A new atmospheric tomographic model totally based on Global Navigation Satellite System (GNSS) observations is proposed and tested against field observations. The method does not require a first guess, does not contain specific constraints on the variability of water vapor density inside the tomographic domain, and is able to produce reasonable results at 6 km horizontal and 500 m vertical resolutions, from short (30 min) GNSS data samples. The inversion method uses the Moore-Penrose

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... se, which is made possible by increasing the rank of the design matrix through angular interpolation and extrapolation of the observations. Comparisons against 30 consecutive 4-h radiosonde observations and model simulations suggest the ability of the method to detect inversions and local maxima aloft, and behave sensibly in the far-field. Further improvements from this method may be expected from higher density and multi-constellation networks. Plain Language Summary Knowing the three-dimensional distribution of water vapor is a key goal of atmospheric observation that has been very difficult to attain, given its space and time variability. A new method of water vapor tomography is proposed, exclusively based on Global Navigation Satellite System observations, such as GPS, which is found to lead to sensible results. These results suggest a feasible tomographic system, using data from all satellite constellations (GPS, Glonass, Beidou, and Galileo) with a dense network of ground stations.