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The accuracy and availability of satellite-based applications like GNSS\udpositioning and remote sensing crucially depends on the knowledge of the\udionospheric electron density distribution. The tomography of the ionosphere\udis one of the major tools to provide link specific ionospheric corrections\udas well as to study and monitor physical processes in the ionosphere.\ud\ud  \ud\udIn this paper, we introduce a simultaneous multiplicative column-normalized\udmethod (SMART) for electron density reconstruction. Further, SMART+ is\uddeveloped by combining SMART with a successive correction method. In this\udway, a balancing between the measurements of intersected and not intersected\udvoxels is realised. The methods are compared with the well-known algebraic\udreconstruction techniques ART and SART. All the four methods are applied to\udreconstruct the 3-D electron density distribution by ingestion of\udground-based GNSS TEC data into the NeQuick model.\ud\ud  \ud\udThe comparative case study is implemented over Europe during two periods of\udthe year 2011 covering quiet to disturbed ionospheric conditions. In\udparticular, the performance of the methods is compared in terms of the\udconvergence behaviour and the capability to reproduce sTEC and electron\uddensity profiles. For this purpose, independent sTEC data of four IGS\udstations and electron density profiles of four ionosonde stations are taken\udas reference. The results indicate that SMART significantly reduces the\udnumber of iterations necessary to achieve a predefined accuracy level.\udFurther, SMART+ decreases the median of the absolute sTEC error up to\ud15, 22, 46 and 67 % compared to SMART, SART, ART and NeQuick\udrespectively

Simultaneous multiplicative column-normalized method (SMART) for 3-D ionosphere tomography in comparison to other algebraic methods