Cross-correlation effect of ARAIM test statistic on false alarm risk

Abstract

The requirement for ARAIM continuity risk due to the monitor false alarm has been outlined in earlier works for ARAIM development (WG-C in ARAIM technical subgroup milestone 3 report, 2016). However, the expected continuity risk comes from an underlying conservative assumption that the correlation between multiple monitors for fault detection is negligible. Thus, we investigate the effect of the cross-correlation across ARAIM solution separation tests on the monitor false alarm probability (\(P_{\text{FA}}\)) by presenting a higher fidelity methodology to evaluate the \(P_{\text{FA}}\) based on highly correlated fault detection tests. We carry out a preliminary assessment of ARAIM false alarm performance by using the proposed method. It was found that considering the cross-correlation among monitor test statistics reduces the predicted \(P_{\text{FA}}\) by up to approximately 50% of the predefined requirement (e.g., \(10^{ - 6}\)) when triple satellite faults were considered. Despite such improvement, the baseline ARAIM implementation does not appear to be overly conservative.