# Impact Analysis of Satellite Geometry Variation on ARAIM Integrity Risk over Exposure Interval
###### Abstract  
Accurate integrity risk evaluation is of significance in ensuring that aviation navigation applications satisfy the predefined integrity requirement. The integrity risk evaluation method over a specified exposure interval has been proposed in previous works for the development of advanced receiver autonomous integrity monitoring (ARAIM) (ARAIM technical subgroup reference airborne algorithm description document v4.1, 2022). However, this method typically relies on an underlying optimistic assumption that the satellite geometry remains constant throughout the exposure interval. The variation in satellite geometry due to potential satellite outages undermines the widely-used geometry constant assumption. Thus, we investigate the influence of satellite geometry variations throughout the exposure interval on the integrity performance by introducing a geometry-sensitive risk-evaluation model. The findings demonstrate that, under the nominal situation, the region where the ARAIM fails to meet predefined integrity requirement could expand by a maximum of 2.93% when accounting for satellite geometry variations. Furthermore, in the situation of a single satellite outage, this hazardous region has significantly expanded from 13.12% of the global coverage to 66.82%. Based on these findings, we recommend that the ARAIM should consider satellite outages as a critical factor in real-time integrity risk evaluation. ARAM; integrity risk; exposure interval; global navigation satellite system; satellite outage 202416286.12.  
whether to abort or to pursue a mission [11]. In most of the literature [11; 12; 13], the integrity risk is evaluated at a single epoch without considering detection across multiple epochs, even though their corresponding requirements are specified over the exposure interval [14]. The literature assumes that when the correlation times of detection statistics and positioning error are significantly greater than the exposure interval, the integrity risk would be nearly constant as if one independent test was executed over the interval [14]. However, there has been some relevant earlier work on ARAIM suggesting that the assumption is not true, and that the actual integrity risk can be much higher [14; 15]. To resolve these issues, [PERSON] et al. [15] and [PERSON] et al. [16] proposed an integrity risk evaluation method that accurately accounts for the time-correlation effect of detection statistics and positioning error by utilizing the number of effective samples (NES). The NES represents the ratio of the integrity risk for a single epoch to the integrity risk over an exposure interval, and it can be computed using a first-order Gauss Markov model. When determining the NES, the upper limit of integrity risk over a given exposure interval can be evaluated based on the integrity risk observed at a single epoch within that interval [17]. At present, this algorithm has been adopted in the ARAIM technical subgroup reference airborne algorithm-description document [1]. However, to simplify the complexity of integrity risk evaluation, this method typically assumes a constant satellite geometry throughout the exposure interval. Unfortunately, the variation in satellite geometry is frequent and presents practical challenges for accurate integrity risk evaluation. This traditional assumption can introduce errors in integrity risk evaluation, particularly as the exposure interval increases. Therefore, we focus on the integrity risk evaluation of ARAIM in the presence of satellite geometry variation in this contribution. Currently, the integrity risk evaluation based on the NES generally assumes a constant satellite geometry throughout the exposure interval. This assumption is regarded as reasonable only under the following conditions: First, the duration of the given exposure interval should be short. For instance, this assumption can be applicable to an LPV-200 approach with an exposure interval of 150 s. Secondly, there should be no satellite outages throughout the exposure interval.