|
Subscriber Access to Full Article (Nonsubscribers may purchase for $9.00, Includes print PDF, file size: 1648116 bytes)
RADIO SCIENCE,
VOL. 42,
RS4018,
doi:10.1029/2006RS003543,
2007
Localized three-dimensional ionospheric tomography with GPS ground receiver measurements
Jeffrey K. Lee
Department of Electrical and Computer Engineering and the Coordinated Science Laboratory, University of Illinois at Urbana-Champaign,
Urbana, Illinois, USA
Farzad Kamalabadi
Department of Electrical and Computer Engineering and the Coordinated Science Laboratory, University of Illinois at Urbana-Champaign,
Urbana, Illinois, USA
Jonathan J. Makela
Department of Electrical and Computer Engineering and the Coordinated Science Laboratory, University of Illinois at Urbana-Champaign,
Urbana, Illinois, USA
Abstract
This paper describes a technique for 3-D tomographic imaging of the ionosphere with high spatial resolution (75 to 95 km in
latitude/longitude and 30 km in altitude). The total electron content (TEC) values are derived from dual-frequency measurements
obtained from GPS satellites by ground-based receivers. When available, ionosonde data are used to construct a priori vertical
profiles modeled using Chapman functions. Two regularization algorithms are investigated for tomographic image reconstruction:
Tikhonov and Total Variation (TV), corresponding to quadratic and l 1 norm minimizations of the penalty constraint, respectively. The TV method is used because it generally preserves discontinuities
in the image effectively and is more resistant to noise. By contrast, Tikhonov, or quadratic, regularization tends to oversmooth
image structures and discontinuities. However, a closed-form solution of the TV method does not exist and so performance depends
heavily on numerical optimization techniques, which are nontrivial to implement because the inverse problem is both ill-posed
and ill-conditioned. We also apply regularization parameter-selection methods to demonstrate their applicability in our study.
The algorithms are demonstrated using real GPS TEC measurements from an observation geometry centered in southern California.
We demonstrate the performance of these techniques under quiet, midlatitude conditions. The resulting reconstructions reasonably
determine the shape of the ionospheric profile. Artifacts can potentially appear near voxels with no raypath information,
which is directly related to the sparseness and nonuniform distribution of the GPS raypaths. We discuss some methods to constrain
the solution to realistic bounds.
Received 11
July
2006;
accepted 19
March
2007;
published 8
August
2007.
Keywords: ionospheric tomography;
GPS;
inverse problems.
Index Terms: 6982 Radio Science: Tomography and imaging (7270, 8180); 3260 Mathematical Geophysics: Inverse theory; 6974 Radio Science: Signal processing (0674); 2443 Ionosphere: Midlatitude ionosphere.
Subscriber Access to Full Article (Nonsubscribers may purchase for $9.00, Includes print PDF, file size: 1648116 bytes)
Citation: Lee, J. K., F. Kamalabadi, and J. J. Makela
(2007),
Localized three-dimensional ionospheric tomography with GPS ground receiver measurements,
Radio Sci.,
42,
RS4018,
doi:10.1029/2006RS003543.
Copyright 2007 by the American Geophysical Union.
|