Visible Light Indoor Positioning with a Single LED and Distributed Single-Element OIRS: An Iterative Approach with Adaptive Beam Steering

The integration of Optical Intelligent Reflective Surfaces (OIRSs) into Visible Light Communication (VLC) systems is gaining momentum as a valid alternative to RF technologies, harnessing the existing lighting infrastructures and the vast unlicensed optical spectrum to enable higher spectral efficiency, improved resilience to Line-of-Sight (LoS) blockages, and enhanced positioning capabilities. This paper investigates the problem of localizing a low-cost Photo Detector (PD) in a VLC-based indoor environment consisting of only a single Light Emitting Diode (LED) as an active anchor, and multiple spatially distributed single-element OIRSs. We formulate the problem within an indirect, computationally efficient localization framework: first, the optimal Maximum Likelihood (ML) estimators of the LoS and Non-Line-of-Sight (NLoS) distances are derived, using a suitable OIRS activation strategy to prevent interferences. To overcome the grid-based optimization required by the ML NLoS estimator, we devise a novel algorithm based on an unstructured noise variance transformation, which admits a closed-form solution. The set of estimated LoS/NLoS distances are then used within a low-complexity localization algorithm combining an Iterative Weighted Least Squares (IWLS) procedure, whose weights are set according to the inverse of the Cram\'er-Rao Lower Bound (CRLB), with an adaptive beam steering strategy that allows the OIRSs network to dynamically align with the PD, without any prior knowledge of its position. Accordingly, we derive the CRLB for both LoS/NLoS distance estimation and PD position estimation. Simulation results demonstrate the effectiveness of our approach in terms of localization accuracy, robustness against OIRSs misalignment conditions, and low number of iterations required to attain the theoretical bounds.