Power-Efficient Positioning for Visible Light Systems via Chance Constrained Optimization

The problem of minimizing total power consumption in light-emitting diode transmitters is investigated for achieving power efficient localization in a visible light communication and positioning system. A robust power allocation approach based on stochastic uncertainties is proposed for total power minimization in the presence of localization accuracy, power, and illumination constraints. Specifically, the power consumption minimization problem is formulated under a chance constraint on the probability of Cramér-Rao lower bound exceeding a tolerable limit, which is a computationally intractable constraint. The sphere bounding method is used to propose a safe convex approximation to this intractable constraint, which makes the resulting problem suitable for standard convex optimization tools. Numerical results demonstrate the advantages of the proposed robust solution over the nonrobust solution and uniform power allocation in the presence of stochastic uncertainty.