Goal: This paper presents an algorithm for accurately estimating pelvis, thigh, and shank kinematics during walking using only three wearable inertial sensors. Methods: The algorithm makes novel use of a constrained Kalman filter (CKF). The algorithm iterates through the prediction (kinematic equation), measurement (pelvis position pseudo-measurements, zero velocity update, flat-floor assumption, and covariance limiter), and constraint update (formulation of hinged knee joints and ball-and-socket hip joints). Results: Evaluation of the algorithm using an optical motion capture-based sensor-to-segment calibration on nine participants ($7$ men and $2$ women, weight $63.0 pm 6.8$ kg, height $1.70 pm 0.06$ m, age $24.6 pm 3.9$ years old), with no known gait or lower body biomechanical abnormalities, who walked within a $4 times 4$ m$^2$ capture area shows that it can track motion relative to the mid-pelvis origin with mean position and orientation (no bias) root-mean-square error (RMSE) of $5.21 pm 1.3$ cm and $16.1 pm 3.2^circ$, respectively. The sagittal knee and hip joint angle RMSEs (no bias) were $10.0 pm 2.9^circ$ and $9.9 pm 3.2^circ$, respectively, while the corresponding correlation coefficient (CC) values were $0.87 pm 0.08$ and $0.74 pm 0.12$. Conclusion: The CKF-based algorithm was able to track the 3D pose of the pelvis, thigh, and shanks using only three inertial sensors worn on the pelvis and shanks. Significance: Due to the Kalman-filter-based algorithms low computation cost and the relative convenience of using only three wearable sensors, gait parameters can be computed in real-time and remotely for long-term gait monitoring. Furthermore, the system can be used to inform real-time gait assistive devices.
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