Explicit Solution for Magnetometer Calibration

A definitive solution is provided in this paper for solving the magnetometer calibration problem by means of ellipsoid fitting. This is achieved by providing an explicit solution for the ensuing constrained least squares problem, which requires a careful exploitation of the design matrices and a detailed analysis of symbolically calculated eigenvalues and eigenvectors. The end result is a direct solution for the magnetometer calibration problem without any recursive loop whatsoever. This is the most favorable solution one can expect for the magnetometer calibration problem, since now the computation time is exclusively determined by the number of data points. Hence, this solution is numerically reliable, fast, and particularly relevant for sliding window adaptive calibration. Simulation results show that the proposed solution is more accurate and faster than the best one available so far.