The iGPS high-integrity precision navigation system combines carrier phase ranging measurements from GPS and low earth orbit Iridium telecommunication satellites. Large geometry variations generated by fast moving Iridium spacecraft enable the rapid floating estimation of cycle ambiguities. Augmentation of GPS with Iridium satellites also guarantees signal redundancy, which enables fault-detection using carrier phase Receiver Autonomous Integrity Monitoring (RAIM). Over short time periods, the temporal correlation of measurement error sources can be exploited to establish reliable error models, hence relaxing requirements on differential corrections. In this paper, a new ionospheric error model is derived to account for Iridium satellite signals crossing large sections of the sky within short periods of time. Then, a fixed-interval positioning and cycle ambiguity estimation algorithm is introduced to process Iridium and GPS code and carrier-phase observations. A residual-based carrier phase RAIM detection algorithm is described and evaluated against single-satellite step and ramp-type faults of all magnitudes and start-times. Finally, a sensitivity analysis focused on ionosphere-related system design variables (ionospheric error model parameters, code-carrier divergence, single and dual-frequency implementations) explores the potential of iGPS to fulfill some of the most stringent navigation integrity requirements with coverage at continental scales.