Abstract
We have implemented the Multiplicative Algebraic Reconstruction Technique (MART) algorithm to the ionospheric electron density inversion from measured total electron contents (TECs) through radio observation of the Global Positioning System (GPS) signals and the Naval Navigation Satellite System (NNSS) transit signals to reconstruct two-dimensional ionospheric structures. We are also going to compare with the tomography results and show good agreement for both of the Global Positioning System / Meteorology (GPS/MET) and the Low-latitude Ionospheric Tomography Network (LITN) programs.
1. Introduction
The mathematical justification for tomographic reconstructions have been deeply rooted in the Radon transform [Radon, 1917;Dean, 1983;Kak and Slaney, 1988]. In a tomographic application, projections in as many directions as practicable and feasible are usually measured. The Fourier slice theorem [Bracewell, 1956] tells us how the two dimensional Fourier transform space of the object function is being filled by each such measured projection. Only when the Fourier space is completely filled can one hope to find a unique object function. Combine the theory of image reconstruction and the computerized processing ability, we may get the high-resolution image. Methods of computerized ionospheric tomography (CIT) from satellite radio measurements have been under development in more than ten years. The earlier experiments were conduced by receiving satellite signals from ground-based stations. In June 1994, National Central University also built up the Low-altitude Ionospheric Tomography Network (LITN). Furthermore, a recent mission termed the Global Positioning System/Meteorology (GPS/MET) program used a low Earth orbiting (LEO) satellite (the MicroLab-1) to receive multi-channel GPS carrier phase signals (~1.5GHz and ~1.2GHz) and demonstrate active limb sounding of the Earth's atmosphere and ionosphere.
In this paper, the LITN and GPS/MET programs will be described and some initial ionospheric tomography result will be presented. In section 2, section 3, the technical details of GPS/MET and LITN will be discussed. In section 4, the multiplicative algebraic reconstruction technique (MART) will be described and some of derived tomography results will be presented. Some future works for imaging the ionosphere will be summarized in section 5.
2. The basic technique of GPS/MET
Since the mid-1960s, the radio occultation technique has been used to study the properties and structure of the atmospheres of Venus, Mars, some other outer planets and many of their moons [Kliore, et. Al, 1965; Lindal, et. Al, 1979, 1981, and 1987]. In 1993 the University Corporation for Atmospheric Research (UCAR) organized a proof-of-concept experiment on a 735-km low Earth orbiting (LEO) satellite (the MicroLab-1 satellite) to receive GPS signals and demonstrate active limb sounding of the Earth's atmosphere and ionosphere by radio occultation techniques. In the geometrical optics approximation as shown as Figure 1, a ray passing through the ionosphere is refracted according to Snell's law due to the vertical gradient of electron density and hence the refractive index n. The overall effect of the atmosphere can be characterized by a total bending angle a, an impact parameter a, and a tangent radius rt as defined in Figure 1. During an occultation, the variation of a with the impact parameter a can be given by Snell's law when local spherical symmetry is assumed and can be expressed by
And then, using the Abel integral transformation under a spherically symmetrical assumption, the corresponding refractivity at a tangent radius rt can be expressed in term of a(a) and the impact parameter a as
where a
t ( =n(r
t )r
t) is the impact parameter for the ray whose tangent radius is
r
t.
Actually, the GPS frequencies bending in the ionosphere is so small.
Even during the daytime and near solar maximum, the absolute magnitude of the bending angle does not exceed
0.03
° for both of L1 and L2 GPS frequencies [Hajj and Romans, 1998; Schreiner et al., 1999] in the F-region. Applying the Abel transformation, as is similarly done with inversions through bending angles with an assumption of local spherical symmetry, the electron density can then be given by the following integral equation:0
We note that the derived electron density from the Abel integral transform can be used an initial condition for the MART algorithm described in later section.
Figure 1. Illustration of the geometry of the GPS-LEO occultation problem for ionosphere observations, where p1 is an occulting LEO point, p2 is an auxiliary LEO point with the same impact distance of p1,
a is the bending angle,
r
t is the ray's tangent radius, and
a is the impact parameter.
