The treatment of attitude errors in satellite geomagnetic data

Vector magnetic field measurements from magnetic field satellites are contaminated by errors from multiple sources. Previously, the effect of these errors has been treated as isotropic, in other words as affecting the components of the vector field independently. This is incorrect. Here we develop a more complete formalism for dealing with attitude uncertainty, the main source of non-isotropic data errors, both for the case where the orientation is equally well known in all directions, and also for when the attitude determination is itself anisotropic. We demonstrate that the new method can be implemented at essentially no computational cost, and produces a small improvement in field models for Magsat-like data. Preliminary estimates of the error budget for the Orsted satellite indicate that in this case correct treatment of attitude errors could be extremely important, particularly in studies of short-wavelength lithospheric fields, and of field-aligned currents.