Near-Field NLOS Localization via Position-Unknown HRIS:From Self-Localization to Target Positioning

Current reconfigurable intelligent surface (RIS)-aided near-field (NF) localization methods assume the RIS position is known a priori, and it has limited their practical applicability. This paper applies a hybrid RIS (HRIS) at an unknown position to locate non-line-of-sight (NLOS) NF targets. To this end, we first propose a two-stage gridless localization framework for achieving HRIS self-localization, and then determine the positions of the NF targets. In the first stage, we use the NF Fresnel approximation to convert the signal model into a virtual far-field model through delay-based cross-correlation of centrally symmetric HRIS elements. Such a conversion will naturally extend the aperture of the virtual array. A single-snapshot decoupled atomic norm minimization (DANM) algorithm is then proposed to locate an NF target relative to the HRIS, which includes a two-dimensional (2-D) direction of arrival (DOA) estimation with automatic pairing, the multiple signal classification (MUSIC) method for range estimation, and a total least squares (TLS) method to eliminate the Fresnel approximation error. In the second stage, we leverage the unique capability of HRIS in simultaneous sensing and reflection to estimate the HRIS-to-base station (BS) direction vectors using atomic norm minimization (ANM), and derive the three-dimensional (3-D) HRIS position with two BSs via the least squares (LS)-based geometric triangulation. Furthermore, we propose a semidefinite relaxation (SDR)-based HRIS phase optimization method to enhance the received signal power at the BSs, thereby improving the HRIS localization accuracy, which, in turn, enhances NF target positionings. The Cramer-Rao bound (CRB) for the NF target parameters and the position error bound (PEB) for the HRIS coordinates are derived as performance benchmarks.