Precise Orbit Determination Solutions Research Articles

Contribution of BDS-3 observations to the precise orbit determination of LEO satellites: a case study of TJU-01

The precise orbit determination (POD) of scientific low Earth orbit (LEO) satellites is a prerequisite for the successful implementation of scientific missions. In recent years, global navigation satellite systems have become the main means of determining the orbits of LEO satellites. The global navigation satellite system receiver onboard the Tianjin University No. 1 (TJU-01) satellite receives both GPS and BDS-2/3 signals, with the addition of BDS-2/3 observations playing an important role in improving the POD of LEO satellites. This study comprehensively analyzes the spaceborne GPS/BDS data quality, including BDS-2/3 and GPS code multipath errors. Appreciable code multipath errors are found for the B1I signal of BDS-2 medium Earth orbit (MEO) satellites at elevations higher than 40°, whereas slight near-field relevant multipath errors of both frequencies are found for GPS and BDS-3 MEO satellites. The GPS and BDS-2/3 code multipath errors are estimated through elevation/azimuth-relevant piece-wise modeling and applied in the POD calculations. Several schemes, namely GPS-based, BDS-based, BDS-based without geo-synchronous (GEO) satellites, and GPS/BDS combined schemes, are designed to evaluate the POD performance. Fourteen days of data are calculated and the average three-dimensional (3D) orbital root mean square (RMS) of orbit overlapping differences obtained from GPS-based and BDS-based POD (without GEO satellites) solutions are 37.4 and 27.1 mm, respectively. The BDS-based solutions are obviously better than the GPS-based solutions, mainly owing to better data availability. The GPS/BDS combined solutions have the best accuracy, with a 3D RMS value of 20.6 mm. In addition, when BDS GEO satellites are included, the 3D RMS of the overlapping orbit differences reduces to 32.9 and 27.4 mm for BDS-based and GPS/BDS combined solutions, respectively. Double-difference (DD) and single-difference (SD) integer ambiguity resolution (IAR) are adopted to further improve the POD performance. The fixed orbit of the TJU-01 satellite is solved through DD IAR and SD IAR, and the contribution of the TJU-01 satellite to ambiguity fixing is analyzed. Relative to the float solution, the improvements made using the two ambiguity fixing approaches are equivalent, both being approximately 13%. The importance of this research is not only the precise determination of the orbit of TJU-01 for occultation service but also the demonstration of the contribution of BDS observations to the performance of the POD of LEO satellites.

Enhanced precise orbit determination for GPS and BDS-2/3 with real LEO onboard and ground observations

Due to the current geographical situation in China that it is difficult to achieve globally well distributed ground monitoring stations for Chinese BeiDou Navigation System (BDS), the BDS Medium Earth Orbit (MEO) satellite orbital accuracy can be seriously affected by the insufficient length of continuous observation arc based on regional ground network. What is more, the highly static characteristics of BDS Geosynchronous Orbiting (GEO) satellites resulting in meter-level orbit determination accuracy is far from satisfactory for precise positioning services. In order to overcome these problems, the low Earth orbit (LEO) satellites serving as fast-moving space monitoring stations can be used as a good supplement for the current BDS ground monitoring stations layout. In this study, real measured spaceborne data from two LEO satellites, namely Fengyun-3D (FY-3D) and Tianjin University No. 1 (TJU-01), are collected and studied for the augmentation of BDS precise orbit determination (POD). The multipath errors of spaceborne code observations are comprehensively analyzed. It is found that not only BDS-2 relevant satellite-induced code bias but also near-field multipath errors, especially distinct in GPS, exist in a spaceborne environment. The piece-wise linear model is therefore established and applied to correct the code observations to reduce the multipath errors in the integrated POD processing. The GPS and BDS-2/3 POD solutions are compared with orbital overlapping differences and Satellite Laser Ranging (SLR) residuals validation. It is demonstrated that including the two LEO satellites can improve the orbit determination accuracy of GPS and BDS-2/3 significantly under a regional ground network, especially in the along component. The average overlapping orbital Root Mean Square (RMS) is decreased by 18.4 %, 34.3 %, 24.9 %, 21.4 %, and 7.8 % for the GPS, GEO, Inclined Geosynchronous Orbit (IGSO), BDS-2 MEO, and BDS-3 MEO satellites, respectively, in the along component. The RMS of SLR residuals is decreased from 37.1 cm to 17.8 cm for the GEO satellites, and the overall improvement is about 8 %-12 % for the BDS MEO satellites. There has also been a slight improvement under a global network, with an average improvement of 2–3 cm in the SLR residuals RMS. However, significant systematic errors are also observed in the SLR residuals in BDS GEO, IGSO, and MEO satellites, and are expected to be improved with refined observation models based on more LEO satellites, i.e., the phase center variation (PCV).

