Orbit reconstruction for HERMES-SP/TP satellite mission

We present techniques for the reconstruction of satellite's low Earth equatorial orbit during a GPS coverage gap for HERMES Pathfinder mission. The HERMES Scientific+Technological Pathfinder mission is conceived to consist of six satellites in a circular, equatorial, low Earth orbit at a height of 500-550 km. Each satellite will be equipped with a single GPS antenna. Therefore, GPS coverage gaps, where the satellite cannot establish contact with at least four GPS satellites, can last up to 25 min. We developed two methods for orbit determination within the coverage gap using known satellite positions before and after the gap: (1) polynomial and Fourier interpolation and (2) first- and second-order corrections to the Keplerian orbit. We tested both methods on simulated data and found them suitable, giving the accuracy required for the location of a satellite <= 30 m in > 99% of simulated gaps. The robustness of the methods was examined against simulated orbits with different values of inclinations and eccentricities. The first method gives consistent performance against eccentricity for coverage gaps lasting up to 20 min, while it shows a noticeable drop in performance at eccentricities above 0.01 for 25 min long gaps. The performance of the second method does not change with eccentricity within the investigated range, it also does not strongly depend on inclination and remains > 98%. With varying inclination, in the first method, the decrease in performance becomes evident for gaps longer than 20 min. The first method gives satellite position in the form of analytical function and can be used as a continuous satellite position determination procedure between two GPS telemetry updates, while the second method is limited by discrete output at expected GPS telemetry updates. Concerning the influence of solar activity on nanosatellite motion, all methods show similar levels of robustness and stability.