Cramer-rao bound for indoor visible light positioning using an aperture-based angular-diversity receiver

In this paper, we investigate the problem of indoor positioning using visible light systems. The directional detector array we use is comprised of a number of receiving elements, each consisting of an aperture and a photo diode, which are arranged to offer good angular diversity, and can be implemented within a compact receiver structure \cite{ref1}. The receiving elements receive the light from a number of white LEDs, which are typically attached to the ceiling, and which act as anchors. In order to get an indication of the received signal strengths of the different LEDs, we average the received signals over time. The relative signal strengths in the different receiving elements do not only provide information on the distance between the LEDs and the detector array, but also about the angle-of-arrival of the light. By combining the information of the receiving elements, the position of the detector can be estimated. In order to assess the accuracy of positioning algorithms based on this approach, we derive the Cramer-Rao lower bound on the position accuracy. Assuming the white LEDs transmit an optical power of 1 W, and the time averaging is done over 1 millisecond, an accuracy of the order of a centimetre can be achieved