Thermosphere mass density and crosswind can be derived from accelerometer and GNSS tracking data. However, present datasets are often provided without comprehensive uncertainty specifications. We present a newly developed method that propagates measurement noise and errors in the satellite specification, thermosphere models, and radiation flux data to density observations to quantify their uncertainty. We focus specifically on density observations derived only from GNSS tracking data, which are limited in resolution along the orbit due to unavoidable smoothing. While the method can be applied to simulated and real data, making it useful for existing datasets and mission design, we demonstrated it using data from the GRACE B satellite. First, we compare the aerodynamic acceleration derived separately from the accelerometer and GNSS tracking data, highlighting the role of two significant noise sources: noise due to the differentiation of the positions and noise from the evaluation of the gravity vector at a noisy position. Averaging substantially reduces the noise in the aerodynamic acceleration as long as the differentiation noise dominates, which is the case at frequencies higher than the orbital frequency. Below, gravity vector evaluation noise becomes the dominating noise source, and consequently, averaging over longer periods leads to only marginal uncertainty reduction. Further, we investigate the uncertainty in the radiation pressure acceleration and demonstrate that averaging over one orbit substantially reduces the uncertainty in the along-track radiation pressure acceleration. We show that the uncertainty of density observations derived from the accelerometer data is about 4% of the density for data from 2003 when the GRACE B satellite was at 490km altitude during high solar activity. In 2008, solar activity was very low, and the altitude was still 476km, resulting in an uncertainty of 5%–20% because GNSS tracking noise and radiation pressure modeling errors play a much larger role as the aerodynamic acceleration becomes smaller. In the case of density observations derived only from GNSS tracking data, the uncertainty is about 5% in 2003 and 20%–50% in 2008 when averaging over one-third orbit. In 2008, GNSS tracking noise explains nearly all uncertainty in the density observation. Averaging over one orbit reduces the uncertainty to 4% and 5% in 2003 and 2008, respectively.@en

Uncertainties in radiation pressure modelling play a significant role in the thermospheric density and crosswind observations derived from the GRACE-FO accelerometer, especially during low solar activity. Under such conditions, the radiation pressure acceleration matches the magnitude of the aerodynamic acceleration along the track and exceeds it in the cross-track direction. The GRACE-FO mission has been operating for several years at such high altitudes during both low and rising solar activity, providing a perfect opportunity to study the effects of radiation pressure. This research uses ray tracing based on a high-fidelity satellite geometry model to calculate the radiation pressure acceleration. We numerically fine-tuned the coefficients describing the thermo-optical surface properties to obtain more accurate radiation pressure accelerations than those specified in the GRACE-FO mission manual. We also used in situ temperature measurements from thermistors on the solar arrays to model the satellite's thermal emission. These temperature measurements allowed a realistic setup of the thermal model, extended by the parameter describing the efficiency of the solar cells, and reproduced the acceleration of the thermal emission with an accuracy of RMS 0.148 nms⁻². The combination of the updated thermal model and the fine-tuning of the surface coefficients improved the accuracy of the crosswind acceleration to an RMS of 0.55 nms⁻², compared to an RMS of 4.22 nms⁻² when using panel models and instantaneous thermal radiation. We compared the observed crosswind with two models: HWM14 and TIE-GCM. While both models capture most of the salient features of the observed crosswind, HWM14 shows particularly good agreement at high latitudes. Compared to the previously employed radiation pressure model, the crosswind observations have been improved in low and mid-latitudes, especially during periods of higher solar activity. Since the effect of radiation pressure is most significant in the crosswind direction, the effect on density was small compared to previously published datasets.

