Model-Based Beam-Steered Optical Wireless Positioning with Single-LED Single-Photodiode for 3D Localization

Abstract

State-of-the-art optical wireless positioning (OWP) commonly reaches centimeter-level accuracy by depending on dense multi-light-emitting diodes (LED) infrastructures, photodiode (PD) arrays, or image-sensor receivers, incurring hardware complexity and deployment cost. This paper introduces a single beam-steered LED, single-PD OWP architecture that achieves three-dimensional (3D) localization without receiver rotation, cameras, or PD arrays; the core idea is to steer the transmitter through K known orientations and exploit the resulting received-signal-strength variations at the PD to estimate LED-to-PD direction and distance. We derive a composite Cramer-Rao lower bound and position-error bound (PEB) for the joint observation model, and cast the steering-pattern design as a genetic algorithm that minimizes the PEB over a 3D testbed. We develop both model-based a constrained nonlinear estimator and closed-form direction estimators: a statistically efficient generalized least squares solution, and a lightweight weighted least squares approximation. Simulations demonstrate centimeter-level accuracy for 3D OWP with a single beam-steered LED and a single PD.

Figures (8)

• Figure 1: Single beam-steered LED / single-PD OWP geometry. A beam-steered LED at $\mathbf t=[0,0,H]^{\mathsf T}$ (e.g., mechanical steering) points along $\{\mathbf n_{t,i}\}_{i=1}^{K}$; the PD is at $\mathbf r=[x,y,z]^{\mathsf T}$.
• Figure 2: Distribution of the PEB across all receiver locations in the $3\times3\times2\,\mathrm{m^3}$ testbed. For each $K$, green shows the GA-optimized orientation set and orange a randomly selected set. Boxes and whiskers summarize the sample distribution, while the shaded profiles depict the corresponding PDF.
• Figure 3: Heat map of the PEB across a $3\times3\,\mathrm{m^2}$ testbed at $z=0.8$ m for $K=5$ orientations: (a) optimal set, (b) random set.
• Figure 4: $\mathrm{PEB}_{90\%}$ versus the number of orientations $K$ for GA-optimized sets at a fixed SNR of $14$ dB and $\Phi_{1/2}\in\{30^\circ,45^\circ,60^\circ\}$. Values are computed over all receiver positions in the $3\times3\times2~\mathrm{m}^3$ testbed.
• Figure 5: $\mathrm{PEB}_{90\%}$ versus SNR for GA-optimized orientation sets with $K\in\{3,\ldots,9\}$ ($\Phi_{1/2}=45^\circ$; remaining parameters in Table \ref{['tab:ga_params']}). Values are computed over all receiver positions in the $3\times3\times2\,\mathrm{m^3}$ testbed.