Application of generalized singular value decomposition to ionospheric tomography

Bhuyan, Kalyan; Singh, Saurabh; Bhuyan, P. K.

doi:10.5194/angeo-22-3437-2004

Cited by 16 publications

(3 citation statements)

References 30 publications

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“…Therefore, SVD is usually combined with other algorithms to solve the ill-conditioned problem. Bhuyan et al (2004) [74] applied a generalized SVD (GSVD) to combine SVD with regularization, and IRI was taken as an initial model. The GSVD solution was found to be less affected by some considerations, such as voxel size and number of ray paths.…”

Section: Singular Value Decompositionmentioning

confidence: 99%

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

Wan

2021

Remote Sensing

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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.

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Section: Singular Value Decompositionmentioning

confidence: 99%

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

Wan

2021

Remote Sensing

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“…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].…”

Section: Introductionmentioning

confidence: 99%

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

Jia

Xing

et al. 2021

PLoS ONE

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Global navigation satellite system (GNSS) is a well-established sensors in the recent ionosphere research. By comparing with classical meteorological equipments, the GNSS application can obtain more reliable and precious ionospheric total electron content (TEC) result. However, the most used GNSS ionospheric tomography technique is sensitive to a priori information due to the sparse and non-uniform distribution of GNSS stations. In this paper, we propose an improved method based on adaptive Laplacian smoothing and algebraic reconstruction technique (ALS-ART). Compared with traditional constant constraints, this method is less dependent on a priori information and adaptive smoothing constraints is closer to the actual situation. Tomography experiments using simulated data show that reconstruction accuracy of ionospheric electron density using ALS-ART method is significantly improved. We also use the method to do the analysis of real observation data and compare the tomography results with ionosonde observation data. The results demonstrate the superiority and reliability of the proposed method compared to traditional constant constraints method which will further improve the capability of obtaining precious ionosphere TEC by using GNSS.

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“…problem, several approaches including regularization techniques (e.g., Lee et al, 2007), neural network methods (Ma et al, 2005), Kalman filters (e.g., Hernandez-Pajares et al, 1999;Ruffini et al, 1998), singular value decomposition (e.g., Bhuyan et al, 2004), consideration of background models (e.g., Spencer et al, 2004) and improvements of the SART method (e.g. Wen, 2007;Wen et al, 2007a, b, c), have been developed.…”

Section: Introductionmentioning

confidence: 99%

Constrained simultaneous algebraic reconstruction technique (C-SART) —a new and simple algorithm applied to ionospheric tomography

2008

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A simple and relatively fast method (C-SART) is presented for tomographic reconstruction of the electron density distribution in the ionosphere using smooth fields. Since it does not use matrix algebra, it can be implemented in a low-level programming language, which speeds up applications significantly. Compared with traditional simultaneous algebraic reconstruction, this method facilitates both estimation of instrumental offsets and consideration of physical principles (expressed in the form of finite differences). Testing using a 2D scenario and an artificial data set showed that C-SART can be used for radio tomographic reconstruction of the electron density distribution in the ionosphere using data collected by global navigation satellite system ground receivers and low Earth orbiting satellites. Its convergence speed is significantly higher than that of classical SART, but it needs to be speeded up by a factor of 100 or more to enable it to be used for (near) real-time 3D tomographic reconstruction of the ionosphere.

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Application of generalized singular value decomposition to ionospheric tomography

Cited by 16 publications

References 30 publications

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

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

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

Constrained simultaneous algebraic reconstruction technique (C-SART) —a new and simple algorithm applied to ionospheric tomography

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