Co-estimation of geomagnetic field and in-orbit fluxgate magnetometer calibration parameters

For the past 20 years, state of the art geomagnetic core field models have relied heavily on magnetic measurements made from space-based instrumentation. These models have revealed rapid global magnetic field variations on sub-decadal timescales originating in Earth's core. With the end of the CHAMP mission in 2010 and the launch of Swarm in late 2013, there has been a 3-year gap in high-quality satellite measurements of the geomagnetic field. Geomagnetic field models have therefore relied on ground observatory data to fill in this gap period. However, ground observatories are unable to provide a truly global picture of the core field and its temporal changes. Many satellites in operation carry vector fluxgate platform magnetometers for attitude control, which can offer an alternative to relying on ground observatory measurements during the gap period. However, these instruments need to be carefully calibrated in order to provide meaningful information on Earth's core field. Some previous studies attempted to calibrate such instruments with a priori geomagnetic field models. This approach has several disadvantages: (1) errors in the model will introduce errors in the calibration parameters, and (2) relying on an a priori model may not be feasible in the post-Swarm era. In this paper, we develop a novel approach to build a time-dependent geomagnetic field model from platform magnetometer data, by co-estimating their calibration parameters with the internal field parameters. This method does not require an a priori geomagnetic field model, but does require a dataset of previously calibrated data. We use CHAMP, Swarm, and ground observatory measurements to supply this dataset, and incorporate platform magnetic measurements from DMSP and Cryosat-2 during the gap years. We find that the calibration parameters of DMSP and Cryosat-2 can be reliably estimated, and these missions provide meaningful information on rapid core field variations during the gap period.