This paper presents a theoretical framework for deriving bounds on location error tolerance that ensure guaranteed detection with probabilistic certificates in safety-critical applications. It unifies detection theory, randomized smoothing, and uncertainty quantification to provide closed-form bounds on tolerable location errors and a certified detection radius formula.
Key findings
Establishes fundamental limits on spatial perturbation a detection system can tolerate.
Derives closed-form bounds on location errors as a function of detection confidence requirements.
Presents a certified detection radius formula based on Gaussian uncertainty propagation.
Extends the Neyman-Pearson framework to balance false negative and false positive rates under spatial uncertainty.
Limitations & open questions
The framework's practical application may be limited by the assumptions made about location uncertainty.