Integrity as a Control Problem: Smooth and Adaptive Protection Levels for Multi-Modal Localization

Protection levels for autonomous vehicle localization are traditionally derived from estimator covariances under Gaussian assumptions. These approaches fail in complex urban environments where sensor anomalies produce heavy-tailed, non-Gaussian error distributions. This paper presents a fundamentally different paradigm that reformulates integrity monitoring as a closed-loop control problem. The method computes an instantaneous error rate from three sources: inertial sensor noise, kinematic drift between filter-based and dead-reckoned displacement, and LiDAR scan-map registration quality weighted by a sensitivity factor. This rate drives a saturation-controlled setpoint dynamics, then an adaptive PID controller with entropy-based gain scheduling produces the final protection level. Asymmetric update laws enforce rapid expansion but cautious contraction of safety bounds. Experiments on three UrbanNavDataset sequences (medium-urban, low-urban, deep-urban) demonstrate that traditional covariance-based methods exhibit high integrity risk, while the proposed framework achieves 0.0% risk in moderate environments and 2.3% under extreme degradation. The resulting protection levels are smooth and well-behaved, compatible with modern motion planners. This control-theoretic approach offers a viable alternative to statistical integrity paradigms in challenging real-world conditions.