Virtual reference station-based computerized ionospheric tomography

Abstract

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.

Virtual Tourism and Digital Heritage: An Analysis of VR/AR Technologies and Applications

“…VRSciT project provides a toolkit to explore new approaches in educational tourism using a VR environment [48]. TIDE Toolkit is a tourism toolkit for European Maritime and Underwater Cultural Heritage [49].…”

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

“…However, these methods may result in unreasonable values in the marginal voxels and the area with many unilluminated voxels. Lu et al (2021) [72] presented an algorithm based on virtual reference stations (VRSs) to decrease the number of unilluminated voxels. The virtual observations of VRSs were generated with the observations from nearby stations.…”

Tomographic Inversion of the Ionosphere by Rejecting Abnormal Corrections and Rays

“…Due to a limited number of ground stations, the above equations are always under-determined or ill-posed, which makes them difficult to be solved [1,[4][5][6]. Many algorithms, including iterative algorithms and non-iterative algorithms, have been developed in the past [7][8][9]. Non-iterative algorithms, such as singular value decomposition (SVD) [10] and generalized singular value decomposition [11], can remove any dependence from the initial background but become very difficult to solve when a large-scale problem is encountered.…”

“…One solution to alleviate the ill-posed problem is to use a hybrid voxel model, where a large voxel resolution is employed in the topside ionosphere to reduce the number of voxels (i.e., the number of unknowns) [6,[13][14][15][16]. Another approach is to add extra observation data or simulation data, such as radio occultation measurements [13,[17][18][19], low Earth orbit satellites with onboard GNSS observations [20], satellite altimetry data [17], ionosonde observations [21], incoherent scatter radar data [14], vertical electron density content [13,18,22], AIS measurements [23] and virtual stations [9] into the tomographic model. However, a more general solution is to include additional constraints in the tomographic model (to make it well-posed) [1].…”