Efficiency of Spatial Correlation for Multi-RIS-Assisted Multi-User Direct Localization

In this paper, the positioning accuracy of multiple reconfigurable intelligent surface (RIS)-assisted multi-user direct localization system is studied. In particular, we incorporate statistical spatial correlation of multi-user locations and develop Bayesian Cramer-Rao bound (BCRB) to measure positioning accuracy. To address the information coupling between neighboring users induced by spatial correlation and position uncertainty, the equivalent Fisher information matrix (EFIM) of users' positions is decomposed to obtain a metric characterizing the efficiency of spatial correlation (EoSC). Random walk model (RWM) is adopted to provide a graph interpretation for EoSC, which unveils the information flow during positioning. Finally, we numerically illustrate the localization accuracy scaling law for several key system parameters.