  In this manuscript, distance and position estimation problems are
investigated for visible light positioning (VLP) systems with red-green-blue
(RGB) light emitting diodes (LEDs). The accuracy limits on distance and
position estimation are calculated in terms of the Cramer-Rao lower bound
(CRLB) for three different scenarios. Scenario~1 and Scenario~2 correspond to
synchronous and asynchronous systems, respectively, with known channel
attenuation formulas at the receiver. In Scenario~3, a synchronous system is
considered but channel attenuation formulas are not known at the receiver. The
derived CRLB expressions reveal the relations among distance/position
estimation accuracies in the considered scenarios and lead to intuitive
explanations for the benefits of using RGB LEDs. In addition, maximum
likelihood (ML) estimators are derived in all scenarios, and it is shown that
they can achieve close performance to the CRLBs in some cases for sufficiently
high source optical powers.
