Precise absolute and relative navigation in Medium-Earth Orbits by means of Global Navigation Satellite Systems and Inter-Satellite Links

Abstract

The first close-up image of a black hole has been taken recently by means of a network of high-resolution telescopes situated all around the globe, also known as Event Horizon Telescope (EHT). In that regard, this Master Thesis reviews the feasibility of establishing accurate inter-satellite baselines in a two-satellite constellation of satellites placed in co-planar Medium Earth Orbits (MEO) equipped with telescopes to, amongst other applications, allow performing Very Long Baseline Interferometry (VLBI) on celestial bodies such as the supermassive black hole in the centre of our galaxy.

Regarding the workflow of this study, first a thorough analysis of the visibility conditions from the GPS and Galileo constellations has been performed for the pair of MEO-placed satellites. The results have shown that the receiver antennas need to adapt a nadir orientation to maximize the number of visibility contacts from mentioned GNSS constellations. Second, an assessment on the impact of different error sources in the absolute orbit accuracy has been conducted for the pair of satellites. The sensitivity analysis comprises errors that derive from realistic uncertainties in the geopotential model, GNSS orbits and clocks, satellites’ solar radiation pressure model, centre of mass and antenna reference point. The results have shown that the error sources that most affect the accuracy of the absolute orbit solution are disturbance aligned with the velocity component in both centre of mass of the satellites and reference point of the receiver antennas.

Furthermore, to achieve the high standards of relative navigation, optical ISL observations with micro-meter precision level were employed. This precision level was determined by the limits of the employed software tool, as the state-of-the-art precision of these measurements is at the nano-metre level. Due to the 1D nature of the ISL observation, it has been found that they cannot be processed alone and require the GNSS code and phase observations to be processed along with them. In these processes, the system architecture of the inter-satellite ranging system has been assumed to be two-way to rule out the errors that derive from the non-synchronization of the satellites’ clocks. The relative POD results have shown that the shorter the distance between the satellites, the higher the precision of the relative orbit solution in radial and along-track components, ultimately being limited by the precision of the ISL observations. The fact that the satellites are placed in co-planar orbits makes the cross-track component not be visible and probably yield conditioning problems to the LSQ matrix. Therefore, the impact of angular separations ranging from 1 to 10 degrees on the relative POD accuracy is also investigated. The most promising results come from the case in which the relative distance between the MEO-placed satellites is low (1,000km) and an angular separation in the orbital planes of 10 degrees has been induced. In that case, the relative orbit solution is improved in all components (radial, along-track and cross-track) and placed in the few millimetre level.