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.

翻译：在技术突破的推动下，室内跟踪与定位在物联网、机器人学和无人机等多种应用中日益重要。为应对室内跟踪中的若干挑战，本研究探索了利用旋转矩阵的SO(3)流形结构所带来的潜在优势，旨在提升扩展卡尔曼滤波器和无迹卡尔曼滤波器在室内环境中对运动目标的三维跟踪性能。实验结果表明，所提出的黎曼扩展卡尔曼滤波算法与黎曼无迹卡尔曼滤波算法在位置和姿态精度方面持续优于传统EKF与UKF。在长楼梯路径测试中，传统EKF与UKF的均方根误差分别为0.36米和0.43米，而所提EKFRie与UKFRie算法分别实现了更低的0.21米和0.10米均方根误差。此外，与采用等腰三角形流形的EKF和UKF算法相比，本文算法同样表现更优：后两者的均方根误差分别为7.26厘米和7.27厘米，而本文算法分别达到6.73厘米和6.16厘米的均方根误差。这些结果充分证明了所提算法的性能提升。