Indoor Position and Attitude Tracking with SO(3) Manifold

Abstract: 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.