A Novel Method to Estimate the Coordinates of LEDs in Wireless Optical Positioning Systems

Traditional visible light positioning (VLP) systems estimate receivers' coordinates based on the known light-emitting diode (LED) coordinates. However, the LED coordinates are not always known accurately. Because of the structural changes of the buildings due to temperature, humidity or material aging, even measured by highly accurate laser range finders, the LED coordinates may change unpredictably. In this paper, we propose an easy and low-cost method to update the position information of the LEDs. We use two optical angle-of-arrival (AOA) estimators to detect the beam directions of the LEDs. Each AOA estimator has four differently oriented photodiodes (PDs). Considering the additive noises of the PDs, we derive the closed-form error expression for the proposed LED coordinates estimator. Both analytical and Monte Carlo experimental results show that the layout of the AOA estimators could affect the estimation error. These results may provide intuitive insights for the design of the optical indoor positioning systems.