be sampled before the 3‐D density distribution can be estimated.…”