Enhancing BeiDou/GNSS integrity with minmax optimization

In navigation scenarios, integrity is a crucial metric for evaluating system availability, with improvements in integrity having implications for transportation, security, and surveillance. This article proposes a novel integrity monitoring strategy, termed the optimal advanced receiver autonomous integrity monitoring (Optimal-ARAIM), which is designed to optimize the vertical protection level (VPL) in the context of BeiDou/global navigation satellite systems (GNSS). Optimal-ARAIM employs a minimax estimator to minimize VPL by adjusting the full-set solution, optimally allocating integrity and continuity risks. To mitigate the combinatorial explosion caused by multiple heterogeneous satellite faults, we introduce a maximum monitoring order mechanism. All worst-case fault scenarios are formulated as a minimax optimization problem, which is approximated by a convex optimization to ensure the global convergence of VPL. To evaluate the performance of Optimal-ARAIM, we utilize BeiDou observation data for validation and almanac data for predictive analysis. The results indicate that the average VPL is consistently maintained below 8 m across five selected stations in the Asian region when using observation data. Additionally, VPL distributions predicted using BeiDou almanac data are predominantly below 10 m. Further validation using GNSS almanac data demonstrates that the proposed method achieves a global availability coverage rate exceeding 93%, meeting the CAT-I standard. These findings confirm that the proposed Optimal-ARAIM effectively reduces the VPL for BeiDou/GNSS, ensuring that navigation operations can be conducted with high robustness and reliability.