Visible Light Positioning for 2D/3D Indoor Environments Using Extreme Learning Algorithms

This paper tackles indoor receiver localization as a regression task using visible light positioning (VLP). This technology has gained prominence as an alternative to conventional indoor positioning. Traditional systems such as WiFi and ZigBee face notable drawbacks: electromagnetic interference, added infrastructure, limited accuracy, and high deployment costs. In general, classical positioning approaches-lateration, triangulation, proximity, and least squares-typically infer location from measurements like received signal strength (RSS), time of arrival (TOA), time difference of arrival (TDOA), or angle of arrival (AOA). However, in real-world VLP scenarios, these methods face difficulties since they depend on ideal signals, which means unaffected by physical obstacles and perfectly aligned between transmitters and receiver. Our work proposes the application of the extreme learning machine (ELM) algorithm, its regularized version (R-ELM) and the Levenberg-Marquardt algorithm (LMA), to predict the receiver s position based simply on the light signals emitted by light-emitting diodes (LEDs) and captured by a photodiode (PD). To evaluate the overall performance of these models, two experimental datasets were used: one in a 2D environment with 7344 RSS samples and another novel in a 3D environment with 27000 training records and 18000 testing samples by analyzing power spectral densities. To assess performance and analyze parameter optimization of ELM, R-ELM, and LMA, metrics such as root mean square error (RMSE), correlation coefficient (R), training and testing times were used. By considering the state of the art, the LMA model proved to be the most accurate in the 2D environment (RMSE less than 10 cm), although its training time was excessive (over one hour), incompatible with for real-time applications (time variant channels). In contrast, the R-ELM achieved an accuracy of RMSE = 12.4806 cm and completed its training in 31.2 ms (real-time learning), positioning it as a much more efficient alternative compared to LMA. For the 3D dataset, the R-ELM also showed the best overall performance, with an average RMSE close to 22.4784 cm and a training time of 1.0250 s. Incorporating both the dominant frequency and power as inputs into the ELM enhanced the model s accuracy compared to using each input separately. Lastly,