Attitude-Independent Magnetometer Calibration Using Nonlinear Least Squares

This article presents a new formulation for attitude-independent calibration of three-axis magnetometers. The proposed solution employs a nonlinear least squares (NLLS) estimator that uses the nonlinear sensor model proposed by Foster and Elkaim in the well-known extended two-step (ETS) algorithm. Our solution has a few advantages over ETS and is more straightforward to implement than many subsequent algorithms. It enables the calculation of the calibration parameters' uncertainties and does not require the assumption that all magnetometer measurements have a constant magnetic field magnitude. The former is essential for evaluating calibration quality, while the latter may be required for on-orbit magnetometer calibration. However, the NLLS has the drawback of requiring an initial parameter estimation to ensure convergence. Therefore, our work presents a new technique to calculate the scale factors and offsets for initializing the NLLS. Simulations and practical implementations demonstrate that our method performs similar to a recently computed analytical solution of the ETS (ETS-A). Furthermore, a Monte Carlo simulation shows that the NLLS algorithm provides a slightly better estimation of the scale factors than the ETS, in addition to the abovementioned advantages.