# Impact Analysis of Satellite Geometry Variation on ARAIM Integrity Risk over Exposure Interval
###### Abstract
Unfortunately, achieving both of these conditions simultaneously is often challenging in real-time aviation navigation applications. There are several factors that can cause satellite outages within the exposure interval, e.g., aircraft banking and ionospheric scintillation. The aircraft attitude affects the reception of the signal because the antenna pattern is such that signals coming from underneath the plane of the aircraft suffer a significant loss of power [18]. Outages can also occur due to ionospheric scintillation, particularly in low latitude regions, which are affected by the equatorial anomaly. The addition or removal of a satellite in the view, especially for weak geometries, can cause significant changes in the satellite geometry. This variation in satellite geometry undermines the widely-used assumption of constant geometry and can result in errors in integrity risk evaluation. Although the ARAIM algorithm incorporates multiple conservative assumptions to constrain the actual integrity risk, to our knowledge, there is a lack of prior studies investigating the influence of satellite geometry variations within the exposure interval on the performance of the NES-based ARAIM. [PERSON] [19] has conducted a simulation analysis in previous research to quantify satellite geometry variations within the exposure interval. However, these quantitative results were primarily focused on a shorter exposure interval, and the impact of satellite geometry variations on integrity risk was not further explored. For this purpose, we investigate the actual integrity performance of the ARAIM under different situations of satellite geometry variation. If the observed performance significantly exceeds the predefined integrity risk requirement, it can provide a foundation for developing a more efficient integrity risk evaluation method to achieve better real-time performance. According to the above analysis, the rigorous integrity risk-evaluation model is primarily constrained by the accurate description of satellite geometry variation within the exposure interval. Monte Carlo (MC) simulation is a straightforward, brute-force method employed to solve a complex model [20]. However, this approach is impractical for our performance verification due to its time-consuming nature, especially when considering worldwide integrity performance. An analytical integrity risk evaluation is more suitable for conducting worldwide performance verification. To the best of our knowledge, a rigorous integrity risk-evaluation model that considers satellite geometry variation within the exposure interval is still absent. In this contribution, we develop a general integrity risk-evaluation model to quantify the impact of satellite geometry variation on integrity performance. The principle of inclusion and exclusion (PIE) is introduced to rigorously characterize the influence of the satellite geometry variation within the exposure interval. It should be noted that our proposed method is designed for application in the offline integrity performance analysis of ARAIM. Through a rigorous assessment of ARAIM's integrity performance, it is poised to furnish a dependable foundation for performance verification, as well as the subsequent update and adjustment of the ARAIM algorithm. The next section introduces the concept of overall integrity risk to clarify the integrity requirements for ARAIM operations. In the following sections, we review the least-squares estimation of states of interest and the current ARAIM fault-detection algorithm to define the hazardously misleading information (HMI). The HMI definition will serve as a foundation for integrity risk evaluation. Next, we provide a detailed overview of the methodology we applied to evaluate the integrity risk of ARAIM. Following the detailed description of the method, we proceed to analyze the bounding tightness of the proposed method to the integrity risk reference, ensuring the effectiveness of the subsequent performance verification.