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The Event Horizon Telescope (EHT) is a ground-based array of Very Long Baseline Interferometry (VLBI) telescopes designed to image the event horizon of black holes. To overcome its limitations, this study explores a mission concept involving a two-satellite constellation of VLBI telescopes deployed in Medium Earth Orbit (MEO). Achieving high-resolution black hole images requires precise baseline determination at the millimetre level. To address this challenge, each satellite in the constellation is equipped with two Global Navigation Satellite System (GNSS) receivers and an optical Intersatellite Link (ISL) to enhance orbit determination. The results highlight the importance of integer ambiguity resolution and reveal that the ISL primarily improves baseline estimation along the link direction, with minimal impact along the black hole direction. Large intersatellite distances lead to sub-optimal relative orbit accuracy, challenging the attainment of the 3.5 mm relative position accuracy goal along the black hole direction.@en

Satellites in Low Earth Orbit (LEO) are essential for sounding the topside ionosphere. In this work, we present and validate a data set of Total Electron Content (TEC) and in situ electron density observations from the Gravity Recovery And Climate Experiment (GRACE) and GRACE-Follow-On missions as well as a TEC data set from the CHAllenging Minisatellite Payload mission. Concerning TEC, special emphasis is put to ensure optimal consistency to the already existing Swarm and Gravity field and steady-state ocean circulation explorer (GOCE) TEC data sets. The newly processed satellite missions allow covering two full solar cycles with LEO slant TEC. Furthermore, the twin satellite missions GRACE and GRACE-FO equipped with inter-satellite K-band ranging allows to derive the horizontal TEC and, due to the small inter-satellite distance of the satellite pairs, an approximation for local electron density. However, the derived value of electron density is relative and requires calibration using external information. In this work, the calibration is performed using the IRI-2016 model. Radar observations, as well as in situ electron density observations available from Swarm B Langmuir probes, are used for validation. Conjunctions between satellites are used to validate the TEC time series. The newly derived data set is shown to be highly consistent with the already existing data sets with standard deviations below 3 TECU for TEC (even 1 TECU was reached for low solar flux) and an offset below 7 × 10¹⁰ m⁻³ with a standard deviation near 1 × 10¹¹ m⁻³ for the electron density.

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We statistically investigate fluctuation amplitudes (normalized to the background values) of dayside low-/mid-latitude upper-thermospheric mass density as observed by the Gravity Recovery and Climate Experiment (GRACE) and GRACE-Follow-On (GRACE-FO) spacecraft at ∼500 km altitude between 2002 and 2022. There are three new findings in our results. First, the climatology closely replicates previous studies on stratospheric and upper-thermospheric gravity waves (GWs) below the GRACE(-FO) altitudes. For example, in low-latitude regions, the fluctuations are stronger above continents than in the oceanic area. Mid-latitude fluctuations prefer the local winter hemisphere to the summer, and the South American/Atlantic region in June solstice hosts stronger fluctuations than in any other low-/mid-latitude locations or seasons. Fluctuations are more intense under lower solar activity. The above-mentioned consistency of the GRACE(-FO) results with previous lower-altitude GW studies confirms that GWs can penetrate up to 500 km. Second, the anti-correlation of upper-thermospheric GW with solar activity, which has been earlier reported for multi-year time scales, can also be identified on the scale of the solar rotation period (∼27 days). Third, we demonstrate asymmetry between pre-noon and post-noon GWs. The former exhibits stronger GW activity, which may result from the colder thermosphere being more favorable for intense mass density fluctuations via secondary/tertiary GW generation.

