Bayes estimation and analysis of GNSS SIS fault rate

Abstract

GNSS SIS fault probabilities Psat and Pconst are the key parameters contained in the Integrity Support Message (ISM) which will be broadcast to GNSS Advanced Receiver Autonomous Monitoring (ARAIM) users. The accurate and reliable SIS fault rate is crucial to ensure the trustiness of ARAIM. Although prior published works have developed the methods to estimate the fault rate, there are lack of a metric to assess the reliability of the fault rate, and then determine the optimal length observation window. Therefore, based on the prior works, we aim to establish the method of reliability assessment for the SIS fault rate estimation. First, the SIS fault rate estimator is derived and its variance are formulated. Then the equivalence between 2-sigma and the error bound of 95% confidence are verified by exposing the inside properties of the posteriori PDF of fault rate. The reliability assessment provides a criterion to determine the optimal length of observation window and finally obtain the reliable fault rate estimators. GPS performance in the period of 2008–2019 is assessed by varying the length of observation window. The optimal estimators of GPS NF rate indicate that the specified fault rate of 1×10-5/sat/hour was achieved in the middle of 2011 and GPS has had a trend of performance improvement since 2011.