JrCUP: Joint RIS Calibration and User Positioning for 6G Wireless Systems

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 <italic>joint RIS calibration and user positioning</italic> (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 (tensor-ESPRIT), 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 Cram&#x00E9;r-Rao lower bounds of the channel parameters and localization parameters are derived to verify the effectiveness of the proposed tensor-ESPRIT-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.