Position, Navigation, and Timing (PNT) platforms provide fundamental support for critical infrastructure, ranging from air traffic control, emergency services, telecom, financial markets, personal navigation, power grids, space applications, etc. However, the problem of defining PNT assurance metrics remains open.
We evaluate an approach that uses probabilistic programming for designing PVT assurance metrics and adaptive PVT estimators that process inputs according to corresponding assurance assessments. The possible worlds semantics developed in the field of Statistical Relational Learning provides a formal framework that can serve as the basis for defining rigorous assurance models for PVT.
Probabilistic programming allows us to define open-universe probabilistic models (OUPMs) (Milch, Russell), which have richer semantics than commonly used Bayesian filters. Concretely, OUPMs allow us to model structural uncertainty that corresponds to the uncertain availability of sensors (satellites, inertial sensors, clocks, etc.) and the presence of an adversary. Additionally, OUPMs allow us to model relational uncertainty (e.g., how adversaries influence observations). Probabilistic programs, in addition to encoding trust and adversarial models, allow us to specify assurance requirements (e.g., related to accuracy, availability, and continuity).