Efficient Closed-Form Solutions for Visible Light Positioning in Low-Cost IoT Devices

Abstract

Visible light positioning (VLP) has drawn great attention in the field of indoor positioning as light communication has been popularized in low-cost Internet-of-Things (IOT) devices. In this paper, we investigate the VLP problem using the received signal strength (RSS) and by only considering the line-of-slight (LOS) propagation. The RSS-based VLP problem is highly nonlinear, and its solutions may be trapped in local optima without a good initial guess. To circumvent this difficulty, we propose closed-form solutions of the VLP problem considering a known or unknown user orientation. By applying the weighted least squares (WLS) method, the closed-form solutions are divided into two stages. In the stage-one WLS solution, the nonlinear VLP problem is transformed into a pseudo-linear form by introducing some auxiliary variables, which are considered to be independent of each other. The estimates of the stage-one WLS solution are further refined in the stage-two WLS solution by exploiting the constrained relationships among these defined variables. The simulation results show that the stage-two WLS solution provides good estimates for the user position and orientation. The proposed stage-two WLS solution outperforms the existing methods especially at a high signal-to-noise ratio (SNR).