  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.
