Error estimate for fluxgate magnetometer in-flight calibration on a spinning spacecraft

Fluxgate magnetometers are widely used for in situ magnetic field measurements in the context of geophysical and solar system studies. Like in most experimental studies, magnetic field measurements using the fluxgate magnetometers are constrained by the associated uncertainties. To evaluate the performance of magnetometers, the measurement uncertainties of calibrated magnetic field data are quantitatively studied for a spinning spacecraft. The uncertainties are derived analytically by perturbing the calibration parameters and are simplified into the first-order expression including the offset errors and the coupling of calibration parameter errors with the ambient magnetic field. The error study shows how the uncertainty sources combine through the calibration process. The final error depends on (1) the magnitude of the magnetic field with respect to the offset error and (2) the angle of the magnetic field to the spacecraft spin axis. The offset uncertainties are the major factor in a low-field environment, while the angle uncertainties (rotation angle in the spin plane, sensor non-orthogonality, and sensor misalignment to the spacecraft reference directions) become more important in a high-field environment in a proportional way to the magnetic field. The error formulas serve as a useful tool in designing high-precision magnetometers in future spacecraft missions as well as in data analysis methods in geophysical and solar system science.