ARAIM 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. Probabilities that test statistics and position errors respectively cross the corresponding test threshold and protection bound over the duration are modelled based on the instant satellite reinclusion approach. A distribution of a normalised random variable the maximum of the standardised first order Gauss-Markov (GM) process during the interval. For the distribution, 108 sample functions of the GM process are generated with a correlation function taking account for all GNSS measurement error sources. We also estimate the likelihood that the no detection and positioning failure conditions co-occur. An upper bound of the actual PHMI over the time is derived by combining those three probabilities, and the valid number of independent samples is identified by comparing the upper bound to the integrity risk allocated to a single epoch. A case study is shown to lead to effective samples of more than 1700 when the temporal correlation effect is considered. It is also found that full capacity of 99.5% availability could no longer be achieved for H-ARAIM RNP 0.1 operation and 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.