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Daedalus MASE (Mission Assessment through Simulation Exercise) is an open-source package of scientific analysis tools aimed at research in the Lower Thermosphere-Ionosphere (LTI). It was created with the purpose to assess the performance and demonstrate closure of the mission objectives of Daedalus, a mission concept targeting to perform in-situ measurements in the LTI. However, through its successful usage as a mission-simulator toolset, Daedalus MASE has evolved to encompass numerous capabilities related to LTI science and modeling. Inputs are geophysical observables in the LTI, which can be obtained either through in-situ measurements from spacecraft and rockets, or through Global Circulation Models (GCM). These include ion, neutral and electron densities, ion and neutral composition, ion, electron and neutral temperatures, ion drifts, neutral winds, electric field, and magnetic field. In the examples presented, these geophysical observables are obtained through NCAR’s Thermosphere-Ionosphere-Electrodynamics General Circulation Model. Capabilities of Daedalus MASE include: 1) Calculations of products that are derived from the above geophysical observables, such as Joule heating, energy transfer rates between species, electrical currents, electrical conductivity, ion-neutral collision frequencies between all combinations of species, as well as height-integrations of derived products. 2) Calculation and cross-comparison of collision frequencies and estimates of the effect of using different models of collision frequencies into derived products. 3) Calculation of the uncertainties of derived products based on the uncertainties of the geophysical observables, due to instrument errors or to uncertainties in measurement techniques. 4) Routines for the along-orbit interpolation within gridded datasets of GCMs. 5) Routines for the calculation of the global coverage of an in situ mission in regions of interest and for various conditions of solar and geomagnetic activity. 6) Calculations of the statistical significance of obtaining the primary and derived products throughout an in situ mission’s lifetime. 7) Routines for the visualization of 3D datasets of GCMs and of measurements along orbit. Daedalus MASE code is accompanied by a set of Jupyter Notebooks, incorporating all required theory, references, codes and plotting in a user-friendly environment. Daedalus MASE is developed and maintained at the Department for Electrical and Computer Engineering of the Democritus University of Thrace, with key contributions from several partner institutions.

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We present new neutral mass density and crosswind observations for the CHAMP, GRACE, and GRACE-FO missions, filling the last gaps in our database of accelerometer-derived thermosphere observations. For consistency, we processed the data over the entire lifetime of these missions, noting that the results for GRACE in 2011- 2017 and GRACE-FO are entirely new. All accelerometer data are newly calibrated. We modeled the temperature-induced bias variations for the GRACE accelerometer data to counter the detrimental effects of the accelerometer thermal control deactivation in April 2011. Further, we developed a new radiation pressure model, which uses ray tracing to account for shadowing and multiple reflections and calculates the satellitea's thermal emissions based on the illumination history. The advances in calibration and radiation pressure modeling are essential when the radiation pressure acceleration is significant compared to the aerodynamic one above 450 km altitude during low solar activity, where the GRACE and GRACE-FO satellites spent a considerable fraction of their mission lifetime. The mean of the new density observations changes only marginally, but their standard deviation shows a substantial reduction compared to thermosphere models, up to 15% for GRACE in 2009. The mean and standard deviation of the new GRACE-FO density observations are in good agreement with the GRACE observations. The GRACE and CHAMP crosswind observations agree well with the physics-based TIE-GCM winds, particularly the polar wind patterns. The mean observed crosswind is a few tens of m·s-1 larger than the model one, which we attribute primarily to the crosswind errors being positive by the definition of the retrieval algorithm. The correlation between observed and model crosswind is about 60%, except for GRACE in 2004- 2011 when the signal was too small to retrieve crosswinds reliably.

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The thermospheric neutral density response to the 7–9 September 2017 storms is investigated based on the Swarm satellite observations and the thermosphere-ionosphere-electrodynamic general circulation model (TIEGCM) simulation. The Swarm data depicted a prominent interhemispheric asymmetry (IHA) in the afternoon sector during the second storm, a feature that was yet explained. Driven by realistic high-latitude electric potential and electron precipitation patterns, the TIEGCM is able to reproduce the observed storm-time neutral density response. The TIEGCM simulation reveals that the differences in the traveling atmospheric disturbances (TADs) is largely responsible for the observed IHA in the neutral mass density response at low and middle latitudes, whereas the difference in mean molecular mass between the two hemispheres may contribute to the IHA in neutral density at higher latitudes. The IHAs in TADs and mean molecular mass are attributed to the IHA in Joule heating dissipation on the night and dawn sides.

