GPS-based radio tomography with edge-preserving regularization

A tomographic forward and inverse model is presented for deriving 3-D images of ionospheric electron density from ground-based dual-frequency Global Positioning System (GPS) measurements and ionosonde data. The GPS observation geometry is discretely modeled, and a linear algebraic relationship is derived between the integrated electron density measurements and the ionospheric electron density. Because the inverse problem is ill conditioned, regularization is used to stabilize the solution in the presence of noise. In this paper, we regularize the inverse problem by incorporating neighborhood smoothness and continuity constraints applicable to general ionospheric conditions. To avoid oversmoothing of edges, nonconvex regularizing functionals are used to capture potential localized ionospheric density structures. A deterministic relaxation technique is used to minimize the proposed cost function. The specific formulation of the reconstruction geometry is directly related to the sparseness and the nonuniform distribution of the GPS ray paths. The grid boundaries, the regularization parameters, the model order, and the grid placement are selected in conjunction with available remote sensing data and appropriate optimality criteria. The algorithm is tested using simulations of ionospheric structures with actual GPS observation geometry. These simulations demonstrate the effectiveness in detecting and reconstructing ionospheric height and density fluctuations, and illustrate the statistical performance and bounds of the inversion technique.