As the authors have shown in previous work, the tomographic approach reduces significantly the mismodeling in the electron content determination using as data the ionosphere-crossing radio signals of global navigation satellite systems (GNSS) such as the Global Positioning System (GPS). We present in this paper the results of a comprehensive study on the performance of an improved tomographic model of the ionosphere. This model is obtained from the GPS L1 and L2 carrier-phase data, and it is used to estimate undifferenced and double-differenced ionospheric corrections in real time and at very long distances between receivers (500--3000 km). The key point of the strategy is the combination of real-time geodetic and ionospheric techniques to achieve a significant improvement in the reliability of carrier-phase ambiguity resolution. This new approach includes also the use of smoothed pseudo-ranges to help in ambiguity resolution. It has been tested under difficult ionospheric conditions, during four consecutive weeks in March--April 2001, at Solar Maximum, and at latitudes ranging from -40 to +40 degrees, so as to include the equatorial region. Dual-frequency satellite altimetry from TOPEX-Poseidon has been used to verify the accuracy of the ionospheric model over the oceans in that region.