Fast Protection Level for Precise Positioning Using PPP-RTK with Robust Adaptive Kalman Filter

Developing advanced receiver autonomous integrity monitoring (ARAIM) for ground real-time precise positioning applications such as autonomous vehicles presents computational challenges, particularly in calculating real-time protection levels (PLs) that bound possible positioning errors under an acceptable integrity risk. This study proposes an enhanced method for fast PL estimation by introducing a segmentation approach to the Gershgorin circle theorem-based technique for computing standard deviation upper bounds (UBs). This method divides satellites into segments based on normalised geometry mapping coefficients, allowing multiple UBs instead of a single bound for all subsets within each fault-tolerant mode. The approach is implemented for PPP-RTK with an improved Classification Adaptive Kalman Filter (CAKF). Testing is conducted using a network of 10 continuously operating reference stations (CORSs) employing dual-frequency multi-constellation GNSS data. Results show that when monitoring single fault mode, the PL ranges from 0.05 to 0.1 m with a PL-to-PE ratio of 30:1, while dual fault modes monitoring yields PL from 1 to 10 m with a ratio of 3700:1. The segmentation method achieves 1–5% tighter PLs, i.e., better integrity monitoring (IM) availability, compared to the classical single UB approach while maintaining the same computational efficiency by reducing processed subsets from 325 to 1 for dual fault modes. While the method provides slight improvement in PL tightness, it can be more computationally efficient when having geometries with dominant off-diagonal correlation that fails the computation of a UB.