Two-Step Calibration Methods for Miniature Inertial and Magnetic Sensor Units

Low-cost inertial/magnetic sensor units have been extensively used to determine sensor attitude information for a wide variety of applications, ranging from virtual reality, underwater vehicles, handheld navigation systems, to biomotion analysis and biomedical applications. In order to achieve precise attitude reconstruction, appropriate sensor calibration procedures must be performed in advance to process sensor readings properly. In this paper, we are aiming to calibrate different error parameters, such as sensor sensitivity/scale factor error, offset/bias error, nonorthogonality error, mounting error, and also soft iron and hard iron errors for magnetometers. Instead of estimating all of these parameters individually, these errors are combined together as the combined bias and transformation matrix. Two-step approaches are proposed to determine the combined bias and transformation matrix separately. For the accelerometer and magnetometer, the combined bias is determined by finding an optimal ellipsoid that can best fit the sensor readings, and the transformation matrix is then derived through a two-step iterative algorithm by exploring the intrinsic relationship among sensor readings. For the gyroscope, the combined bias can be easily determined by placing the sensor node stationary. For the transformation matrix estimation, the intrinsic relationship among gyroscope readings is explored again, and an unscented Kalman filter is employed to determine such matrix. The calibration methods are then applied to our sensor nodes, and the good performance of the orientation estimation has illustrated the effectiveness of the proposed sensor calibration methods.