Satellite laser ranging to GNSS-based Swarm orbits with handling of systematic errors

Satellite laser ranging (SLR) retroreflectors along with GNSS receivers are installed onboard numerous active low earth orbiters (LEOs) for the independent validation of GNSS-based precise orbit determination (POD) products. SLR validation results still contain many systematic errors that require special handling of various biases. For this purpose, we derive methods of reducing systematic effects affecting the SLR residuals to LEO Swarm satellites. We test solutions incorporating the estimation of range biases, station coordinate corrections, tropospheric biases, and horizontal gradients of the troposphere delays. When estimating range biases once per day, the standard deviation (STD) of Swarm-B SLR residuals is reduced from 10 to 8 mm for the group of high-performing SLR stations. The tropospheric biases estimated once per day, instead of range biases, further reduce the STD of residuals to the level of 6 mm. The systematic errors that manifest as dependencies of SLR residuals under different measurement conditions, e.g., elevation angle, are remarkably diminished. Furthermore, introducing troposphere biases allows for the comparison of the orbit quality between kinematic and reduced-dynamic orbits as the GPS-based orbit errors become more pronounced when SLR observations are freed from elevation-dependent errors. Applying tropospheric biases in SLR allows obtaining the consistency between the POD solution and SLR observations that are two times better than when neglecting to model of systematic effects and by 29% better when compared with solutions considering present methods of range bias handling.

Enhanced orbit determination for formation-flying satellites based on M-estimation

The classical least-squares estimation (LS) has been widely used for parameter estimation in satellite precise orbit determination (POD). However, the classical LS estimation with uniform weighting is very sensitive to outliers in the observations. To overcome this issue, we use the M-estimation on the basis of the LS estimation to improve the POD solutions. To demonstrate the added value of the M-estimation, we use one year of GPS data collected by the GRACE Follow-On mission, and two sets of orbits are produced using both the LS and M-estimation. The obtained orbits are assessed through orbit formal error analysis, orbit comparison, residual analysis of satellite laser ranging (SLR), and K-band ranging (KBR) measurements. Formal error analysis shows that the precision can be improved with the M-estimation notably by 25 and 40% for the dynamic and kinematic orbit, respectively. Orbit comparison reveals that the M-estimation can offer better solution consistency between the dynamic and kinematic orbit, with the differences being reduced by 23% when compared to the LS estimation. KBR validation reports that the relative precision can be improved with the M-estimation significantly by 23 and 40% for the dynamic and kinematic orbit, respectively. Specifically, the KBR residuals are reduced from 0.65 to 0.50 mm for dynamic orbit, and from 3.24 to 1.96 mm for kinematic orbit. These results demonstrate that the M-estimation can improve the orbit precision in both absolute and relative senses. Finally, we find that the current orbit accuracy is likely dominated by systematic errors, which can obscure the contribution of the M-estimation. The SLR measurements, with precision at 5–10 mm level, also seem to be not precise enough to validate the potential contribution. As a result, the improvements as indicated by the SLR validation are shown to be insignificant.

Research on the Impact of BDS-2/3 Receiver ISB on LEO Satellite POD

In recent years, the multi-GNSS positioning application is becoming more and more popular, same to the low Earth orbit (LEO) satellite precise orbit determination (POD) based on the onboard multi-GNSS measurements. The third-generation Beidou navigation satellite system (BDS-3) provides a new option to obtain the LEO satellite orbit solutions. However, the receiver intersystem bias (ISB) of different GNSS is unavoidable in multi-GNSS data processing. This paper’s main goal is absorption of the impact of the ISB between BDS-3 and BDS-2 on the LEO satellite POD. Taking GPS-based POD solutions for the reference orbit, this paper evaluates the orbit accuracy of BDS-2-based POD, BDS-3-based POD, BDS-2 and BDS-3 combined PODs with/without ISB. The BDS-3-based POD accuracy is 6.57 cm in the 3D direction, a 56% improvement over BDS-2-based POD. When the ISB between BDS-3 and BDS-2 is estimated, the BDS-2/3 combined POD accuracy of 5.37 cm in the 3D direction is better than that without ISB, which is a 64% improvement over BDS-2-based POD and 18% improvement over BDS-3-based POD. For GPS and BDS-2/3 combined POD, the GPS and BDS-3 joint POD solutions have the smallest RMS differences in overlapping consistency and smallest RMS differences compared to GPS-based POD. This study indicates that estimating the BDS-2/3 receiver ISB in BDS-2/3 joint POD could improve the orbit accuracy, and the GPS and BDS-3 joint POD solution is better than another combined POD. This paper will provide meaningful references for the LEO satellite multi-GNSS-based POD.

