Three‐dimensional ionospheric tomography via band‐limited constrained iterative cross‐entropy minimization

Abstract

[1] The problem of reconstructing ionospheric electron density from ground-based receiver to satellite total electron content (TEC) measurements is formulated as an underdetermined discrete linear inverse problem. If receivers and satellite orbit are coplanar, then a single two-dimensional (2-D) imaging plane can be used as a geometrical model. In most cases, receiver locations are determined by convenience and availability of sites, and thus a 3-D imaging volume is required in order to capture the part of the electron density solution that is associated with gaps between receiver stations within a chain. It is well understood that spurious features, or ''wings,'' associated with these gaps can be produced in tomographic image reconstructions where ray path coverage from individual stations is lost or minimal. In this paper, a 3-D reconstruction system that takes advantage of a multiple-chain data acquisition geometry and provides a solution consistent with available TEC data everywhere within a receiver chain is presented. The reconstruction system exploits the fact that gaps, created by longitudinally unaligned receivers within a chain, can be captured as additional planes of constant longitudes within the 3-D imaging volume. With parameterized ionospheric model (PIM)-generated data as a nonnegative prior estimate of the electron density, the reconstruction algorithm uses constraints based on prior knowledge of the 3-D spatial Fourier transform of the prior electron density as a smoothing mechanism in the tomographic reconstruction process. Consequent to the underlined Fourier transform formulation, a unique solution is produced at locations that contributed to the measured TEC data, and a solution is interpolated within the remainder of the imaging volume. The band-limited BISMART algorithm has been evaluated using a multiple-receiver chain TEC data acquisition system, under known ionospheric conditions. The algorithm satisfactorily reconstructs density solutions, consistent with small-scale enhancements, irregularities, and troughs in the auroral ionosphere, from the available TEC data. The quality of the density reconstructions, coupled with the computational efficiency of this algorithm, indicates the potential utility of this technique for real-time three-and four-dimensional ionospheric tomography.Citation: Cornely, P.-R. J., and W. S. Kuklinski (2005), Three-dimensional ionospheric tomography via band-limited constrained iterative cross-entropy minimization, Radio Sci., 40, RS5S90,

A Double-Adaptive Adjustment Algorithm for Ionospheric Tomography

“…At present, the theoretical and algorithmic investigations of these techniques are the focus of ionospheric tomography. The main difficulty surrounding these techniques is that the IED reconstruction is usually an ill-posed problem due to insufficient input data and uneven distribution of ground GNSS observation stations [13][14][15][16][17][18]. The ill-posed nature of this problem can cause large errors in approximate solutions even if the input data have only arbitrary, small errors.…”

An improved method using adaptive smoothing for GNSS tomographic imaging of ionosphere

“…In the field of global navigation satellite system (GNSS) atmosphere, the principle of computerized ionospheric tomography (CIT) becomes applicable with the increasing number of GNSS satellites and the build-up of ground-based GNSS stations in the 1990s [1][2][3][4]. Since then, a variety of CIT approaches based on GNSS observation data have been developed for the accurate reconstruction of ionospheric electron density (IED) distribution in the upper atmosphere [5][6][7][8][9][10][11][12][13][14]. An overview about the direction and challenges of an area at the forefront of CIT research is provided by Bust and Mitchell [15].…”