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Exospheric temperature is one of the key parameters in constructing thermospheric models and has been extensively studied with in situ observations and remote sensing. The Global-scale Observations of the Limb and Disk (GOLD) at a geosynchronous vantage point provides dayglow limb images for two longitude sectors, from which we can estimate the terrestrial exospheric temperature since 2018. In this paper, we investigate climatological behavior of the exospheric temperature measured by GOLD. The temperature has positive correlations with solar and geomagnetic activity and exhibits a morning-afternoon asymmetry, both of which agree with previous studies. We have found that the arithmetic sum of F_10.7 (solar) and Ap (geomagnetic) indices is highly correlated with the exospheric temperature, explaining ∼64% of the day-to-day variability. Furthermore, the exospheric temperature has good correlation with thermospheric parameters (e.g., neutral temperature, O₂ density, and NO emission index) sampled at various heights above ∼130 km, in spite of the well-known thermal gradient below ∼200 km. However, thermospheric temperature at altitudes around 100 km is not well correlated with the GOLD exospheric temperature. The result implies that effects other than thermospheric heating by solar Extreme Ultraviolet and geomagnetic activity take control below a threshold altitude that exists between ∼100 and ∼130 km.

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One of the most important parameters in the atmosphere, the neutral temperature, becomes difficult to measure at high altitudes such as the exosphere. Therefore, based on the assumption of static equilibrium and isothermal atmosphere, a new method was developed to derive quiet-time exospheric temperatures using neutral atmospheric densities from 470 km to 550 km, which were obtained from the Swarm satellites. The derived neutral temperatures were obtained at an altitude of approximately 500 km in the low and middle latitudes from mid-April 2014 to early August 2014. The results were evaluated with nighttime temperatures from ground-based Fabry Perot Interferometers at 250 km. The mean deviation between the derived temperatures and FPI was 30.80 K and the standard deviation of the mean was 106.20 K. The diurnal variations of the exospheric temperatures, which tended to reach their maximum in the late afternoon, were in good consistency with the NRL-MSISE00 model simulations. This novel method performs well at low and middle latitudes. The greatest source of uncertainty is the mean molecular mass, which is also not well determined at these high altitudes. Hence, a measurement called “Satellite-tethered Mass Spectrometer Detection” was proposed to address this.@en

Cold Atom technology has undergone rapid development in recent years and has been demonstrated in space in the form of cold atom scientific experiments and technology demonstrators, but has so far not been used as the fundamental sensor technology in a science mission. The European Space Agency therefore funded a 7-month project to define the CASPA-ADM mission concept, which serves to demonstrate cold-atom interferometer (CAI) accelerometer technology in space. To make the mission concept useful beyond the technology demonstration, it aims at providing observations of thermosphere mass density in the altitude region of 300–400 km, which is presently not well covered with observations by other missions. The goal for the accuracy of the thermosphere density observations is 1% of the signal, which will enable the study of gas–surface interactions as well as the observation of atmospheric waves. To reach this accuracy, the CAI accelerometer is complemented with a neutral mass spectrometer, ram wind sensor, and a star sensor. The neutral mass spectrometer data is considered valuable on its own since the last measurements of atmospheric composition and temperature in the targeted altitude range date back to 1980s. A multi-frequency GNSS receiver provides not only precise positions, but also thermosphere density observations with a lower resolution along the orbit, which can be used to validate the CAI accelerometer measurements. In this paper, we provide an overview of the mission concept and its objectives, the orbit selection, and derive first requirements for the scientific payload.

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The lower-Thermosphere-ionosphere (LTI) system consists of the upper atmosphere and the lower part of the ionosphere and as such comprises a complex system coupled to both the atmosphere below and space above. The atmospheric part of the LTI is dominated by laws of continuum fluid dynamics and chemistry, while the ionosphere is a plasma system controlled by electromagnetic forces driven by the magnetosphere, the solar wind, as well as the wind dynamo. The LTI is hence a domain controlled by many different physical processes. However, systematic in situ measurements within this region are severely lacking, although the LTI is located only 80 to 200 km above the surface of our planet. This paper reviews the current state of the art in measuring the LTI, either in situ or by several different remote-sensing methods. We begin by outlining the open questions within the LTI requiring high-quality in situ measurements, before reviewing directly observable parameters and their most important derivatives. The motivation for this review has arisen from the recent retention of the Daedalus mission as one among three competing mission candidates within the European Space Agency (ESA) Earth Explorer 10 Programme. However, this paper intends to cover the LTI parameters such that it can be used as a background scientific reference for any mission targeting in situ observations of the LTI.

