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This paper describes a new method for human joint angle calculation based on inertial measurement data. By exploiting kinematic constraints based on anatomical knowledge, a method is developed that avoids the assumption that the sensors must be mounted in certain orientations towards the body segments. The joint axis is identified by calculating the inertial measurement units’ (IMUs’) quaternion, and then the joint angle is calculated from segment acceleration and angular velocity data according to the joint axis, respectively. As a tool for sensor fusion, a Kalman filter is used to combine both angles. There are two parameters in the Kalman filter that are always assigned to experiential values. In this paper, a standard subject experiment is designed to optimize the parameter combination in two dimensions by using the ant colony algorithm. The results showed that the root-mean-square error (RMSE) between the estimated rotation angles and the programmed angles was less than 1 degree after the optimal parameters’ values were found by the ant colony algorithm. Introduction Gait analysis is crucial to the application of rehabilitation exercises and sports training etc. Since the 1970s, gait analysis has growing popularity and attracted a lot of attention from the researchers and clinicians. In the 1980s, a video camera system was developed to track the human movements for gait analysis, which has been the primary method for gait analysis for a long time [1] . Typically, this kind of system is expensive and limited to indoor environments, such as laboratories or clinics. With the development of micro-electromechanical systems (MEMS) technology, a series of lightweight, low power, MEMS inertial sensors were developed, which are known as inertial measurement units (IMUs) [2] . These inertial sensors, such as accelerometers, gyroscopes and magnetometers, measure the acceleration, angular velocity and magnetic field vector in their own local coordinate system. By using some appropriate algorithms, the orientation of the sensors can be estimated. One of the main factors in gait analysis is the angle of the lower extremity, such as the knee angle and hip angle etc. Lots of algorithms have been proposed for IMU-based knee angle estimation. There are two major challenges to this estimation. First, converting the coordinate system of the IMUs to the coordinate system of the body segments is problematic. Previous scholars have avoided this problem by assuming that the IMUs can be precisely mounted in an expected orientation towards the joint in some publications [3, 4] . However, unlike robotic devices, the human body lacks even surfaces and right angles, which makes this assumption unrealistic. To solve this problem, many methods have been proposed. The most common approach is to apply a calibration procedure. Some researchers use calibration postures [5-7] . They make the subject stand upright for a few seconds with the segment’s longitudinal axis parallel to the gravitational acceleration vector, which can be measured by an accelerometer. Besides the upstanding calibration procedure, additional sitting calibration posture is also applied in [5-7]. Calibration motions can also be useful in coordinate system conversion [8, 9] . Another method that exploits kinematic constraints is proposed. It identifies the knee joint axis coordinates from arbitrary motion data rather than predefined postures or motions data [10] , but, this method is more complicated and hard to apply to real-time situations. The other major challenge is the inertial sensors’ offset, which results in accumulated drift after integration. The calibration of the IMUs is necessary to minimize the offset. Even a precise

Inertial Sensor-based Knee Angle Estimation for Gait Analysis Using the Ant Colony Algorithm to Find the Optimal Parameters for Kalman Filter