Probabilistic Models for Assured Position, Navigation, and Timing

Position, navigation, and timing (PNT) user equipment produces position, velocity, and time (PVT) estimates by combining measurements from multiple Global Navigation Satellite Systems (GNSS) and from additional sensors. PVT estimates are computed using linear estimators or Bayesian filters. However, because linear estimators and Bayesian filters are susceptible to adversarial manipulation, it is challenging to assess the trust of PVT estimates that rely on these approaches. We investigate the suitability of open-universe probabilistic models OUPMs-introduced by Milch and Russell-as a foundation to design PVT assurance metrics and adaptive PVT estimators. These estimators output PVT information together with trust assessments of PVT inputs and outputs. OUPMs model structural uncertainty (object uncertainty and relational uncertainty) necessary to measure assurance when the availability of sensors and the absence of adversaries cannot be guaranteed. We describe the challenges of designing PVT assurance metrics using traditional methods, and we illustrate how OUPMs-represented as probabilistic programs-allow us to address these challenges. In particular, we provide concrete examples of how to combine multiple sources of information to compute assurance assessments using the Texas Spoofing Test Battery. Furthermore, we demonstrate how to leverage PVT assurance metrics to design adaptive PVT estimators designed to operate through attacks.