A New Quaternion-Based Kalman Filter for Human Body Motion Tracking Using the Second Estimator of the Optimal Quaternion Algorithm and the Joint Angle Constraint Method with Inertial and Magnetic Sensors

Human body motion tracking is a key technique in robotics, virtual reality and other human–computer interaction fields. This paper proposes a novel simple-structure Kalman filter to improve the accuracy of human body motion tracking, named the Second EStimator of the Optimal Quaternion Kalman Filter (E2QKF). The new algorithm is the combination of the Second Estimator of the Optimal Quaternion (ESOQ-2) algorithm, the linear Kalman filter and the joint angle constraint method. In the proposed filter, the ESOQ-2 algorithm is used to produce an observation quaternion by preprocessing accelerometer and magnetometer measurements. The compensation for the accelerometer added in the ESOQ-2 algorithm is to eliminate the influence of human body motion acceleration included in the results. The state vector of the filter is the quaternion, which is calculated with gyroscope measurements, and the Kalman filter is to calculate the optimal quaternion by fusing the state quaternion and the observation quaternion. Therefore, the filter becomes a simple first-order linear system model, which avoids the linearization error of measurement equations and reduces the computational complexity. Furthermore, the joint angle constraint is considered in the proposed algorithm, which makes the results more accurate. To verify the accuracy of the proposed algorithm, inertial/magnetic sensors are used to perform the upper limb motion experiment, and the result of E2QKF (without joint angle constraint) is compared with an optical motion capture system and two traditional methods. Test results demonstrate the effectiveness of the proposed filter: the root mean square error (RMSE) of E2QKF is less than 2.0° and the maximum error is less than 4.6°. The result of E2QKF (with joint angle constraint) is compared with E2QKF (without joint angle constraint). Test results demonstrate the superiority of E2QKF (with joint angle constraint): the joint angle constraint method can further improve the accuracy of human body motion tracking.