On the impact of LED power uncertainty on the accuracy of 2D and 3D Visible Light Positioning

Abstract

This paper presents a simulation study of the impact of Light Emitting Diode (LED) output power uncertainty on the accuracy of Received Signal Strength (RSS)-based two-dimensional (2D) and three-dimensional (3D) Visible Light Positioning (VLP). The actual emitted power of a LED is never exactly equal to the value that is tabulated in the datasheet, with possible variations (or tolerances) up to 20%. Since RSS-based VLP builds on converting estimated channel attenuations to distances and locations, this uncertainty will impact VLP accuracy in real-life setups. For 2D, a typical configuration with four LEDs is assumed here, and a Monte-Carlo simulation is executed to investigate the distribution of the resulting positioning errors for four tolerance values at seven locations. It is shown that median errors are the highest just below the LEDs, when using a traditional Least-Squares minimization metric. When tolerance values on the LED power increase from 5% to 20%, median errors vary from at most 2 cm to at most 10 cm. Maximal errors can be as high as 17 cm just below the LED, already for tolerance values of only 5%, and increase up to 40 cm for tolerance values of 20%. An alternative cost metric using normalized Least-Squares minimization makes the errors spatially more homogeneously distributed and reduces them by 35%. For a 3D case, median errors of around 5 cm for a tolerance value of 5% increase to as much as 22 cm for a tolerance value of 20%. As the receiver heights increase, positioning errors decrease significantly.