Hybrid TDOA/RSS Based Localization for Visible Light Systems

In a visible light positioning (VLP) system, a receiver can estimate its location based on signals transmitted by light emitting diodes (LEDs). In this manuscript, we investigate a quasi-synchronous VLP system, in which the LED transmitters are synchronous among themselves but are not synchronized with the receiver. In quasisynchronous VLP systems, position estimation can be performed by utilizing time difference of arrival (TDOA) information together with channel attenuation information, leading to a hybrid localization system. To specify accuracy limits for quasi-synchronous VLP systems, the Cramér-Rao lower bound (CRLB) on position estimation is derived in a generic three-dimensional scenario. Then, a direct positioning approach is adopted to obtain the maximum likelihood (ML) position estimator based directly on received signals from LED transmitters. In addition, a two-step position estimator is proposed, where TDOA and received signal strength (RSS) estimates are obtained in the first step and the position estimation is performed, based on the TDOA and RSS estimates, in the second step. The performance of the two-step positioning technique is shown to converge to that of direct positioning at high signal-to-noise ratios based on asymptotic properties of ML estimation. Finally, CRLBs and performance of the proposed positioning techniques are investigated through simulations.