Effect of Temporal Correlation on ARAIM, an Analysis on the Number of Effective Samples

In the realm of satellite navigation, ensuring the accuracy and reliability of position information is paramount, and this is particularly true in the aviation domain. Receiver Autonomous Integrity Monitoring (RAIM) has long been a fundamental concept in this pursuit, providing a means for GNSS receivers to detect and mitigate errors that may compromise navigation integrity. As technology advances, so does the need for more sophisticated techniques, leading to the emergence of Advanced RAIM (ARAIM). This evolution addresses the challenges posed by the increasing complexity of satellite constellations, atmospheric conditions, and signal interferences, while exploiting the future capabilities brought by dual-frequency multi-constellation (DFMC) navigation. Horizontal ARAIM (H-ARAIM) is intended to support RNP operations, where the integrity risk is defined over one hour of exposure time. Known reference H-ARAIM algorithms work on a snapshot-basis, which implies a need to translate the integrity and continuity requirements, given over the exposure time, down to the single epoch. To account for the aforementioned need, the notion of the Number of Effective Samples (Nes) has been introduced. Temporal correlation of nominal errors affecting the navigation solutions play a major role in determining Nes, together with the fault profile in case of the fault hypothesis. In this paper, temporal correlation of main error components, like multipath and orbit and clock errors, are derived from real data analysis, while the temporal correlation of other error contributions are taken from literature. Nominal errors are treated as 1st Order Gauss-Markov processes, and the Nes for integrity is estimated under different geometries, fault modes and fault profiles. The analysis shows that the Nes, under realistic assumptions, is much lower than the theoretical upper limit set by the required Time to Alert. This is also true when taking very conservative values for the temporal correlation. Making use of a realistic – yet bounding - Nes avoids penalizing availability. The use of an adequate Nes can indeed have several practical implications. It may lead to improved performance in challenging operational conditions (e.g. a reduced number of satellites in view). Additionally, it can enhance the efficiency of HARAIM algorithms, making them more adaptable to varying conditions and reducing the computational burden on receivers. In fact, a receiver can make a trade-off by reducing the number of satellites subsets to process in order to limit the computational load. Thanks to a lower Nes, H-ARAIM can optimize the use of available measurements, ultimately enhancing the reliability and robustness of satellite navigation systems in dynamic and challenging scenarios even beyond the aviation sector.