Closed-Form Location and Orientation Estimation in Optical Wireless Systems

Accurate indoor localization is crucial for enabling 6G applications, such as smart homes, augmented reality, and advanced healthcare systems. Optical wireless systems utilizing Light-Emitting Diodes (LEDs) offer centimeter-level accuracy due to their dominant line-of-sight (LoS) characteristics. However, most existing methods assume fixed and known user orientations, limiting their practical applicability in real-world scenarios with random orientations. In this paper, we propose an LED-based visible light positioning (VLP) scheme that accurately, through closed form equations, localizes users with arbitrary orientations using optical received signal strength (RSS) measurements. The proposed method achieves high localization accuracy, without requiring hardware for orientation measurements. Finally, an analytical expression for the error is derived, while Monte Carlo simulations validate the scheme's performance, highlighting the critical role of the parameters of the system in achieving accurate localization.