3D ionospheric tomography over southeast China using a new scheme of constrained least squares with parameter weight matrix

Abstract Computerized ionospheric tomography (CIT) technique allows reconstructing the 3-dimensional and even 4-dimensional state of the ionosphere in terms of electron content. It is typically denoted as an inverse problem. Due to the unevenly distributed measurements collected from ground receivers, together with limited cut-off elevation angle and density of observations, the normal matrix of the inverse problem becomes sparse, which makes it difficult to solve and potentially unstable. The main methods to resolve the problem are the constraint algorithms during the process of the electron density inversion. A new approach is proposed for CIT that aims to mitigate the ill-posed problem and improve the precision of ionospheric electron density (IED) resolution by using constrained least squares. In this method, a new scheme of constructing parameter weight matrices in both horizontal and vertical directions is designed using the correlation of IED among those neighboring voxels, which helps to add the information needed in CIT, and the ill-posed problem is efficiently resolved. The accuracy and feasibility of the additional constraints in CIT algorithms are verified by numerical simulation tests. Finally, this newly developed method of constrained least squares is used to effectively perform the tomographic reconstruction of IED distribution over southeast China.