The integration of ranging signals from multiple satellite constellations opens the possibility for rapid, robust and accurate positioning over wide areas. Algorithms for the simultaneous estimation of carrier phase cycle ambiguities and user position and for the detection of faults over a fixed smoothing time-interval were derived in previous work. For high-integrity precision applications, ensuring the robustness of measurement error and fault-models is an exacting task, especially when considering sequences of observations. In this research, a new RAIM-based approach is established, which aims at directly determining the worst-case single-satellite fault profile. Also, the robustness of newly derived ionospheric error models is experimentally evaluated using dual-frequency GPS data collected over several months at multiple locations. An integrity analysis is devised to quantify the impact of traveling ionospheric disturbances (TIDs) on the final user position solution. Finally, overall navigation system performance is assessed for various combinations of GPS, Galileo and low earth orbiting Iridium satellite signals.