Mega-constellations in Low Earth Orbit have the potential to revolutionise
worldwide internet access. The concomitant potential of these
mega-constellations to impact space sustainability, however, has prompted
concern from space actors as well as provoking concern in the ground-based
astronomy community. Increasing the knowledge of the orbital state of
satellites in mega-constellations improves space situations awareness, reducing
the need for collision avoidance manoeuvres and allowing astronomers to prepare
better observational mitigation strategies. In this paper, we create a model of
Phase 1 of Starlink, one of the more well-studied megaconstellations, and
investigate the potential of cooperative localisation using time-ofarrival
measurements from the optical inter-satellite links in the constellation. To
this end, we study the performance of any unbiased estimator for localisation,
by calculating the instantaneous Cram r-Rao bound for two
situations; one in which inter-satellite measurements and measurements from
ground stations were considered, and one in which only relative navigation from
inter-satellite measurements were considered. Our results show that
localisation determined from a combination of inter-satellite measurements and
ground stations can have at best an an average RMSE of approximately 10.15
metres over the majority of a satellite's orbit. Relative localisation using
only inter-satellite measurements has a slightly poorer performance with an
average RMSE of 10.68 metres. The results show that both anchored and
anchorless inter-satellite cooperative localisation are dependent on the
constellation's geometry and the characteristics of the inter-satellite links,
both of which could inform the use of relative navigation in large satellite
constellations in future.