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

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.

Complementing regional ground GNSS-STEC computerized ionospheric tomography (CIT) with ionosonde data assimilation

A near-real-time computerized ionospheric tomography (CIT) technique was developed over the East Asian sector to specify the 3-D electron density field. The technique is based on a plethora of Global Navigation Satellite System observables within the region of interest which is bounded horizontally 110°–160°E and 10°–60°N and extending from 80 to 25,000 km in altitude. Prior to deployment, studies validated the CIT results using ionosonde, middle-upper atmosphere radar and occultation data and found the technique to adequately reconstruct the regional ionosphere vertical structure. However, with room for improvement in estimating the peak height and avoiding physically unrealistic negative densities in the final solution, we present preliminary results from a technique that addresses these issues by incorporating CIT results into a data assimilation (DA) technique. The DA technique adds ionosonde bottomside measurements into CIT results, thereby improving the accuracy of the reconstructed bottomside 3-D structure. More specifically, on average CIT NmF2 and hmF2 improve by more than 60%. Further, during analysis, ionospheric electron densities are assumed to be better described by probability log-normal distribution, which introduces the positivity constraint that is mandatory in ionospheric imaging.

Virtual reference station-based computerized ionospheric tomography

In computerized ionospheric tomography (CIT) with ground-based GNSS, the voxels without satellite-receiver ray traversing cannot be reconstructed directly. We present a CIT algorithm based on virtual reference stations (VRSs), called VRS–CIT, to decrease the number of unilluminated voxels and improve the precision of the estimated ionospheric electron density (IED). The VRSs are set at the nodes of grids with a 0.5° × 0.5° resolution in longitude and latitude. We generate the virtual observations with the observations from nearby six or three stations selected according to azimuths and distances. The generation utilizes multi-quadric surface fitting with six stations and triangular linear interpolation with three stations. With the virtual observations added, the IED distribution is reconstructed by the multiplicative algebraic reconstruction technique with the initial values obtained from IRI-2016. The performance of VRS–CIT is examined by using the data from 127 GNSS stations located in 24–46° N and 122–146° E to derive the IED every 30 min. The study focuses on April 29, 2014, with the adaptability of VRS–CIT analyzed by 12 days, evenly distributed around equinoxes and solstices of 2014. The accuracy of the virtual observation is about 1 TECU. Comparing to that derived from CIT with only real observations, the unsolvability of VRS–CIT declined by 4–12% for the whole region, and for the main area, the improvement can be up to 70%. Taking two IED profiles from radio occultation as reference measurements, the mean absolute error (MAE) of IED by VRS–CIT decreases by 6.88% and 8.43%, respectively. Comparing with slant total electron content (STEC) extracted from five additional GNSS stations, the MAE and the root mean square error of the estimated STEC can be reduced up to 17.24% and 33.81%, respectively.