Estimating Lower Limb Kinematics Using a Lie Group Constrained Extended Kalman Filter with a Reduced Wearable IMU Count and Distance Measurements

Tracking the kinematics of human movement usually requires the use of equipment that constrains the user within a room (e.g., optical motion capture systems), or requires the use of a conspicuous body-worn measurement system (e.g., inertial measurement units (IMUs) attached to each body segment). This paper presents a novel Lie group constrained extended Kalman filter to estimate lower limb kinematics using IMU and inter-IMU distance measurements in a reduced sensor count configuration. The algorithm iterates through the prediction (kinematic equations), measurement (pelvis height assumption/inter-IMU distance measurements, zero velocity update for feet/ankles, flat-floor assumption for feet/ankles, and covariance limiter), and constraint update (formulation of hinged knee joints and ball-and-socket hip joints). The knee and hip joint angle root-mean-square errors in the sagittal plane for straight walking were 7.6 +/- 2.6 degrees and 6.6 +/- 2.7 degrees, respectively, while the correlation coefficients were 0.95 +/- 0.03 and 0.87 +/- 0.16, respectively. Furthermore, experiments using simulated inter-IMU distance measurements show that performance improved substantially for dynamic movements, even at large noise levels (sigma=0.2 m). However, further validation is recommended with actual distance measurement sensors, such as ultra-wideband ranging sensors.