Precise Relative Navigation in Medium Earth Orbits with Global Navigation Satellite Systems and Intersatellite Links for Black Hole Imaging

Abstract

The Event Horizon Telescope (EHT) is a global array of telescopes that employs Very Long Baseline Interferometry (VLBI) techniques to image the event horizon of black holes. To overcome the limitations of ground-based telescopes, this thesis explores the mission concept involving a two-satellite constellation of space-borne telescopes deployed in Medium Earth Orbit (MEO). The attainment of high-resolution black hole images requires extremely precise baseline determination at the few millimetre level. To address this challenge, each satellite within the constellation is equipped with two hemispherical Global Navigation Satellite System (GNSS) receivers and an optical Intersatellite Link (ISL) for relative navigation. This study aims to assess the feasibility of achieving highly accurate relative positioning within the constellation, particularly considering the large intersatellite distances involved.

The methodology employed in this simulation study encompasses several steps. Initially, the satellite orbits are estimated independently for each satellite using GNSS observations. Following this, the orbit of one of the satellites is held fixed as a reference, while the orbit of the other satellite is re-estimated by incorporating the ISL observations. To enhance the accuracy of the orbit estimation, integer GNSS ambiguity resolution is implemented in the precise orbit determination process. The simulated data incorporates an extensive set of realistic error sources, including thermal noise, instrumental delays, clock biases, errors in the GNSS ephemerides and clocks, uncertainties in the geopotential and solar radiation pressure models, and white noise in the ISL observations.

The results highlight the importance of integer ambiguity resolution in meeting the stringent relative navigation requirements of the mission. The analysis also reveals that the ISL observations primarily improve the baseline estimation along the direction of the link itself. However, in the direction of the black hole, the impact of ISL observations is minimal, indicating that the ISL does not significantly contribute to meeting the specific relative navigation requirements. Furthermore, the study identifies that large intersatellite distances lead to degraded relative orbit accuracy due to fewer shared errors between the two satellites. As a consequence, the objective of achieving a 3.5 mm (3-sigma) one-dimensional relative position accuracy along the black hole direction is not met, with the obtained results showing a 3-sigma of 8.29 mm. To tackle this, it is recommended to focus on mitigating the most prominent error sources, namely uncertainties in the dynamical model and errors in the GNSS orbits and clocks. Other alternatives, such as a network processing scheme, could also be investigated in the future to overcome this challenge.