Theoretical lower bound for indoor visible light positioning using received signal strength measurements and an aperture-based receiver

Indoor visible light positioning (VLP) using signals transmitted by lighting LEDs is a topic attracting increasing interest within the research community. In the recent years, VLP techniques using a range of receiver structures and positioning algorithms have been described. In this paper, we analyze the performance of a VLP system, which uses an aperture-based receiver and measurements of received signal strength. An aperture-based receiver has a number of receiving elements, each consisting of a photodiode and an associated aperture. It has been shown that receivers of this form can be designed which are compact and provide both a wide overall field-of-view and good angular diversity. As a result, they can efficiently extract position-related information from light transmitted by nondirectional LEDs. In our approach, we correlate the signals at the outputs of the photodiodes with a set of reference signals. The resulting observations include information on the received signal strength as well as the angle-of-arrival, and are used to directly estimate the receiver's position. In order to assess the performance of positioning algorithms based on this approach, we derive the Cramer-Rao lower bound on the position estimate. We show that the Cramer-Rao bound depends on the selected reference signal, and that subcentimetre to centimetre accuracy can be obtained, using only a limited number of nondirectional LEDs.