Comparison of angle measurements between integral-based and quaternion-based methods using inertial sensors for gait evaluation

The measurement method of lower limb angles, which were based on the integral of angular velocity with Kalman filter, was validated previously in measurement of angles in a plane with a rigid body model of double pendulum and shown to be practical in measurement of angles in the sagittal plane during gait of healthy subjects. In this paper, in order to realize practical measurements of 3 dimensional (3D) movements with inertial sensors, the previously developed integral-based angle calculation method with variable Kalman gain and a quaternion-based one with fixed gain were tested. First, the quaternion-based method showed higher measurement accuracies for angles in the sagittal and the frontal planes during 3D movements of a rigid body model of lower limb than that of the integral-based one. Second, the integral-based method was shown to be effective in measurement of angles in the sagittal plane of healthy subjects during treadmill walking compared to the quaternion-based one, which suggested effectiveness of the variable Kalman gain method. Third, the integral-based method was shown to cause inappropriate results in some cases of calculation of lower limb angles of hemiplegic subjects during gait, while some of such cases could be measured appropriately with the quaternion-based one. The results of this paper suggested that the quaternion-based method would be more effective with a variable Kalman-gain for measurement of 3D movements. The integralbased method was also suggested to be useful for measurement of angles in the sagittal plane of healthy subjects during gait.