Human motion estimation on Lie groups using IMU measurements

TLDR: The proposed Lie Group Extended Kalman Filter (LG-EKF), thus explicitly accounting for the non-Euclidean geometry of the state space, is derived and is compared to the EKF based on Euler angle parametrization.

Abstract: This paper proposes a new algorithm for human motion estimation using inertial measurement unit (IMU) measurements. We model the joints by matrix Lie groups, namely the special orthogonal groups SO(2) and SO(3), representing rotations in 2D and 3D space, respectively. The state space is defined by the Cartesian product of the rotation groups and their velocities and accelerations, given a kinematic model of the articulated body. In order to estimate the state, we propose the Lie Group Extended Kalman Filter (LG-EKF), thus explicitly accounting for the non-Euclidean geometry of the state space, and we derive the LG-EKF recursion for articulated motion estimation based on IMU measurements. The performance of the proposed algorithm is compared to the EKF based on Euler angle parametrization in both simulation and real-world experiments. The results show that for motion near gimbal lock regions, which is common for shoulder movement, the proposed filter is a significant improvement over the Euler angles EKF.