Precise orbit determination was investigated for a satellite constellation comprised of two different missions, the CHAllenging Minisatellite Payload (CHAMP) satellite and the Gravity Recovery And Climate Experiment (GRACE) twin satellites. The orbital planes of these two missions aligned closely during March to May 2005, allowing precise baseline determinations between the associated three satellites based on their onboard BlackJack Global Positioning System (GPS) receivers. The GRACE-A/B satellites fly in tandem formation with a baseline of around 220 km, whereas the baselines between CHAMP and the GRACE tandem vary from about 110 to 7500 km during 24-h orbital arcs centered around the points of closest approaches. A number of factors had to be dealt with for orbit determinations, including the cross-talk between the CHAMP GPS main navigation and occultation antennas, the different levels of non-gravitational accelerations, and the rapidly changing geometry that complicates the fixing of integer ambiguities for the GPS carrier-phase observations. Quality assessments of the orbit solutions were based on comparisons with Satellite Laser Ranging (SLR) observations, best orbit solutions had a precision of typically 1.7–2.3 cm. Consistency checks between reduced-dynamic and kinematic orbit solutions were done. For the GRACE baselines, the reduced-dynamic/kinematic baseline consistency was typically better than 1 cm, with an ambiguity fixing success rate of around 94%. The agreement with the K/Ka-Band Radar Ranging (KBR) measurements was about 0.6 mm. For the CHAMP/GRACE pairs, the reduced-dynamic/kinematic baseline consistency varied from 0.5 to 2.5 cm, where better consistency was obtained for shorter arcs.@en

Precise absolute and relative orbit determination, referred to as Precise Orbit Determination (POD) and Precise Baseline Determination (PBD), are a prerequisite for the success of many Low Earth Orbit (LEO) satellite missions. With the spaceborne, high-quality, multi-channel, dual-frequency Global Positioning System (GPS) receivers, typically a precision of the order of a few cm is possible for single-satellite POD, and of a few mm for dual-satellite PBD of formation flying spacecraft with baselines up to hundreds of km. The research in this dissertation addresses and expands methods for computing reliable orbits for not only stable satellite formations such as the US/German GRACE (Gravity Recovery And Climate Experiment) and lower pair of the European Space Agency (ESA) Swarm missions, but also for satellite constellations that include rapidly varying baselines, such as all three Swarm satellites or the combination of the German CHAllenging Minisatellite Payload (CHAMP) and GRACE missions. The POD and PBD solutions are based on an Iterative Extended Kalman Filter (IEKF) that is capable of using relative spacecraft dynamics constraints for enhancing the robustness of the solutions. Moreover, the IEKF allows to iteratively fix the Double-Differenced (DD) carrier-phase integer ambiguities by the Least-squares AMBiguity Decorrelation Adjustment (LAMBDA) method. A subset fixing strategy allowing for partial ambiguity resolution was used instead of the full-set fixing which only accepts ambiguities when all integer ambiguities were fixed for certain epochs. The nominal products of the IEKF are reduceddynamic POD and PBD solutions, but also include the possibility to derive kinematic PBD solutions afterwards. The internal consistency of the reduced-dynamic and kinematic solutions is used as a quality measure in addition to comparisons with POD and PBD solutions by other institutes. @en

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.

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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.

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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.

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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 constellation consists of two satellites flying in pendulum formation in low earth polar orbits and one satellite flying separately in a higher polar orbit. The three identical Swarm satellites are equipped with high-precision 8-channel dualfrequency Global Positioning System (GPS) receivers, which make the Swarm constellation a good test bed for baseline determination. High-precision baseline determination between low earth orbiting satellites is relevant for e.g. Interferometric Synthetic Aperture Radar (InSAR) research, proximity operations between spacecraft, and possibly gravity field determination. For Swarm, special attention has to be paid to several aspects regarding the baseline determination. These aspects include the synchronization of the GPS observations collected by the GPS receivers on the different Swarm satellites, the determination of inflight frequency-dependent Phase Center Variation (PCV) and Code Residual Variation (CRV) antenna patterns, and half-cycle carrier-phase ambiguity resolution. In addition, a number of GPS receiver modifications were made in the October 2014 to August 2016 time frame, such as changes in the Fieldof- View (FoV), tracking loop bandwidth, and Receiver Independent Exchange Format (RINEX) converter updates. Moreover, the on-board GPS receiver performance is greatly influenced by the seasonal ionospheric scintillation, which is caused by irregular plasma bubbles that mostly occur at equatorial and polar areas. The impact of the factors mentioned above is assessed for baseline determination of the pendulum formation flying Swarm-A and -C satellites. They fly at altitudes lower than Swarm-B and their baseline length varies between 30 and 180 km. The assessment is done for four different periods: August 2014, November 2014, August 2016 and November 2016 - are implemented, respectively. These four periods have been selected to especially study the impact of different levels of ionospheric scintillations (normally low in August and high in November) and GPS receiver modifications. The assessment includes a consistency check between so-called kinematic and reduced-dynamic baseline solutions, a validation of the associated absolute orbit solutions by comparison with Satellite Laser Ranging (SLR) observations, overlap analyses between consecutive baseline solutions, success rate of ambiguity fixing, and analysis of observation residuals. First results indicate the usefulness and importance of the GPS receiver modifications and RINEX converter updates. It is found that the GPS receiver modifications significantly reduce the impact of ionospheric scintillations and improve the baseline determination. Especially, a larger carrier phase tracking loop bandwidth is found to be the most beneficial factor for baseline determination. @en