CUSUM-Based Real-Time Risk Metrics for Augmented GPS and GNSS

Sigma monitoring is a key component of the real-time integrity verification capability demonstrated by the Stanford University Local Area Augmentation System (LAAS) Ground Facility prototype known as the Integrity Monitor Testbed (IMT). The IMT has both sigma estimation and sigma Cumulative Sum (CUSUM) algorithms to detect small and large sigma violations, respectively. When combined with a prior probability distribution for the sigma parameter being monitored and the use of Bayes’ rule, the CUSUM can provide a realtime posterior distribution of sigma based on the current CUSUM state. This paper presents the methodology for this “Bayesian CUSUM” technique and shows how it could be used to enhance integrity monitoring while better preserving continuity and availability.