The emerging BeiDou navigation satellite system has contributed to global precise positioning and has recently moved toward space-borne applications. However, the contribution of BeiDou on LEO orbit determination applications is limited by the poor precision of the GEO satellite orbit and clock products. Current researches suggest that BeiDou GEO satellites should not be included in LEO precise orbit determination. Based on analyzing the characteristics of errors existing in BeiDou GEO orbit products, we propose a feasible method to mitigate the offsets in BeiDou GEO orbit errors by in-flight calibration of the systematic daily constant biases in the along-track and cross-track of BeiDou GEO satellites. The proposed method is investigated and validated using one entire month of onboard BDS data from the Chinese FY-3C satellite. The average daily RMS compared with the GPS-derived orbit indicates that our method achieves 6.2 cm three-dimensional precision. When compared to the solutions that disregard the GEO orbit errors scheme and roughly exclude the GEO scheme, the FY-3C orbit precision has been improved by 89.1% and 20.2%, respectively. The average daily RMS values of phase residuals are about one centimeter for solutions that exclude GEO and that estimate systematic biases in GEO orbits. The calibrated orbits of GEO with the decimeter level in along-track and cross-track can be reconstructed by correcting the orbit biases estimated in the FY-3C precise orbit determination. Statistics of the FY-3C orbit quality, observation residuals, and precision of the recovered GEO orbits demonstrate that calibration of daily orbit biases in GEO can improve the precision of LEO orbit determination and enhance the reliability of the solution.

GPS data collected by satellite gravity missions can be used for extracting the long-wavelength part of the Earth’s gravity field. We propose a new data processing method which makes use of the ‘average acceleration’ approach to gravity field modelling. In this method, satellite accelerations are directly derived from GPS carrier phase measurements with an epoch-differenced scheme. As a result, no ambiguity solutions are needed and the systematic errors that do not change much from epoch to epoch are largely eliminated. The GPS data collected by the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite mission are used to demonstrate the added value of the proposed method. An analysis of the residual accelerations shows that accelerations derived in this way are more precise, with noise being reduced by about 20 and 5% at the cross-track component and the other two components, respectively, as compared to those based on kinematic orbits. The accelerations obtained in this way allow the recovery of the gravity field to a slightly higher maximum degree compared to the solution based on kinematic orbits. Furthermore, the gravity field solution has an overall better performance. Errors in spherical harmonic coefficients are smaller, especially at low degrees. The cumulative geoid height error is reduced by about 15 and 5% up to degree 50 and 150, respectively. An analysis in the spatial domain shows that large errors along the geomagnetic equator, which are caused by a high electron density coupled with large short-term variations, are substantially reduced. Finally, the new method allows for a better observation of mass transport signals. In particular, sufficiently realistic signatures of regional mass anomalies in North America and south-west Africa are obtained.

Earth’s gravity field recovery from GPS observations collected by low earth orbiting (LEO) satellites is a well-established technique, and kinematic orbits are commonly used for that purpose. Nowadays, more and more satellites are flying in close formations. The GPS-derived kinematic baselines between them can reach millimeter precision, which is more precise than the centimeter-level kinematic orbits. Thus, it has long been expected that the more precise kinematic baselines can deliver better gravity field solutions. However, this expectation has not been met yet in practice. In this study, we propose a new approach to gravity field modeling, in which kinematic orbits of the reference satellite and baseline vectors between the reference satellite and its accompanying satellite are jointly inverted. To validate the added value, data from the Gravity Recovery and Climate Experiment (GRACE) satellite mission are used. We derive kinematic orbits and inter-satellite baselines of the twin GRACE satellites from the GPS data collected in the year of 2010. Then two sets of monthly gravity field solutions up to degree and order 60 are produced. One is derived from kinematic orbits of the twin GRACE satellites (‘orbit approach’). The other is derived from kinematic orbits of GRACE A and baseline vectors between GRACE A and B (‘baseline approach’). Analysis of observation postfit residuals shows that noise in the kinematic baselines is notably lower than the kinematic orbits by 50, 47 and 43% for the along-track, cross-track and radial components, respectively. Regarding the gravity field solutions, analysis in the spectral domain shows that noise of the gravity field solutions beyond degree 10 can be significantly reduced when the baseline approach is applied, with cumulative errors up to degree 60 being reduced by 34%, when compared to the orbit approach. In the spatial domain, the recovered mass changes with the baseline approach are more consistent with those inferred from the K-Band Ranging based solutions. Our results demonstrate that the proposed baseline approach is able to provide better gravity field solutions than the orbit approach. The findings may facilitate, among others, bridging the gap between GRACE and GRACE Follow-On satellite mission.

To monitor temporal variations of the Earth’s gravity field and mass transport in the Earth’s system, data from gravity recovery and climate experiment (GRACE) satellite mission and its successor GRACE Follow-On (GFO) are used. To fill in the temporal gap between these missions, other satellites’ kinematic orbits derived from GPS-based high-low satellite-to-satellite tracking data may be considered. However, it is well known that kinematic orbits are highly sensitive to various systematic errors. These errors are responsible for a non-stationary noise in the kinematic orbits, which is difficult to handle. As a result, the quality of the obtained gravity field solutions is reduced. In this research, we propose to apply an epoch-difference (ED) scheme in the context of the classical dynamic approach to gravity field recovery. Compared to the traditional undifferenced (UD) scheme, the ED scheme is able to mitigate constant or slowly varying systematic errors. To demonstrate the added value of the ED scheme, three sets of monthly gravity field solutions produced from 6 years of GRACE kinematic orbits are compared: two sets produced in-house (with the ED and UD scheme), and a set produced with the undifferenced scheme in the frame of the short-arc approach (Zehentner and Mayer-Gürr in J Geodesy 90(3):275–286, 2015. https://doi.org/10.1007/s00190-015-0872-7). As a reference, we use state-of-the-art ITSG-Grace2018 monthly gravity field solutions. A comparison in the spectral domain shows that the gravity field solutions suffer from a lower noise level when the ED scheme is applied, particularly at low-degree terms, with cumulative errors up to degree 20 being reduced by at least 20%. In the spatial domain, the ED scheme notably reduces noise levels in the mass anomalies recovered. In addition, the signals in terms of mean mass anomalies in selected regions become closer to those inferred from ITSG-Grace2018 solutions, while showing no evidence of any damping, when the ED scheme is used. We conclude that the proposed ED scheme is preferable for time-varying gravity field modeling, as compared to the traditional UD scheme. Our findings may facilitate, among others, bridging the gap between GRACE and GFO satellite mission.

This study validated and investigated elevation- and frequency-dependent systematic biases observed in ground-based code measurements of the Chinese BeiDou navigation satellite system, using the onboard BeiDou code measurement data from the Chinese meteorological satellite Fengyun-3C. Particularly for geostationary earth orbit satellites, sky-view coverage can be achieved over the entire elevation and azimuth angle ranges with the available onboard tracking data, which is more favorable to modeling code biases. Apart from the BeiDou-satellite-induced biases, the onboard BeiDou code multipath effects also indicate pronounced near-field systematic biases that depend only on signal frequency and the line-of-sight directions. To correct these biases, we developed a proposed code correction model by estimating the BeiDou-satellite-induced biases as linear piece-wise functions in different satellite groups and the near-field systematic biases in a grid approach. To validate the code bias model, we carried out orbit determination using single-frequency BeiDou data with and without code bias corrections applied. Orbit precision statistics indicate that those code biases can seriously degrade single-frequency orbit determination. After the correction model was applied, the orbit position errors, 3D root mean square, were reduced from 150.6 to 56.3 cm.