Micromagnetometer calibration for accurate orientation estimation

Micromagnetometers, together with inertial sensors, are widely used for attitude estimation for a wide variety of applications. However, appropriate sensor calibration, which is essential to the accuracy of attitude reconstruction, must be performed in advance. Thus far, many different magnetometer calibration methods have been proposed to compensate for errors such as scale, offset, and nonorthogonality. They have also been used for obviate magnetic errors due to soft and hard iron. However, in order to combine the magnetometer with inertial sensor for attitude reconstruction, alignment difference between the magnetometer and the axes of the inertial sensor must be determined as well. This paper proposes a practical means of sensor error correction by simultaneous consideration of sensor errors, magnetic errors, and alignment difference. We take the summation of the offset and hard iron error as the combined bias and then amalgamate the alignment difference and all the other errors as a transformation matrix. A two-step approach is presented to determine the combined bias and transformation matrix separately. In the first step, the combined bias is determined by finding an optimal ellipsoid that can best fit the sensor readings. In the second step, the intrinsic relationships of the raw sensor readings are explored to estimate the transformation matrix as a homogeneous linear least-squares problem. Singular value decomposition is then applied to estimate both the transformation matrix and magnetic vector. The proposed method is then applied to calibrate our sensor node. Although there is no ground truth for the combined bias and transformation matrix for our node, the consistency of calibration results among different trials and less than 3° root mean square error for orientation estimation have been achieved, which illustrates the effectiveness of the proposed sensor calibration method for practical applications.