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

The Event Horizon Telescope (EHT) is a ground-based array of Very Long Baseline Interferometry (VLBI) telescopes designed to image the event horizon of black holes. To overcome its limitations, this work explores a mission concept involving a two-satellite constellation of VLBI telescopes deployed in circular and polar Medium Earth Orbit (MEO) at more than 8000 km altitude.  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 Global Navigation Satellite System (GNSS) receivers and an optical Intersatellite Link (ISL) for relative navigation. This work assesses 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. The work will show the accuracy obtained with the simulations, the assumptions considered, and the next steps needed.