Estimating Lower Body Kinematics using a Lie Group Constrained Extended Kalman Filter and Reduced IMU Count

Goal: This paper presents an algorithm for estimating pelvis, thigh, shank, and foot kinematics during walking using only two or three wearable inertial sensors. Methods: The algorithm makes novel use of a Lie-group-based extended Kalman filter. The algorithm iterates through the prediction (kinematic equation), measurement (pelvis position pseudo-measurements, zero-velocity update, and flat-floor assumption), and constraint update (hinged knee and ankle joints, constant leg lengths). Results: The inertial motion capture algorithm was extensively evaluated on two datasets showing its performance against two standard benchmark approaches in optical motion capture (i.e., plug-in gait (commonly used in gait analysis) and a kinematic fit (commonly used in animation, robotics, and musculoskeleton simulation)), giving insight into the similarity and differences between the said approaches used in different application areas. The overall mean body segment position (relative to mid-pelvis origin) and orientation error magnitude of our algorithm ($n=14$ participants) for free walking was $5.93 \pm 1.33$ cm and $13.43 \pm 1.89^\circ$ when using three IMUs placed on the feet and pelvis, and $6.35 \pm 1.20$ cm and $12.71 \pm 1.60^\circ$ when using only two IMUs placed on the feet. Conclusion: The algorithm was able to track the joint angles in the sagittal plane for straight walking well, but requires improvement for unscripted movements (e.g., turning around, side steps), especially for dynamic movements or when considering clinical applications. Significance: This work has brought us closer to comprehensive remote gait monitoring using IMUs on the shoes. The low computational cost also suggests that it can be used in real-time with gait assistive devices.