Bounding GPS-Based Positioning and Navigation Uncertainty for Autonomous Drifting via Reachability

The study of autonomous drifting is motivated by the need to ensure the safe operation of autonomous vehicles, particularly under extreme dynamics where driver safety may be compromised. In such safety-critical applications, the worst-case positioning performance under measurement uncertainty must be considered. Reachability analysis (RA) is a technique that is commonly used to provide formal guarantees on the position under such uncertainty. In this work, we integrate a set-based RA estimation framework with nonlinear drift dynamics and double-difference GPS pseudorange measurements to provide positioning bounds for an autonomous drifting vehicle. We validate our framework on high-fidelity simulated drifting experiments with varied GPS measurement noise profiles. We show that the positioning bounds from our framework successfully bound the trajectories from a particle filter across all validation cases.