A Fuzzy Tuned and Second Estimator of the Optimal Quaternion Complementary Filter for Human Motion Measurement with Inertial and Magnetic Sensors

To accurately measure human motion at high-speed, we proposed a simple structure complementary filter, named the Fuzzy Tuned and Second EStimator of the Optimal Quaternion Complementary Filter (FTECF). The FTECF is applicable to inertial and magnetic sensors, which include tri-axis gyroscopes, tri-axis accelerometers, and tri-axis magnetometers. More specifically, the proposed method incorporates three parts, the input quaternion, the reference quaternion, and the fuzzy logic algorithm. At first, the input quaternion was calculated with gyroscopes. Then, the reference quaternion was calculated by applying the Second EStimator of the Optimal Quaternion (ESOQ-2) algorithm on accelerometers and magnetometers. In addition, we added compensation for accelerometers in the ESOQ-2 algorithm so as to eliminate the effects of limb motion acceleration in high-speed human motion measurements. Finally, the fuzzy logic was utilized to calculate the fusion factor for a complementary filter, so as to adaptively fuse the input quaternion with the reference quaternion. Additionally, the overall algorithm design is more simplified than traditional methods. Confirmed by the experiments, using a commercial inertial and magnetic sensors unit and an optical motion capture system, the efficiency of the proposed method was more improved than two well-known methods. The root mean square error (RMSE) of the FTECF was less than 2.2° and the maximum error was less than 5.4°.