Performance comparison and analysis on different optimization models for high-precision three-dimensional visible light positioning

With the development of visible light communication, indoor visible light positioning (VLP) becomes popular for researchers in the communication industry. However, most existing VLP algorithms only provide solutions for positioning on a two-dimensional plane, and those focusing on three-dimensional (3-D) positioning usually contain various sensors or hybrid algorithms. To solve these problems, first we transform the 3-D location model in VLP into an optimization model and adopt distance based optimization model (DBOM) for positioning based on the measured distances from the positioning terminal to multiple LEDs base stations. Second, we further come up with an area-based optimization model (ABOM) for localization by the intersection of three circles based on the received signal strength trilateration algorithm. The proposed ABOM converts the 3-D optimization problem into a one-dimensional searching problem, thereby ensuring the real-time positioning performance. Third, an effective 3-D optimization algorithm is adopted to judge the positioning performances of two proposed models. Last but not least, we also set up an extended simulation, analyzing the nonlinearity of the Lambert model and the positioning unit size’s effect on the maximum positioning height, which has never been considered by existing works. Our simulation shows that the average positioning error is 0.96 cm for ABOM and 3.21 cm for DBOM. Besides, the experimental results of the actual scene also confirm that the mentioned system can achieve an average 3-D positioning error of 4.34 cm.