  In ultra-dense LEO satellite networks, conventional communication-oriented
beam pattern design cannot provide multiple favorable signals from different
satellites simultaneously, and thus leads to poor positioning performance. To
tackle this issue, in this paper, we propose a novel cooperative beam hopping
(BH) framework to adaptively tune beam layouts suitable for multi-satellite
coordinated positioning. On this basis, a joint user association, BH design and
power allocation optimization problem is formulated to minimize average
Cram\'er-Rao lower bound (CRLB). An efficient flexible BH control algorithm
(FBHCA) is then proposed to solve the problem. Finally, a thorough experimental
platform is built following the Third Generation Partnership Project (3GPP)
defined non-terrestrial network (NTN) simulation parameters to validate the
performance gain of the devised algorithm. The numerical results demonstrate
that FBHCA can significantly improve CRLB performance over the benchmark
scheme.
