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.

翻译：在本手稿中,对红色绿色蓝色发光二极管的可见光定位系统(VLP)的距离和位置估计问题进行了调查;对三种不同情景的Cramer-Rao较低约束值(CRLB)计算了距离和位置估计的准确性限值;设想1和设想2分别对应同步和不同步系统,接收器的频道衰减公式为人所知;设想3中,考虑同步系统,但接收器不知道频道衰减公式。衍生的CRLB表达式揭示了所考虑的情景中的距离/位置估计孔径之间的关系,并导致对使用RGB LED的好处作出直观解释。此外,所有情景中都得出了最大可能性(ML)估计值,并表明在某些情况下,对于足够高的源光学能力,它们能够接近CRLB。