Direct positioning in synchronous and asynchronous visible light systems

In this paper, direct positioning approaches are investigated for both synchronous and asynchronous visible light systems. First, the maximum likelihood estimator (MLE) and the Cramér-Rao lower bound (CRLB) are derived for the synchronous scenario by considering the information from both channel attenuation factors and time delay parameters. Then, asynchronous visible light positioning (VLP) systems are investigated and the corresponding CRLBs and MLEs are obtained based on received signal strength (RSS) information. It is shown that the direct and two-step position estimators are equivalent in the asynchronous scenario under mild conditions. Numerical examples are provided to illustrate the theoretical results.