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

Technical Summary: Visible Light Indoor Positioning with a Single LED and Distributed Single-Element OIRS

Problem Statement
This paper addresses the challenge of localizing a low-cost Photo Detector (PD) in an indoor Visible Light Communication (VLC) environment. The specific scenario involves a system with only a single active Light Emitting Diode (LED) anchor and multiple spatially distributed single-element Optical Intelligent Reflective Surfaces (OIRSs). The primary difficulties include the lack of prior knowledge regarding the PD's position, the need to mitigate Line-of-Sight (LoS) blockages, and the computational constraints of low-cost devices. Existing solutions often rely on multiple LEDs, direct localization paradigms requiring numerical optimization, or prior knowledge of the user's location, which limits their applicability in cost-sensitive or dynamic scenarios.

Methodology
The authors propose an indirect, two-step localization framework that avoids direct inference of position from raw signals. The methodology consists of three main phases:

1. Distance Estimation:

   • LoS Estimation: The system first estimates the direct distance between the LED and the PD. The authors derive a Maximum Likelihood (ML) estimator that accounts for signal-dependent noise variance (shot noise). They also propose a Relaxed ML (RML) estimator that treats noise variance as a nuisance parameter, yielding a closed-form solution based on the sample mean.
   • NLoS Estimation: To estimate distances via OIRSs, the system employs a structured activation protocol where only one OIRS is active at a time to prevent interference. The LoS component is subtracted from the received signal to isolate the Non-Line-of-Sight (NLoS) reflection. While the optimal ML estimator for NLoS distance requires a computationally intensive grid search, the authors derive a closed-form RML estimator based on an unstructured noise variance transformation. This estimator uses the sample mean of the isolated NLoS signal as a sufficient statistic.

2. Iterative Position Estimation:

   • The estimated LoS and NLoS distances are fed into an Iterative Weighted Least Squares (IWLS) algorithm to estimate the PD's 2D position.
   • The weighting matrix in the IWLS is dynamically set according to the inverse of the Cramér-Rao Lower Bound (CRLB) for the estimated distances, accounting for path-dependent uncertainty.
   • Crucially, the algorithm operates without initial position knowledge. It begins with an assumption that OIRSs are perfectly aligned (using their geometric centers as reflection points) and iteratively refines this.

3. Adaptive Beam Steering:

   • After each position estimate, the system updates the tilt angles (pitch and yaw) of the distributed OIRSs. The steering strategy aligns the OIRS surface normal to the bisector of the angle formed by the LED and the estimated PD position. This adaptive reconfiguration progressively corrects initial misalignments, enhancing the signal quality for subsequent iterations.

Key Contributions

• Closed-Form Estimators: The derivation of optimal ML estimators for LoS distance and a novel, computationally efficient closed-form RML estimator for NLoS distances, eliminating the need for grid-based optimization.
• Indirect Localization Framework: A low-complexity iterative algorithm that combines distance estimation with adaptive beam steering, requiring no prior knowledge of the PD location.
• Theoretical Bounds: The derivation of the Cramér-Rao Lower Bound (CRLB) for both distance and position estimation in a single-LED, single-element OIRS setup, providing a benchmark for performance analysis.
• Complexity Reduction: A demonstration that the proposed indirect approach achieves performance comparable to state-of-the-art direct ML methods but with significantly lower computational complexity.

Results
Simulation results, based on a 5m × 5m × 3m room scenario, demonstrate the following:

• Distance Accuracy: Both ML and RML estimators achieve Root Mean Squared Error (RMSE) close to the theoretical Distance Error Bound (DEB). The RML estimator performs nearly identically to the ML estimator but with a closed-form solution.
• Robustness: The estimators exhibit robustness against OIRS misalignment, maintaining centimeter-level accuracy even with orientation errors up to 20°.
• Positioning Performance: The iterative algorithm with adaptive beam steering converges to the Position Error Bound (PEB) within two iterations. It achieves millimeter-level accuracy, comparable to a state-of-the-art direct ML estimator that requires a 2D exhaustive grid search.
• Coverage: With 12 distributed OIRSs, the system achieves feasible localization coverage for approximately 80% of the room area.
• Computational Efficiency: The proposed iterative algorithm requires less than 0.5% of the execution time of the direct ML estimator. Specifically, the RML NLoS estimator reduces distance estimation time by approximately 99.6% compared to the grid-search-based ML estimator.

Significance
The paper claims that its approach offers a viable, low-cost alternative for high-precision indoor positioning by leveraging existing lighting infrastructure and OIRS technology. By decoupling distance estimation from position inference and utilizing adaptive beam steering, the method overcomes the limitations of direct localization (high computational cost, need for priors) and the constraints of single-LED systems (LoS blockages). The work highlights that high accuracy can be attained with minimal hardware (single LED, single-element OIRSs) and low computational overhead, making it suitable for deployment in resource-constrained environments.