  The recent research in the emerging technology of reconfigurable intelligent
surfaces (RISs) has identified its high potential for localization and sensing.
However, to accurately localize a user placed in the area of influence of an
RIS, the RIS location needs to be known a priori and its phase profile is
required to be optimized for localization. In this paper, we study the problem
of the joint localization of a hybrid RIS (HRIS) and a user, considering that
the former is equipped with a single reception radio-frequency (RF) chain
enabling simultaneous tunable reflections and sensing via power splitting.
Focusing on the downlink of a multi-antenna base station, we present a
multi-stage approach for the estimation of the HRIS position and orientation as
well as the user position. Our simulation results, including comparisons with
the Cram\'er-Rao lower bounds, demonstrate the efficiency of the proposed
localization approach, while showcasing that there exists an optimal HRIS power
splitting ratio for the desired multi-parameter estimation problem.
