Optimal Optical Omnidirectional Angle-of-Arrival Estimator With Complementary Photodiodes

Angle-of-arrival (AOA) estimator is the core device in visible light positioning (VLP) systems with AOA algorithms. However, existing AOA estimators suffer from high computational complexity, narrow field-of-view (FOV), low accuracy, or high power consumption. In this work, we propose a novel AOA estimator based on an array of tilted complementary photodiodes (CPDs), where the estimator's FOV can be $2\pi$ rad, and the AOA estimation only requires the solution of a linear equation set. The orientations of the CPDs in the AOA estimator are optimized with respect to the average error power, resulting in closed-form optimal orientation expressions for an arbitrary number of CPDs. We also derive closed-form expressions for the probability density function and the cumulative distribution function (CDF) of the AOA estimation error. On the basis of CDF expression, we derive closed-form asymptotic bounds for the positioning outage probability of a fundamental VLP system. Analytical, simulation, and experimental results verify that the optimal AOA estimator can minimize the estimation error, and it can be employed in AOA positioning systems perusing high accuracy, low complexity, large FOV, low cost, low power consumption, and high response speed.