Improved Lower Bounds for Ranging in Synchronous Visible Light Positioning Systems

In this study, the Ziv-Zakai bound (ZZB) is derived for synchronous visible light positioning (VLP) systems. The proposed ZZB extracts ranging information from the prior information, the time delay parameter, and the channel attenuation factor based on the Lambertian pattern. In addition to the ZZB, the Bayesian Cramer-Rao bound (CRB) and the weighted CRB (WCRB) are calculated for synchronous VLP systems. Furthermore, a closed-form expression is obtained for the expectation of the conditional CRB (ECRB). Numerical examples are presented to compare the bounds against each other and against the maximum a posteriori probability (MAP) estimator. It is observed that the ZZB can provide a reasonable lower limit on the performance of MAP estimators. On the other hand, the WCRB and the ECRB converge to the ZZB in regions of low and high source optical powers, respectively; however, they are not tight in other regions.