Fast Polarized Skylight Heading Detection Utilizing the Additivity of Zenith Circular Polarization Patterns

Skylight polarization is a significant physical characteristic of Earth's atmosphere. Inspired by the biological use of polarized skylight for navigation, polarization heading provides a reliable solution for autonomous navigation in environments where satellite navigation is denied. However, due to high computational complexity, polarization heading still faces challenges in dynamic experiments. This paper presents a fast and polarized heading detection algorithm that utilizes solely the additive property of polarization angles, ensuring its effectiveness and speed under clear, open sky conditions. Firstly, the additive criterion of the zenith is presented and theoretically proven. The mean value of the polarization angles at measurement points within a circular area centered at the zenith equals the solar azimuth angle. This criterion facilitates fast polarization heading. Subsequently, a method for analyzing the complexity of polarized heading is proposed, applicable to current polarization heading algorithms. The analysis indicates that the complexity of the existing polarized heading algorithms has been reduced from O(n2) and O(n3) to O(n). Finally, the heading of the carrier is determined by selecting the region that satisfies the additivity criterion based on the attitude angles. The experiment was conducted under open-sky conditions using a self-developed prototype of a polarized skylight compass, including simulation, static rotation experiments, and dynamic experiments. The experimental results demonstrate that, compared to classical algorithms, the proposed algorithm in this paper can reduce the time cost by up to 95%. Particularly in dynamic experiments, the algorithm processes each frame in less than 0.02 second without compromising heading accuracy, further enhancing its potential for application on a quadrirotor drone.