RIS Position and Orientation Estimation via Multi-Carrier Transmissions and Multiple Receivers

Reconfigurable intelligent surfaces (RISs) are considered as an enabling technology for the upcoming sixth generation of wireless systems, exhibiting significant potential for radio localization and sensing. An RIS is usually treated as an anchor point with known position and orientation when deployed to offer user localization. However, it can also be attached to a user to enable its localization in a semi-passive manner. In this paper, we consider a static user equipped with an RIS and study the RIS localization problem (i.e., joint three-dimensional position and orientation estimation), when operating in a system comprising a single-antenna transmitter and multiple synchronized single-antenna receivers with known locations. We present a multi-stage estimator using time-of-arrival and spatial frequency measurements, and derive the Cram\'er-Rao lower bounds for the estimated parameters to validate the estimator's performance. Our simulation results demonstrate the efficiency of the proposed RIS state estimation approach under various system operation parameters.