  Positioning is an essential service for various applications and is expected
to be integrated with existing communication infrastructures in 5G and 6G.
Though current Wi-Fi and cellular base stations (BSs) can be used to support
this integration, the resulting precision is unsatisfactory due to the lack of
precise control of the wireless signals. Recently, BSs adopting reconfigurable
holographic surfaces (RHSs) have been advocated for positioning as RHSs' large
number of antenna elements enable generation of arbitrary and highly-focused
signal beam patterns. However, existing designs face two major challenges: i)
RHSs only have limited operating bandwidth, and ii) the positioning methods
cannot adapt to the diverse environments encountered in practice. To overcome
these challenges, we present HoloFed, a system providing high-precision
environment-adaptive user positioning services by exploiting multi-band(MB)-RHS
and federated learning (FL). For improving the positioning performance, a lower
bound on the error variance is obtained and utilized for guiding MB-RHS's
digital and analog beamforming design. For better adaptability while preserving
privacy, an FL framework is proposed for users to collaboratively train a
position estimator, where we exploit the transfer learning technique to handle
the lack of position labels of the users. Moreover, a scheduling algorithm for
the BS to select which users train the position estimator is designed, jointly
considering the convergence and efficiency of FL. Our simulation results
confirm that HoloFed achieves a 57% lower positioning error variance compared
to a beam-scanning baseline and can effectively adapt to diverse environments.
