Astronomical Institute

LEO- and Gravity Field Determination

SWARM-Mission: Orbit Determination and Derived Gravity Field

ESA’s Earth Explorer Mission Swarm consists of three identical satellites (launched on 22 November 2013) orbiting the Earth in nearly polar orbits at (initial) altitudes of about 460 km (Swarm-A and Swarm-C) and 530 km (Swarm-B), respectively. The main mission objective is to measure the magnetic field produced by the Earth’s core, mantle, crust, oceans, ionosphere and magnetosphere. However, it may also serve as a gravity field mission. Equipped with GPS receivers, accelerometers, star-tracker assemblies and laser retro-reflectors, the three Swarm satellites are potentially capable to be used as a high-low satellite-to-satellite tracking (hl-SST) observing system, following the missions CHAMP (first single-satellite hl-SST mission), GRACE (twin-satellite mission with additional ultra-precise low-low SST) and GOCE (single-satellite mission additionally equipped with a gradiometer). GRACE, dedicated to measure the time-variability of the gravity field, is the only mission still in orbit, but its lifetime might end before launch of its follow-on mission GRACE-FO in August 2017, primarily due to aging of the onboard batteries after meanwhile more than 14 years of operation. In such a case, Swarm is a suitable candidate to provide time-variable gravity field solutions and to fill the gap between GRACE and GRACE-FO.

In the framework of calibration and validation effort, the Astronomical Institute of the University of Bern (AIUB) computes precise orbits for all three Swarm satellites based on GPS data, using the Bernese GNSS Software in its latest development status (Dach et al., 2007). Two types of orbits are determined. The first type is a reduced-dynamic orbit, parametrized by the six Keplerian elements, as well as empirical accelerations - in radial, along-track and cross-track direction - to absorb non-gravitational accelerations like air drag and solar radiation pressure. The second orbit type is a kinematic orbit. This is a purely geometric orbit consisting of kinematic positions at every observation epoch. Both orbits are estimated from undifferenced ionosphere-free GPS observations, using empirical phase center variation maps for the Swarm satellites. For the GPS satellites, the CODE final orbits and 5s clocks are introduced (Bock et al., 2009). The onboard laser retro-reflectors allow for an independent validation of the computed orbits by means of satellite laser ranging (SLR) observations. Figure 1 shows the SLR residuals (difference between range observed at SLR station and range computed from orbit) for the three Swarm satellites over the entire year 2014. The Figure shows that the computed orbits agree with the SLR observations within a few centimeters.

SLR residuals for reduced-dynamic orbits of the three Swarm satellites for year 2014.

The GPS-derived positions of the kinematic Swarm orbits are subsequently used as pseudo-observations for a gravity field recovery using the Celestial Mechanics Approach (CMA, Beutler et al., 2010), in which orbit and gravity field parameters are estimated simultaneously. Orbit parameters comprise initial states at the beginning of each 24-hour arc, constant empirical accelerations over each arc, and piecewise constant empirical accelerations with 15 minutes step size. The gravity field is parametrized by setting up spherical harmonic coefficients up to degree and order 60. Long-term mean as well as monthly gravity field solutions can be generated from all three Swarm satellites individually, and these individual solutions can then be combined on normal equation level to obtain the potentially best solutions based on data from Swarm-A, -B and -C. Figure 2 shows difference degree amplitudes w.r.t. the used background gravity field model EGM2008 and degree amplitudes of the formal errors for a combined Swarm solution over 2 months compared to a corresponding GRACE solution which is also based on hl-SST observations only. It can be seen that up to degree and order 18, Swarm and GRACE solutions are of similar quality. Thus, it is promising to also study large-scale time variations of the Earth’s gravity field from Swarm as soon as longer time series can be processed.

Difference degree amplitudes w.r.t. EGM2008 and formal errors of a combined Swarm-A, -B, -C and a combined GRACE-A, -B solution, both based on two months (12/2013 – 01/2014)


Beutler, G., Jäggi, A., Mervart, L., Meyer, U. (2010). The celestial mechanics approach: theoretical foundations. Journal of Geodesy, 84(10), 605-624.

Bock, H., Dach, R., Jäggi, A., Beutler, G. (2009). High-rate GPS clock corrections from CODE: Support of 1 Hz applications. Journal of Geodesy, 83(11), 1083-1094.

Dach, R., Hugentobler, U., Fridez, P., Meindl, M. (2007). Bernese GPS Software 5.0, Astronomical Institute, University of Bern.