Gravity fields derived from GPS tracking of the three Swarm satellites have shown artifacts near the geomagnetic equator, where the carrier phase tracking on the L2 frequency is unable to follow rapid ionospheric path delay changes due to a limited tracking loop bandwidth of only 0.25 Hz in the early years of the mission. Based on the knowledge of the loop filter design, an analytical approach is developed to recover the original L2 signal from the observed carrier phase through inversion of the loop transfer function. Precise orbit determination and gravity field solutions are used to assess the quality of the correction. We show that the a posteriori RMS of the ionosphere-free GPS phase observations for a reduced-dynamic orbit determination can be reduced from 3 to 2 mm while keeping up to 7% more data in the outlier screening compared to uncorrected observations. We also show that artifacts in the kinematic orbit and gravity field solution near the geomagnetic equator can be substantially reduced. The analytical correction is able to mitigate the equatorial artifacts. However, the analytical correction is not as successful compared to the down-weighting of problematic GPS data used in earlier studies. In contrast to the weighting approaches, up to 9–10% more kinematic positions can be retained for the heavily disturbed month March 2015 and also stronger signals for gravity field estimation in the equatorial regions are obtained, as can be seen in the reduced error degree variances of the gravity field estimation. The presented approach may also be applied to other low earth orbit missions, provided that the GPS receivers offer a sufficiently high data rate compared to the tracking loop bandwidth, and provided that the basic loop-filter parameters are known.@en

As part of the “GPS Attitude, Positioning, and Profiling experiment (GAP)” of the Canadian CASSIOPE science and technology mission, a set of four geodetic GPS receivers connected to independent antennas on the top-panel of the spacecraft can be operated concurrently to collect dual-frequency code and phase measurements on both the L1 and L2 frequencies. The qualification of the commercial off-the-shelf (COTS) GPS receivers is discussed, and flight results of precise orbit and attitude determination are presented. Pseudorange and carrier phase errors amount to roughly 65 cm and 8 mm for the ionosphere-free dual-frequency combination, which compares favorably with other missions using fully qualified space GPS receivers and is mainly limited by choice of simple patch antennas without choke rings. Precise orbit determination of CASSIOPE using GPS observations can achieve decimeter-level accuracy during continued operations but suffers from onboard and mission restrictions that limit the typical data availability to less than 50% of each day and induce regular long-duration gaps of 4–10 h. Based on overlap analyses, daily peak orbit determination errors can, however, be confined to 1 m 3D on 84% of all days, which fulfills the mission needs for science data processing of other instruments. The attitude of CASSIOPE can be determined with a representative precision of about 0.2° in the individual axes using three GAP receivers and antennas. Availability of dual-frequency measurements is particularly beneficial and enables single-epoch ambiguity fixing in about 97% of all epochs. Overall, the GAP experiment demonstrates the feasibility of using COTS-based global navigation satellite system receivers in space and the benefits they can bring for small-scale science missions.@en

After the detection of many anomalies in the Swarm accelerometer data, an alternative method has been developed to determine thermospheric densities for the three-satellite mission. Using a precise orbit determination approach, non-gravitational and aerodynamic-only accelerations are estimated from the high-quality Swarm GPS data. The GPS-derived non-gravitational accelerations serve as a baseline for the correction of the Swarm-C along-track accelerometer data. The aerodynamic accelerations are converted directly into thermospheric densities for all Swarm satellites, albeit at a much lower temporal resolution than the accelerometers would have been able to deliver. The resulting density and acceleration data sets are part of the European Space Agency Level 2 Swarm products. To improve the Swarm densities, two modifications have recently been added to our original processing scheme. They consist of a more refined handling of radiation pressure accelerations and the use of a high-fidelity satellite geometry and improved aerodynamic model. These modifications lead to a better agreement between estimated Swarm densities and NRLMSISE-00 model densities. The GPS-derived Swarm densities show variations due to solar and geomagnetic activity, as well as seasonal, latitudinal and diurnal variations. For low solar activity, however, the aerodynamic signal experienced by the Swarm satellites is very small, and therefore it is more difficult to accurately resolve latitudinal density variability using GPS data, especially for the higher-flying Swarm-B satellite. Therefore, mean orbit densities are also included in the Swarm density product.@en

Precise science orbits for the first 4 years of the Swarm mission have been generated from onboard GPS measurements in a systematic reprocessing using refined models and processing techniques. Key enhancements relate to the introduction of macro-models for a more elaborate non-gravitational force modeling (solar radiation pressure, atmospheric drag and lift, earth albedo), as well as carrier phase ambiguity fixing. Validation using satellite laser ranging demonstrates a 30% improvement in the precision of the reduced dynamic orbits with resulting errors at the 0.5–1 cm level (1D RMS). A notable performance improvement is likewise achieved for the kinematic orbits, which benefit most from the ambiguity fixing and show a 50% error reduction in terms of SLR residuals while differences with respect to reduced dynamic ephemerides amount to only 1.7 cm (median of daily 3D RMS). Compared to the past kinematic science orbits based on float-ambiguity estimates, the new kinematic position solutions exhibit a factor of reduction of two to three in Allan deviation at time scales of 1000s and higher, and promise an improved recovery of low-degree and -order gravity field coefficients in Swarm gravity field analyses.@en