Accurate Analytical Accelerometer-Magnetometer Axes Alignment Guaranteeing Exact Orthogonality

A complete analytical solution to the problem of aligning the sensitivity axes (coordinate frames) of a three-axis accelerometer and a three-axis magnetometer, fixed on the same rigid platform, is introduced. It exploits the magnetic inclination phenomenon to analytically derive the axes alignment rotation matrix and the inclination angle. Starting from a popular formulation of the problem as a constrained optimization one, it introduces a transformation and a parameterization, converting it to an unconstrained one within the special orthogonal group. In contrast to existing methods using the same principle, it guarantees the orthogonality of the axes-alignment rotation matrix and achieves best-of-class accuracy at the same time. It is two orders of magnitude faster than the gradient descent and Newton-Raphson-based methods and about three times faster than state-of-the-art semianalytical approaches achieving the same accuracy. Multiple sets of the sensor data are used to demonstrate the method's accuracy and computational efficiency.