LEO-GAPM: a novel geometry and probability model for analyzing GNSS monitoring performance of LEO constellations

Abstract Global navigation satellite system (GNSS) integrity monitoring relies on continuous, worldwide observation of satellite signals. While ground-based monitoring networks are constrained by geographical coverage and political boundaries, low Earth orbit (LEO) constellations offer a promising space-based alternative due to their global distribution and dynamic characteristics. Current performance evaluations of satellite constellations often rely on real or simulated ephemerides. Although the geometry and probability model (GAPM) can estimate Earth coverage without such data, it cannot model the ‘inverse coverage’ of LEO satellites monitoring high-altitude GNSS satellites. To address this gap, we propose the LEO GAPM, which explicitly models this ‘inverse coverage’ by introducing the concept of relative inclination and reformulating the observation probability function. This model estimates key performance metrics, such as monitoring coverage fold and satellite geometry dilution of precision (SGDOP), using only a small set of orbital parameters. Validation experiments show that the average difference in estimated coverage fold between LEO-GAPM and orbital propagation methods is less than 0.14, and the underestimation rate of SGDOP ranges between 5% and 13%. The model was further employed to analyze two representative LEO constellations (Iridium NEXT and CENTISPACE) for BDS-3 monitoring, assessing how coverage capability varies with the number of LEO satellites. This analysis demonstrates that constellation configuration, orbital inclination, and satellite count are key determinants of monitoring performance. Additionally, the study quantifies the number of satellites required to achieve an average coverage fold of 3–10. Overall, our study provides a computationally efficient tool for preliminary design and resource allocation in space-based GNSS monitoring systems.