Magnitude of the Distance Estimation Bias in Received Signal Strength Visible Light Positioning

In several works, statistical precision of distance estimators in visible light positioning was studied by evaluating the Cramér-Rao lower bound, assuming that the estimator is unbiased. Here, it is demonstrated that the maximum likelihood estimator of the distance is not unbiased. Consequently, the inverse of the Fisher information value is no longer a strict lower bound. We evaluate this bias for several illumination levels and it is found that the impact is very small. For many practical situations, the inverse of the Fisher information can serve as the approximation for the mean-squared error of the maximum likelihood estimator of the distance.