  Reconfigurable intelligent surface (RIS)-assisted localization has attracted
extensive attention as it can enable and enhance localization services in
extreme scenarios. However, most existing works treat RISs as anchors with
known positions and orientations, which is not realistic in applications with
mobile or uncalibrated RISs. This work considers the joint RIS calibration and
user positioning (JrCUP) problem with an active RIS. We propose a novel
two-stage method to solve the considered JrCUP problem. The first stage
comprises a tensor-estimation of signal parameters via rotational invariance
techniques (tensorESPRIT), followed by a channel parameters refinement using
least-squares. In the second stage, a two-dimensional search algorithm is
proposed to estimate the three-dimensional user and RIS positions,
one-dimensional RIS orientation, and clock bias from the estimated channel
parameters. The Cramer-Rao lower bounds of the channel parameters and
localization parameters are derived to verify the effectiveness of the proposed
tensorESPRIT-based algorithms. In addition, simulation results reveal that the
active RIS can significantly improve the localization performance compared to
the passive case under the same system power supply in practical regions.
Moreover, we observe the presence of blind areas with limited JrCUP
localization performance, which can be mitigated by either leveraging more
prior information or deploying extra base stations.
