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Recent research and development interests deal with metasurfaces for wirelesssystems beyond their consideration as intelligent tunable reflectors. Among thelatest proposals is the simultaneously transmitting (a.k.a. refracting) andreflecting reconfigurable intelligent surface (STAR-RIS) which intends toenable bidirectional indoor-to-outdoor, and vice versa, communications thanksto its additional refraction capability. This double functionality providesincreased flexibility in concurrently satisfying the quality-of-servicerequirements of users located at both sides of the metasurfaces, for example,the achievable data rate and localization accuracy. In this paper, we focus onSTAR-RIS-empowered simultaneous indoor and outdoor three-dimensional (3D)localization, and study the fundamental performance limits via Fisherinformation analyses and Cram\'er Rao lower bounds (CRLBs). We also devise anefficient localization algorithm based on an off-grid compressive sensing (CS)technique relying on atomic norm minimization (ANM). The impact of the trainingoverhead, the power splitting at the STAR-RIS, the power allocation between theusers, the STAR-RIS size, the imperfections of the STAR-RIS-to-BS channel, aswell as the role of the multi-path components on the positioning performanceare assessed via extensive computer simulations. It is theoretically showcasedthat high-accuracy, up to centimeter level, 3D localization can besimultaneously achieved for indoor and outdoor users, which is alsoaccomplished via the proposed ANM-based estimation algorithm.

STAR-RIS-Enabled Simultaneous Indoor and Outdoor 3D Localization: Theoretical Analysis and Algorithmic Design