Real-time integrity monitoring is essential for autonomous vehicle positioning, requiring high availability and manageable computational load. This research proposes precise point positioning real-time kinematic (PPP-RTK) as the positioning method, combined with an improved classification adaptive Kalman filter for processing. PPP-RTK enhances integrity-monitoring availability by allowing undifferenced and uncombined observations, enabling individual observation exclusion during fault detection and exclusion. The filter reduces computational load using a robustness test and improves precision and availability in protection-level estimation. Epoch-wise weighting adjustments create a more accurate stochastic model, aided by an adaptive unit weight variance calculated with a sliding window, achieving a 7%-28% variance reduction. Three test scenarios with up to four simultaneous faults in code and phase observations demonstrated successful identification and de-weighting of faults, resulting in maximum positioning errors of 6 mm horizontally and 11 mm vertically. The method reduced computational load by 50%-99.999% compared with other approaches.