Modeling the ionospheric gradient by using VSS base functions and GPS data over Iran

The spatial and temporal variations of ionosphere play an important role in positioning and navigation by the space geodetic techniques. Therefore, the ionospheric gradient should be calculated, analyzed, and applied in both space and time. Spatial gradients of the ionosphere have remarkable delay on the propagation of electromagnetic waves. This study intends to propose a new method for simultaneous modeling of the spatial gradients of ionosphere and VTECs in the local scale for Iran. Vector Spherical Slepian (VSS) base functions are used for the development of this method.Five VSS models with the maximal degrees of L = 30, 35, 40, 45 and 50 are taken into account. For implementing the VSS method, 24 permanent GPS stations from the Iranian Permanent GPS Network (IPGN) have been used. The unknown coefficients are estimated with the observations of these stations with least squares technique. Four other stations are used for evaluating the accuracy of the models. Repeatability of baselines is the measure that is used for this purpose. Based on the results obtained, L = 40 is the optimum degree for the VSS model with this input data over Iran.The baselines’ repeatability showed that ionospheric gradients have more influence on the north–south component. Moreover, the spatial gradient is negligible in the east–west and up-down component when a short baseline is processed. In other words, this kind of ionospheric modeling has significant application for baseline, which is longer than 1000 km. In the study, proposed method has improved the long baselines' solution by more than 12%, 18% and 10% in east–west, north–south and up-down components, respectively.