A three-step calibration method for tri-axial field sensors in a 3D magnetic digital compass

In a 3D magnetic compass, it is important to calibrate the tri-axial magnetometers and accelerometers so the compass will provide accurate heading and attitude information. Previous researchers have used two methods to calibrate these two field sensors separately, i.e. the classic independent ellipsoid fitting method and the independent dot product invariant method, respectively. Both methods are easy to use, and no highly accurate, external equipment is required. However, self-calibration with ellipsoid fitting has the disadvantage that it interfuses an orthogonal matrix, and the dot product invariant method requires the use of pre-calibrated internal field sensors, which may be unavailable in many cases. In this paper, we have introduced and unified an error model of two tri-axial field sensors. Accordingly, the orthogonal matrix caused by ellipsoid fitting was mathematically proved to be the combination of two sources, the mounting misalignment and the rotation misalignment. Moreover, a new method, which we call optimal resultant vector, was proposed to further calibrate multi-sensor systems on the basis of ellipsoid fitting and dot product invariant methods, establishing a new, three-step calibration method. The superiority of the proposed method over the state-of-the-art approaches were demonstrated by simulations and a 3D compass experiment. (paper)