  This paper presents an algorithm that makes novel use of a Lie group
representation of position and orientation alongside a constrained extended
Kalman filter (CEKF) to accurately estimate pelvis, thigh, and shank kinematics
during walking using only three wearable inertial sensors. The algorithm
iterates through the prediction update (kinematic equation), measurement update
(pelvis height, zero velocity update, flat-floor assumption, and covariance
limiter), and constraint update (formulation of hinged knee joints and
ball-and-socket hip joints). The paper also describes a novel Lie group
formulation of the assumptions implemented in the said measurement and
constraint updates. Evaluation of the algorithm on nine healthy subjects who
walked freely within a $4 \times 4$ m$^2$ room shows that the knee and hip
joint angle root-mean-square errors (RMSEs) in the sagittal plane for free
walking were $10.5 \pm 2.8^\circ$ and $9.7 \pm 3.3^\circ$, respectively, while
the correlation coefficients (CCs) were $0.89 \pm 0.06$ and $0.78 \pm 0.09$,
respectively. The evaluation demonstrates a promising application of Lie group
representation to inertial motion capture under reduced-sensor-count
configuration, improving the estimates (i.e., joint angle RMSEs and CCs) for
dynamic motion, and enabling better convergence for our non-linear
biomechanical constraints. To further improve performance, additional
information relating the pelvis and ankle kinematics is needed.