Effects of New Level-1B Data on GRACE Temporal Gravity Field Models and Precise Orbit Determination Solutions

The quality of Gravity Recovery and Climate Experiment (GRACE) observation is the prerequisite for obtaining the high-precision GRACE temporal gravity field model. To study the influence of new-generation GRACE Level-1B Release 03 (RL03) data and the new atmosphere and ocean de-aliasing (AOD1B) products on recovering temporal gravity field models and precise orbit determination (POD) solutions, we combined the global positioning system and K-band ranging-rate (KBRR) observations of GRACE satellites to estimate the effect of different data types on these solutions. The POD and monthly gravity field solutions are obtained from 2005 to 2010 by SHORDE software developed by the Shanghai Astronomical Observatory. The post-fit residuals of the KBRR data were decreased by approximately 10%, the precision of three-direction positions of the GRACE POD was improved by approximately 5%, and the signal-to-noise ratio of the monthly gravity field model was enhanced. The improvements in the new release of monthly gravity field model and POD solutions can be attributed to the enhanced Level-1B KBRR data and the AOD1B model. These improvements were primarily due to the enhanced of KBRR data; the effect of the AOD1B model was not significant. The results also showed that KBRR data slightly improve the satellite orbit precision, and obviously enhance the precision of the gravity field model.

Sentinel-6A precise orbit determination using a combined GPS/Galileo receiver

The Sentinel-6 (or Jason-CS) altimetry mission provides a long-term extension of the Topex and Jason-1/2/3 missions for ocean surface topography monitoring. Analysis of altimeter data relies on highly-accurate knowledge of the orbital position and requires radial RMS orbit errors of less than 1.5 cm. For precise orbit determination (POD), the Sentinel-6A spacecraft is equipped with a dual-constellation GNSS receiver. We present the results of Sentinel-6A POD solutions for the first 6 months since launch and demonstrate a 1-cm consistency of ambiguity-fixed GPS-only and Galileo-only solutions with the dual-constellation product. A similar performance (1.3 cm 3D RMS) is achieved in the comparison of kinematic and reduced-dynamic orbits. While Galileo measurements exhibit 30–50% smaller RMS errors than those of GPS, the POD benefits most from the availability of an increased number of satellites in the combined dual-frequency solution. Considering obvious uncertainties in the pre-mission calibration of the GNSS receiver antenna, an independent inflight calibration of the phase centers for GPS and Galileo signal frequencies is required. As such, Galileo observations cannot provide independent scale information and the estimated orbital height is ultimately driven by the employed forces models and knowledge of the center-of-mass location within the spacecraft. Using satellite laser ranging (SLR) from selected high-performance stations, a better than 1 cm RMS consistency of SLR normal points with the GNSS-based orbits is obtained, which further improves to 6 mm RMS when adjusting site-specific corrections to station positions and ranging biases. For the radial orbit component, a bias of less than 1 mm is found from the SLR analysis relative to the mean height of 13 high-performance SLR stations. Overall, the reduced-dynamic orbit determination based on GPS and Galileo tracking is considered to readily meet the altimetry-related Sentinel-6 mission needs for RMS height errors of less than 1.5 cm.

A Comparative Study on the Solar Radiation Pressure Modeling in GPS Precise Orbit Determination

For Global Positioning System (GPS) precise orbit determination (POD), the solar radiation pressure (SRP) is the dominant nongravitational perturbation force. Among the current SRP models, the ECOM and box-wing models are widely used in the International GNSS Service (IGS) community. However, the performance of different models varies over different GPS satellites. In this study, we investigate the performances of different SRP models, including the box-wing and adjustable box-wing as a priori models, and ECOM1 and ECOM2 as parameterization models, in the GPS POD solution from 2017 to 2019. Moreover, we pay special attention to the handling of the shadow factor in the SRP modeling for eclipsing satellites, which is critical to achieve high-precision POD solutions but has not yet been fully investigated. We demonstrate that, as an a priori SRP model, the adjustable box-wing has better performance than the box-wing model by up to 5 mm in the orbit day boundary discontinuity (DBD) statistics, with the largest improvement observed on the BLOCK IIR satellites using the ECOM1 as a parameterization SRP model. The box-wing model shows an insignificant orbit improvement serving as the a priori SRP model. For the eclipsing satellites, the three-dimensional (3D) root mean square (RMS) values of orbit DBD are improved when the shadow factor is applied only in the D direction (pointing toward to Sun) than that in the three directions (D, Y, and B) in the satellite frame. Different SRP models have comparable performance in terms of the Earth rotation parameter (ERP) agreement with the IERS EOP 14C04 product, whereas the magnitude of the length of day (LoD) annual signal is reduced when the shadow factor is applied in the D direction than in the three directions. This study clarifies how the shadow factor should be applied in the GPS POD solution and demonstrates that the a priori adjustable box-wing model combined with ECOM1 is more suitable for high-precision GPS POD solutions, which is useful for the further GNSS data analysis.

