GPS tomography of the ionospheric electron content with a correlation functional

The authors develop a minimization functional in order to regularize the inverse problem associated with three-dimensional (3D) ionospheric stochastic tomography. This functional is designed to yield, upon minimization, a solution which maximizes the frequency content of the solution below a certain cutoff, while keeping χ² constant. The authors show how this functional can be rewritten in terms of the correlation function of the image, thereby facilitating the algorithmic implementation of the method. They then implement this functional in a Kalman filter and obtain a smoothing algorithm that acts in both space and time. Finally, they use this technique to perform global scale Global Positioning System (GPS) tomography of the ionospheric electron content