A receiver autonomous integrity monitoring (RAIM) algorithm is proposed, and used to analyze the integrity monitoring capabilities of potential sole-means (or stand-alone) systems based on integrated use of GPS and GLONASS, GPS supplemented with a geostationary overlay, and enhanced GPS constellations. As in the other RAIM algorithms, the idea is to take advantage of the redundant measurements. Our focus, however, is on the quality of the position estimate, rather than on diagnosing whether the system is working as intended. The proposed approach uses the redundant measurements to generate a position estimate and a measure of its quality. The latter, called integrity level, is defined as an upper bound on the position error. The estimation of the integrity level is the main innovation in the proposed scheme. The RAIM algorithm is tailored to an abundant redundancy of the measurements, and addresses the following issue: Given a snapshot of the pseudo range measurements, one of which may be in error, can we compute a position estimate that can be shown with high confidence to meet the user's accuracy requirement?