Effectiveness of Variable-Gain Kalman Filter Based on Angle Error Calculated from Acceleration Signals in Lower Limb Angle Measurement with Inertial Sensors

The wearable sensor system developed by our group, which measured lower limb angles using Kalman-filtering-based method, was suggested to be useful in evaluation of gait function for rehabilitation support. However, it was expected to reduce variations of measurement errors. In this paper, a variable-Kalman-gain method based on angle error that was calculated from acceleration signals was proposed to improve measurement accuracy. The proposed method was tested comparing to fixed-gain Kalman filter and a variable-Kalman-gain method that was based on acceleration magnitude used in previous studies. First, in angle measurement in treadmill walking, the proposed method measured lower limb angles with the highest measurement accuracy and improved significantly foot inclination angle measurement, while it improved slightly shank and thigh inclination angles. The variable-gain method based on acceleration magnitude was not effective for our Kalman filter system. Then, in angle measurement of a rigid body model, it was shown that the proposed method had measurement accuracy similar to or higher than results seen in other studies that used markers of camera-based motion measurement system fixing on a rigid plate together with a sensor or on the sensor directly. The proposed method was found to be effective in angle measurement with inertial sensors. 1. Introduction Wearable inertial sensors have been used in many studies to estimate human kinetic data. Those sensors have advantages of low cost, small size, and practical usefulness compared to traditional lab tools such as optical motion measurement system or electric goniometers. As has been reported in previous studies, segment and joint angles [1–11], stride length [1, 3, 5], walking speed [1, 5], gait event timing [5, 12, 13], and so on can be estimated using inertial sensors. Therefore, a wearable inertial sensor system can be effective for objective and quantitative evaluation in rehabilitation of motor function. That is, inertial sensors are considered to be suitable for clinical applications. In our previous studies, a method of measuring lower limb angles using wireless inertial sensors was developed to realize simplified wearable gait evaluation system for rehabilitation support. The method was tested in measurement of gait of healthy subjects [14, 15]. Although the method was shown to have practical accuracy, measurement errors varied depending on movement speeds or subjects. In the angle measurement method of our previous studies, Kalman filter was applied using angle calculated from acceleration