Multi-Stage Estimation for 3D Joint Localization in SIMO Systems with Hybrid RIS

This paper focuses on the joint three-dimensional (3D) localization and synchronization problem for a user equipment (UE) and a hybrid reconfigurable intelligent surface (HRIS) in a far-field scenario under single-input multiple-output (SIMO) system. A multi-stage estimation approach, which consists of constructing a maximum likelihood (ML) framework. First, root-MUSIC algorithm is used to estimate the time-of-arrival (TOA) in each channel. Subsequently, the signal received at the HRIS terminal is exploited to formulate an ML estimator. The angular parameters in the channel are estimated through 2D searchs. Finally, derive the location parameters based on the channel parameters. The simulation results indicate that the mean square error performance of the estimated channel and position parameters approaches the Cramér-Rao bound.