In this work, a new time-sequential positioning and fault detection method is developed for dual-frequency, multi-constellation Advanced Receiver Autonomous Integrity Monitoring (ARAIM). Unlike conventional “snapshot” ARAIM, sequential ARAIM exploits changes in satellite geometry at the cost of slightly higher computation and memory loads. From the perspective of users on Earth, the motion of any given GNSS satellite is small over short time intervals. But the accumulated geometry variations of redundant satellites from multiple GNSS can be substantial. This paper quantifies performance benefits brought by satellite motion to ARAIM. It specifically addresses the following challenges: (a) defining raw GNSS code and carrier error models over time, (b) designing estimators and fault detectors exploiting geometric diversity for positioning, cycle ambiguity estimation, and integrity evaluation, and (c) formulating these algorithms in a computationally efficient implementation. Performance improvements provided by sequential ARAIM over snapshot ARAIM are evaluated by worldwide availability analysis for aircraft approach navigation.