Sample Temporal Correlation Effect on PHMI

Abstract : The current Advanced Reciever Autonomous Integrity Monitoring (ARAIM) airborne user algorithm [1] takes a simple approach to modelling the integrity risk, i.e., the specific risk of loss of integrity for a given approach is allocated to each epoch so that the user receiver can derive its protection level. This paper aims to investigate the impact of the temporal correlation of ARAIM fault detection tests and position errors on the probability of hazardous misleading information (PHMI) by deriving the valid number of samples. A methodology is presented to estimate the actual PHMI over a given time interval and define the effective number. Probabilities that position errors cross the protection bound and then stay above the bound for time-to-alert (TTA) and test statistics cross the test threshold after the positioning failures during the TTA are modelled based on Monte Carlo runs of the normalized first-order Gauss-Markov (GM) process and a newly proposed operational satellite exclusion approach. A practical model for the valid number of samples is constructed based on the proposed methodology, and the modified integrity allocation is proposed using the derived model. We also examine the impact the satellite reinclusion which is the baseline approach to the temporal correlation analysis for the current ARAIM monitoring algorithm by employing some valid sample numbers (e.g., a few hundred for RNP 0.1) from previous studies and comparing ARAIM availability and protection bound based on the proposed exclusion method with those based on the satellite reinclusion method. A case study shows that the proposed exclusion method reduces the number of valid samples up to around 0.9 which is consistent with the traditional ARAIM assumption. It is also found that the 99.5% V-ARAIM availability for LPV-200 is reduced by approximately 6% when the actual risk allocation through the effective number of samples is applied to the protection level calculation. In particular, the proposed exclusion method is shown to mitigate the impact of sample temporal correlation by reducing protection level up to about 11% compared to the satellite reinclusion approach.