Figure 1: Geometry of an ionospheric tomography system.
Ionospheric tomography is a technique for remotely sensing ionospheric electron density that has been extensively studied in recent years. An ionospheric tomography system uses a satellite and several ground stations to collect total electron content (TEC) data along paths between the ground stations and the satellite orbit, as shown in Figure 1. From these data, an image of ionospheric electron density in the vertical plane defined by the ground stations and the satellite orbit is reconstructed using tomographic techniques [Aus88], [Na91], [Ray90], [Kun92], [Pry92], [Fre92]. The practical feasibility of ionospheric tomography has been demonstrated in several recent studies [And90], [Pry92], [Pry93], [Fre94], [Ker94], [Fos94], [Pak95], [Kro95].
The principle difficulty associated with ionospheric tomography is that the data are not very sensitive to the vertical distribution of electron density, resulting in very poor vertical resolution for the ionospheric tomography system [Na90], [Yeh91], [Na92], [RaF94], [NaS94], [Na94], [Sut95]. Ionospheric tomography reconstruction algorithms address this problem by using a priori information. A priori information must be used in such a way that it supplements the information contained in the data but does not overwhelm it. For example, it is possible to perform reconstructions very easily by assuming a vertical distribution and solving only for the horizontal component, but this method ignores some of the information contained in the data.
Ionospheric tomography algorithms can be divided into two classes: pixel-based methods and nonpixel-based methods. Pixel-based methods include maximum entropy reconstruction [Fou95], model-assisted ionospheric tomography [RaB94], and reconstruction using smoothness constraints [Feh94]. Nonpixel-based methods include expansion in model ionospheres (EMI) [RaF94], weighted, damped least squares (WDLS) [Fre94], and orthogonal decomposition (OD) [Na91], [Su94b], [Sut95]. Most algorithms in both classes allow for a priori information to be entered in the form of an initial guess. A priori information can be used in pixel-based methods to specify relationships between pixels. In all of the nonpixel-based methods cited above, EMI, WDLS, and OD, a priori information is used to limit the solution to a space consisting of reasonable solutions.
This paper presents a new algorithm called the residual correction method (RCM) for ionospheric tomography reconstruction. RCM is an iterative algorithm that is numerically stable and converges quickly. The new algorithm uses orthogonal decomposition and separable basis functions based on a priori information. A realistic example will be given to demonstrate the properties of the new algorithm.