Pose Estimation for Visible Light Systems Using a Quadrature Angular Diversity Aperture Receiver

Abstract

The quadrature angular diversity aperture (QADA) receiver, consisting of a quadrant photodiode (QPD) and an aperture placed above the QPD, has been investigated for pose estimation for visible light systems. Current work on pose estimation for the QADA receiver uses classical camera sensor algorithms well known in computer vision. To this end, however, the light spot center first has to be obtained based on the RSS. However, this is less straightforward than for camera sensors, as in contrast to such sensors where the relationships are linear, the RSS output from the QADA is a non-linear function of the light spot position. When applying closed form solutions or iterative methods for cameras on a QADA, the non-linearity will degrade their performance. Furthermore, since in practice the aperture is not always perfectly aligned with the QPD, a procedure to calibrate the receiver is needed. Current work on calibration requires additional sophisticated equipment to measure the pose during calibration, which increases the difficulty of implementation. In this paper, we target the above problems for pose estimation and calibration of the QADA receiver. To this end, we first study the effect of the strategy of differencing and normalization on the probability density function (PDF), a commonly applied strategy for the QPD's robustness against RSS variation, and it is shown that the applied strategy results in a complex PDF, which makes an effective and efficient estimation hard to achieve. Therefore, we derive an approximated PDF in a simple closed-form, based on which the calibration and the pose estimation algorithms using the least squares principle are proposed. The proposed calibration does not require any information about the pose of the receiver and is robust to variation of the received power and imperfect knowledge of the radiation pattern of the LED, making it easy to implement. We also derive the corresponding Cramer-Rao lower bound on the misalignment to benchmark the performance of the misalignment and to serve as an indicator to determine the required signal-to-noise ratio (SNR) or number of LEDs to obtain a desired accuracy. The calibration and pose estimation are evaluated by means of a Monte Carlo simulation. Computer simulations show that this theoretical bound is close to the RMSE of the proposed estimator and that the proposed pose estimator outperforms the PnP algorithm.