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The satellite acceleration data from the CHAMP, GRACE, GOCE, and Swarm missions provide detailed information on the thermosphere density over the last two decades. Recent work on reducing errors in modelling the spacecraft geometry has greatly reduced scale differences between the thermosphere data sets from these missions. However, residual inconsistencies between the data sets and between data and models are still present. To a large extent, these differences originate in the modelling of the gas-surface interactions (GSI), which is part of the satellite aerodynamic modelling used in the acceleration to density data processing. Physics-based GSI models require in-situ atmospheric composition and temperature data that are not measured by any of the above-mentioned satellites and, as a consequence, rely on thermosphere models for these inputs. To reduce the dependence on existing thermosphere models, we choose a GSI model with a constant energy accommodation coefficient per mission, which we optimize exploiting particular attitude manoeuvres and wind analyses to increase the self-consistency of the multi-mission thermosphere mass density data sets. We compare our results with those based on variable energy accommodation obtained by different studies and semi-empirical models to show the principal differences. The presented comparisons provide novel opportunity to quantify the discrepancies between current GSI models. Among the presented data, density variations with variable accommodation are within ±10%, and peaks can reach up to 15% at the poles. The largest differences occur during low solar activity periods. In addition, we utilize a series of attitude manoeuvres performed in May 2014 by the Swarm A and C satellites, which are flying in close proximity, to evaluate the residual inconsistency of the density observations as a function of the energy accommodation coefficient. Our analysis demonstrates that an energy accommodation coefficient of 0.85 maximizes the consistency of the Swarm density observations during the attitude manoeuvres. Using such coefficient, for Swarm A and Swarm C, the new density would be lower in magnitude with a 4-5% difference. In recent studies, similar energy accommodation coefficients were retrieved for the CHAMP and GOCE missions by investigating thermospheric winds. These new values for the energy accommodation coefficient provide a higher consistency among different missions and models. A comparison of neutral densities between current thermosphere models and observations indicates that semi-empirical models such as NRLMSISE-00 and DTM-2013 significantly overestimate the density, and that an overall higher consistency between the observations from the different missions can be achieved with the presented assumptions. The new densities from this work provide consistencies of 4.13% and 3.65% between the minimum and maximum mean ratios among the selected missions with NRLMSISE-00 and DTM-2013, respectively. A comparison with the WACCM-X general circulation model is also performed. Similar to the other models, WACCM-X seems to provide higher estimates of mass density especially under high and moderate solar activities. This work has the objective to guide density data users over the multiple data sets and highlight the remaining uncertainties associated with different GSI models.

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Space weather phenomena such as scintillations of Global Navigation Satellite Systems (GNSS) signals are of increasing importance for aviation, the maritime, and civil engineering industries. The ionospheric plasma irregularities causing scintillations are associated with strong gradients in ionospheric plasma density. To provide nowcasts and forecasts of space weather effects, it is vital to monitor the ionosphere and detect strong density variations. To reconstruct plasma density variations in the polar cap ionosphere, we use total electron content (TEC) estimates from the Swarm satellites' GPS receivers. By considering events where the Swarm satellites are in close proximity, we obtain plasma density variations by inverting TEC measurements on a two-dimensional grid. We first demonstrate the method using synthetic test data, before applying it to real data. The method is validated using in situ Langmuir probe measurements and ground-based TEC observations. We find that the new method can reproduce density variations, although it is sensitive to the geometry of the Swarm satellite constellation and to the calculated plasma temperature. Our proposed method opens new possibilities for ionospheric plasma monitoring that uses GPS receivers aboard low Earth orbit (LEO) satellites.

