  This paper presents an optimal calibration scheme and a weighted least
squares (LS) localization algorithm for received signal strength (RSS) based
visible light positioning (VLP) systems, focusing on the often overlooked
impact of light emitting diode (LED) tilt. By optimally calibrating LED tilt
and gain, we significantly enhance VLP localization accuracy. Our algorithm
outperforms both machine learning Gaussian processes (GPs) and traditional
multilateration techniques. Against GPs, it achieves improvements of 58% and
74% in the 50th and 99th percentiles, respectively. When compared to
multilateration, it reduces the 50th percentile error from 7.4 cm to 3.2 cm and
the 99th percentile error from 25.7 cm to 11 cm. We introduce a low-complexity
estimator for tilt and gain that meets the Cramer-Rao lower bound (CRLB) for
the mean squared error (MSE), emphasizing its precision and efficiency.
Further, we elaborate on optimal calibration measurement placement and refine
the observation model to include residual calibration errors, thereby improving
localization performance. The weighted LS algorithm's effectiveness is
validated through simulations and real-world data, consistently outperforming
GPs and multilateration, across various training set sizes and reducing outlier
errors. Our findings underscore the critical role of LED tilt calibration in
advancing VLP system accuracy and contribute to a more precise model for indoor
positioning technologies.
