This letter considers a common calibration problem in robotics: determining the orientation of a three-axis gyro relative to a three-axis magnetometer. This letter first forms the calibration problem as

$R_i X m_i = R_j X m_j$

and then presents two methods to solve the equation on

$SO(3)$

. The first method is to solve for

$X$

directly by regarding the equation as a homogeneous linear equation with respect to

$X$

and subsequently enforce the solution onto

$SO(3)$

. The second approach, utilizing geometrical properties of

$SO(3)$

, transforms the equation into an equivalent linear equation in the form of

$Ax = b$

and invokes a recursive least-squares algorithm to solve. The proposed calibration algorithms succeed in their computational and memory efficiency and suitability for the real-time implementation on embedded systems. Both simulation and experiments on large-scale bulky unmanned aerial vehicles (UAVs) are provided to show that the proposed formulation along with the two solvers can successfully calibrate large misalignments under small and casual movements of the UAV.

Jianyu Song

Real-Time Calibration of Gyro-Magnetometer Misalignment