Baseline determination for the European Space Agency Swarm magnetic field mission is investigated. Swarm consists of three identical satellites -A, -B and -C. The Swarm-A and -C form a pendulum formation whose baseline length varies between about 30 and 180 km. Swarm-B flies in a higher orbit, causing its orbital plane to slowly rotate with respect to those of Swarm-A and -C. This special geometry results in short periods when the Swarm-B satellite is adjacent to the other Swarm satellites. Ten 24-hr periods around such close encounters have been selected, with baseline lengths varying between 50 and 3500 km. All Swarm satellites carry high-quality, dual-frequency and identical Global Positioning System receivers not only allowing precise orbit determination of the single Swarm satellites, but also allowing a rigorous assessment of the capability of precise baseline determination between the three satellites. These baselines include the high-dynamic baselines between Swarm-B and the other two Swarm satellites. For all orbit determinations, use was made of an Iterative Extended Kalman Filter approach, which could run in single-, dual-, and triple-satellite mode. Results showed that resolving the issue of half-cycle carrier phase ambiguities (present in original release of GPS RINEX data) and reducing the code observation noise by the German Space Operations Center converter improved the consistency of reduced-dynamic and kinematic baseline solutions for both the Swarm-A/C pendulum pair and other combinations of Swarm satellites. All modes led to comparable consistencies between the computed orbit solutions and satellite laser ranging observations at a level of 2 cm. In addition, the consistencies with single-satellite ambiguity fixed orbit solutions by the German Space Operations Center are at comparable levels for all the modes, with reduced-dynamic baseline consistency at a level of 1-3 mm for the pendulum Swarm-A/C formation and 3-5 mm for the high-dynamic Swarm-B/A and -B/C satellite pairs in different directions.

The European Space Agency (ESA) Swarm mission is a satellite constellation launched on 22 November 2013 aiming at observing the Earth geomagnetic field and its temporal variations. The three identical satellites are equipped with high-precision dual-frequency Global Positioning System (GPS) receivers, which make the constellation an ideal test bed for baseline determination. From October 2014 to August 2016, a number of GPS receiver modifications and a new GPS Receiver Independent Exchange Format (RINEX) converter were implemented. Moreover, the on-board GPS receiver performance has been influenced by the ionospheric scintillations. The impact of these factors is assessed for baseline determination of the pendulum formation flying Swarm-A and -C satellites. In total 30 months of data - from 15 July 2014 to the end of 2016 - is analyzed. The assessment includes analysis of observation residuals, success rate of GPS carrier phase ambiguity fixing, a consistency check between the so-called kinematic and reduced-dynamic baseline solution, and validations of orbits by comparing with Satellite Laser Ranging (SLR) observations. External baseline solutions from The German Space Operations Center (GSOC) and Astronomisches Institut - Universität Bern (AIUB) are also included in the comparison. Results indicate that the GPS receiver modifications and RINEX converter changes are effective to improve the baseline determination. This research eventually shows a consistency level of 9.3/4.9/3.0 mm between kinematic and reduced-dynamic baselines in the radial/along-track/cross-track directions. On average 98.3% of the epochs have kinematic solutions. Consistency between TU Delft and external reduced-dynamic baseline solutions is at a level of 1 mm level in all directions.

Precision Orbit Determination (POD) is a prerequisite for the success of many Low Earth Orbiting (LEO) satellite missions. With high-quality, dual-frequency Global Positioning System (GPS) receivers, typically precisions of the order of a few cm are possible for single-satellite POD, and of a few mm for relative POD of formation flying spacecraft with baselines up to hundreds of km. To achieve the best precision, the use of Phase Center Variation (PCV) maps is indispensable. For LEO GPS receivers, often a-priori PCV maps are obtained by a pre-launch ground campaign, which is not able to represent the real space-borne environment of satellites. Therefore, in-flight calibration of the GPS antenna is more widely conducted. This paper shows that a further improvement is possible by including the so-called Code Residual Variation (CRV) maps in absolute/undifferenced and relative/Double-differenced (DD) POD schemes. Orbit solutions are produced for the GRACE satellite formation for a four months test period (August-November, 2014), demonstrating enhanced orbit precision after first using the in-flight PCV maps and a further improvement after including the CRV maps. The application of antenna maps leads to a better consistency with independent Satellite Laser Ranging (SLR) and K-band Ranging (KBR) low-low Satellite-to-Satellite Tracking (ll-SST) observations. The inclusion of the CRV maps results also in a much better consistency between reduced-dynamic and kinematic orbit solutions for especially the cross-track direction. The improvements are largest for GRACE-B, where a cross-talk between the GPS main antenna and the occultation antenna yields higher systematic observation residuals. For high-precision relative POD which necessitates DD carrier-phase ambiguity fixing, in principle frequency-dependent PCV maps would be required. To this aim, use is made of an Extended Kalman Filter (EKF) that is capable of optimizing relative spacecraft dynamics and iteratively fixing the DD carrier-phase ambiguities. It is found that PCV maps significantly improve the baseline solution. CRV maps slightly enhance the baseline precision, more significantly they lead to a much better initialization of the ambiguity fixing. The GRACE single-satellite orbit solutions compare to within a few cm 3-dimensionally with state-of-the-art external orbit solutions and SLR observations, whereas for the baseline a consistency of better than 0.7 mm with KBR observations is achieved.