A hybrid reconstruction algorithm for 3-D ionospheric tomography

In this paper, a hybrid reconstruction algorithm (HRA) is presented to solve the ill-posed inverse problem associated with 3-D ionospheric stochastic tomography. In this new method, the ionospheric electron density (IED) can be inverted by using two steps. First, a truncated singular value decomposition (TSVD) method, whose value is independent on any initial estimation, is used to resolve the ill-posed problem of the tomography system. Second, taking into account the "approximation" of its solution, an iterative improvement process of the solution is then implemented by utilizing the conventional algebraic reconstruction algorithm (ART). The HRA, therefore, offers a more reasonable approach to choose an initial approximate for the ART and to improve the quality of the final reconstructed image. A simulated experiment demonstrates that the HRA method is superior to the TSVD or the ART alone for the tomographic inversion of IED. Finally, the HRA is used to perform GPS-based tomographic reconstruction of the IED at mid- and low-latitude regions

GNSS troposphere tomography based on two-step reconstructions using GPS observations and COSMIC profiles

Traditionally, balloon-based radiosonde soundings are used to study the spatial distribution of atmospheric water vapour. However, this approach cannot be frequently employed due to its high cost. In contrast, GPS tomography technique can obtain water vapour in a high temporal resolution. In the tomography technique, an iterative or non-iterative reconstruction algorithm is usually utilised to overcome rank deficiency of observation equations for water vapour inversion. However, the single iterative or non-iterative reconstruction algorithm has their limitations. For instance, the iterative reconstruction algorithm requires accurate initial values of water vapour while the non-iterative reconstruction algorithm needs proper constraint conditions. To overcome these drawbacks, we present a combined iterative and non-iterative reconstruction approach for the three-dimensional (3-D) water vapour inversion using GPS observations and COSMIC profiles. In this approach, the non-iterative reconstruction algorithm is first used to estimate water vapour density based on a priori water vapour information derived from COSMIC radio occultation data. The estimates are then employed as initial values in the iterative reconstruction algorithm. The largest advantage of this approach is that precise initial values of water vapour density that are essential in the iterative reconstruction algorithm can be obtained. This combined reconstruction algorithm (CRA) is evaluated using 10-day GPS observations in Hong Kong and COSMIC profiles. The test results indicate that the water vapor accuracy from CRA is 16 and 14% higher than that of iterative and non-iterative reconstruction approaches, respectively. In addition, the tomography results obtained from the CRA are further validated using radiosonde data. Results indicate that water vapour densities derived from the CRA agree with radiosonde results very well at altitudes above 2.5 km. The average RMS value of their differences above 2.5 km is 0.44 g m⁻³

A three-dimensional time-dependent algorithm for ionospheric imaging using GPS

Global Positioning System (GPS) satellite receivers provide a world-wide network of phase and group delay measurements. The combination of two-frequency measurements can be used to derive the integral of the electron concentration along each satellite-to-receiver path, a parameter known as the Total Electron Content (TEC). At this stage these slant TEC data are diffi cult to interpret as they originate from a combination of a temporally changing ionosphere and spatially changing observation geometry. In this paper TEC data are inverted to evaluate the underlying distribution and time evolution of electron concentration. Accordingly, a new three-dimensional, time-dependent algorithm is presented here for imaging ionospheric electron concentration using GPS signals. The inversion results in a three-dimensional movie rather than a static image of the electron-concentration distribution. The technique is demonstrated using simulated ground-based GPS data from actual measurement geometry over Europe

Imaging of fast moving electron-density structures in the polar cap

The imaging of fast-moving electron-density structures in the polar cap presents a unique set of challenges that are not encountered in other ionospheric imaging problems. GPS observations of total electron content in the polar cap are sparse compared to other regions in the Northern Hemisphere. Furthermore, the slow relative motion of the satellites across the sky complicates the problem since the velocity of the plasma can be large in comparison and traditional approaches could result in image blurring. This paper presents a Kalman-filter based method that incorporates a forward projection of the solution based on a model plasma drift velocity field. This is the first time that the plasma motion, rather than just integrations of electron density, has been used in an ionospheric imaging algorithm. The motion is derived from the Weimer model of the electric field. It is shown that this novel approach to the implementation of a Kalman filter provides a detailed view of the polar cap ionosphere under severe storm conditions. A case study is given for the October 2003 Halloween storm where verification is provided by incoherent scatter radars