A Double-Adaptive Adjustment Algorithm for Ionospheric Tomography

Abstract

A double-adaptive adjustment algorithm (DAAA) is proposed to reconstruct three-dimensional ionospheric electron density (IED) distribution. In the DAAA method, the relaxation factor of the multiplicative algebraic reconstruction technique (MART) is first adaptively adjusted by introducing adaptive MART (AMART). To avoid the voxels without any rays traversing them becoming dependent on the initial IED values, smoothing constraints are generally imposed on the adaptive multiplicative algebraic reconstruction technique (AMART). In general, the elements of the smoothing matrices are invariant in the iterative process. They affect the accuracy and efficiency of the IED inversion. To overcome the above limitation, the adaptive adjustments of the constrained matrix elements are subsequently carried out. Both numerical simulation and actual global navigation satellite system (GNSS) experimental results validate that the accuracy and efficiency of ionospheric tomography have been improved by the DAAA method. Finally, the new algorithm is applied to reconstruct the three-dimensional structure of the ionosphere during different geomagnetic activities. The comparisons show that the vertical profiles of the DAAA method are in agreement with those recorded from the ionosonde, and the inverted vertical total electron content (VTEC) of the DAAA method also agrees with the ionospheric products of center for orbit determination in Europe (CODE) during geomagnetic quiet and geomagnetic storms. The comparisons confirm the reliability and superiority of the DAAA method.