用旋转矩阵的SO(3)流形结构，提升室内定位精度。
Indoor Position and Attitude Tracking with SO(3) Manifold
- 将旋转矩阵的SO(3)流形特性融入卡尔曼滤波，优化姿态估计。
- 在长楼梯路径上，定位误差降至0.21米（原0.36米）。
- 适合需要高精度姿态跟踪的无人机与机器人应用。
受技术突破推动，室内定位在物联网、机器人和无人机等领域日益重要。为应对室内追踪挑战，本文探索将旋转矩阵的SO(3)流形结构纳入算法设计，以提升扩展卡尔曼滤波器（EKF）和无迹卡尔曼滤波器（UKF）在室内环境中对运动目标的三维追踪性能。实验表明，所提出的黎曼扩展卡尔曼滤波器（EKFRie）与黎曼无迹卡尔曼滤波器（UKFRie）在位置与姿态精度上持续优于传统EKF与UKF。在长楼梯路径测试中，传统EKF与UKF的均方根误差（RMSE）分别为0.36米和0.43米，而新方法分别降低至0.21米和0.10米。相较于基于等腰三角形流形的方法（RMSE为7.26厘米和7.27厘米），本方法进一步将误差降至6.73厘米和6.16厘米，验证了其优越性。
原文摘要 · Abstract (English)
Driven by technological breakthroughs, indoor tracking and localization have gained importance in various applications including the Internet of Things (IoT), robotics, and unmanned aerial vehicles (UAVs). To tackle some of the challenges associated with indoor tracking, this study explores the potential benefits of incorporating the SO(3) manifold structure of the rotation matrix. The goal is to enhance the 3D tracking performance of the extended Kalman filter (EKF) and unscented Kalman filter (UKF) of a moving target within an indoor environment. Our results demonstrate that the proposed extended Kalman filter with Riemannian (EKFRie) and unscented Kalman filter with Riemannian (UKFRie) algorithms consistently outperform the conventional EKF and UKF in terms of position and orientation accuracy. While the conventional EKF and UKF achieved root mean square error (RMSE) of 0.36m and 0.43m, respectively, for a long stair path, the proposed EKFRie and UKFRie algorithms achieved a lower RMSE of 0.21m and 0.10m. Our results show also the outperforming of the proposed algorithms over the EKF and UKF algorithms with the Isosceles triangle manifold. While the latter achieved RMSE of 7.26cm and 7.27cm, respectively, our proposed algorithms achieved RMSE of 6.73cm and 6.16cm. These results demonstrate the enhanced performance of the proposed algorithms.
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