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Transient signal loss of the global positioning system (GPS) has been frequently observed by receivers on board the European Space Agency's Swarm mission when the satellites encounter ionospheric plasma irregularities. In this study we provided the first comparison of the GPS signal amplitude degradations from receivers on board low Earth orbiting satellites at different altitudes. Intense carrier phase variations but almost no amplitude fades (less than 2 dB Hz) are observed when the spaceborne receiver lies right inside the ionospheric plasma irregularities, like the case for the Swarm and CHAMP satellites flying at about 400–500 km. This indicates that the strong phase variation, but not the amplitude fades, causes the receivers to stop tracking the GPS signals. When the receiver is located 100–200 km below the slab of plasma irregularities, like the case for the GOCE satellite flying at about 250 km, signal amplitude fades exceeding 10 dB Hz are observed, in addition to strong phase variation. Our results suggest that a considerable distance of the receiver to the plasma irregularity slab is needed to affect the Fresnel diffractive process and further causes GPS signal amplitude fades.

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Although the knowledge of the gravity of the Earth has improved considerably with CHAMP, GRACE, and GOCE (see appendices for a list of abbreviations) satellite missions, the geophysical community has identified the need for the continued monitoring of the time-variable component with the purpose of estimating the hydrological and glaciological yearly cycles and long-term trends. Currently, the GRACE-FO satellites are the sole dedicated provider of these data, while previously the GRACE mission fulfilled that role for 15 years. There is a data gap spanning from July 2017 to May 2018 between the end of the GRACE mission and start the of GRACE-FO, while the Swarm satellites have collected gravimetric data with their GPS receivers since December 2013. We present high-quality gravity field models (GFMs) from Swarm data that constitute an alternative and independent source of gravimetric data, which could help alleviate the consequences of the 10-month gap between GRACE and GRACE-FO, as well as the short gaps in the existing GRACE and GRACE-FO monthly time series. The geodetic community has realized that the combination of different gravity field solutions is superior to any individual model and set up the Combination Service of Time-variable Gravity Fields (COST-G) under the umbrella of the International Gravity Field Service (IGFS), part of the International Association of Geodesy (IAG). We exploit this fact and deliver the highest-quality monthly GFMs, resulting from the combination of four different gravity field estimation approaches. All solutions are unconstrained and estimated independently from month to month. We tested the added value of including kinematic baselines (KBs) in our estimation of GFMs and conclude that there is no significant improvement. The non-gravitational accelerations measured by the accelerometer on board Swarm C were also included in our processing to determine if this would improve the quality of the GFMs, but we observed that is only the case when the amplitude of the non-gravitational accelerations is higher than during the current quiet period in solar activity Using GRACE data for comparison, we demonstrate that the geophysical signal in the Swarm GFMs is largely restricted to spherical harmonic degrees below 12. A 750 km smoothing radius is suitable to retrieve the temporal variations in Earth's gravity field over land areas since mid-2015 with roughly 4 cm equivalent water height (EWH) agreement with respect to GRACE. Over ocean areas, we illustrate that a more intense smoothing with 3000 km radius is necessary to resolve large-scale gravity variations, which agree with GRACE roughly at the level of 1 cm EWH, while at these spatial scales the GRACE observes variations with amplitudes between 0.3 and 1 cm EWH. The agreement with GRACE and GRACE-FO over nine selected large basins under analysis is 0.91 cm, 0.76 cm yr-1, and 0.79 in terms of temporal mean, trend, and correlation coefficient, respectively. The Swarm monthly models are distributed on a quarterly basis at ESA's Earth Swarm Data Access (at https://swarm-diss.eo.esa.int/, last access: 5 June 2020, follow Level2longterm and then EGF) and at the International Centre for Global Earth Models (http://icgem.gfz-potsdam.de/series/02_COST-G/Swarm, last access: 5 June 2020), as well as identified with the DOI https://doi.org/10.5880/ICGEM.2019.006 (Encarnacao et al., 2019).

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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.

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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

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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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.

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