LEO-Constellation-Augmented BDS Precise Orbit Determination Considering Spaceborne Observational Errors

The precise orbit determination (POD) accuracy of the Chinese BeiDou Navigation Satellite System (BDS) is still not comparable to that of the Global Positioning System because of the unfavorable geometry of the BDS and the uneven distribution of BDS ground monitoring stations. Fortunately, low Earth orbit (LEO) satellites, serving as fast moving stations, can efficiently improve BDS geometry. Nearly all studies on Global Navigation Satellite System POD enhancement using large LEO constellations are based on simulations and their results are usually overly optimistic. The receivers mounted on a spacecraft or an LEO satellite are usually different from geodetic receivers and the observation conditions in space are more challenging than those on the ground. The noise level of spaceborne observations needs to be carefully calibrated. Moreover, spaceborne observational errors caused by space weather events, i.e., solar geomagnetic storms, are usually ignored. Accordingly, in this study, the actual spaceborne observation noises are first analyzed and then used in subsequent observation simulations. Then, the observation residuals from the actual-processed LEO POD during a solar storm on 8 September 2017 are extracted and added to the simulated spaceborne observations. The effect of the observational errors on the BDS POD augmented with different LEO constellation configurations is analyzed. The results indicate that the noise levels from the Swarm-A, GRACE-A, and Sentinel-3A satellites are different and that the carrier-phase measurement noise ranges from 2 mm to 6 mm. Such different noise levels for LEO spaceborne observations cause considerable differences in the BDS POD solutions. Experiments calculating the augmented BDS POD for different LEO constellations considering spaceborne observational errors extracted from the solar storm indicate that these errors have a significant influence on the accuracy of the BDS POD. The 3D root mean squares of the BDS GEO, IGSO, and MEO satellite orbits are 1.30 m, 1.16 m, and 1.02 m, respectively, with a Walker 2/1/0 LEO constellation, and increase to 1.57 m, 1.72 m, and 1.32 m, respectively, with a Walker 12/3/1 constellation. When the number of LEO satellites increases to 60, the precision of the BDS POD improves significantly to 0.89 m, 0.77 m, and 0.69 m for the GEO, IGSO, and MEO satellites, respectively. While 12 satellites are sufficient to enhance the BDS POD to the sub-decimeter level, up to 60 satellites can effectively reduce the influence of large spaceborne observational errors, i.e., from solar storms.

Single-Differenced Ambiguity Resolution for Orbit Determination of the Haiyang-2B

In ambiguity resolution, the Hatch-Melbourne-Wübbena code and carrier phase combination is usually used to fix the wide-lane (WL) ambiguity, and thus, the quality of the code observations directly affects the fixing success rate, especially when there are some kind of serious bias errors. Unfortunately, we found that the P1 code multipath (MP) errors of the Haiyang-2B calculated using the MP combination formula rapidly increases from sub-meter to several meters at elevation less than 40°. These rapid variations lead to biases in the fixed WL ambiguities. In this article, we create a static correction map on a grid with 5° x 5° resolution. Using this correction map, we reduced the root mean square of the P1 code bias errors from 1.04 to 0.47 m, which corresponds to an improvement of 54.8%. By comparing the different precise orbit determination solutions, we found that the ambiguity resolution significantly reduced the satellite laser ranging (SLR) residuals from 1.63 to 1.31 cm with an average improvement of 19.6%. However, because of the code errors, the ambiguity fixing rate of the P1 ambiguity-fixed solutions was much lower than that of the C1 solutions. By modeling this static correction, the impact of these errors was effectively reduced. The ambiguity fixing rate for the P1 solutions was improved by 15.6% and a 1-3 mm reduction in the SLR residuals was small but noticeable.

Integrated processing of ground- and space-based GPS observations: improving GPS satellite orbits observed with sparse ground networks

The precise orbit determination (POD) of Global Navigation Satellite System (GNSS) satellites and low Earth orbiters (LEOs) are usually performed independently. It is a potential way to improve the GNSS orbits by integrating LEOs onboard observations into the processing, especially for the developing GNSS, e.g., Galileo with a sparse sensor station network and Beidou with a regional distributed operating network. In recent years, few studies combined the processing of ground- and space-based GNSS observations. The integrated POD of GPS satellites and seven LEOs, including GRACE-A/B, OSTM/Jason-2, Jason-3 and, Swarm-A/B/C, is discussed in this study. GPS code and phase observations obtained by onboard GPS receivers of LEOs and ground-based receivers of the International GNSS Service (IGS) tracking network are used together in one least-squares adjustment. The POD solutions of the integrated processing with different subsets of LEOs and ground stations are analyzed in detail. The derived GPS satellite orbits are validated by comparing with the official IGS products and internal comparison based on the differences of overlapping orbits and satellite positions at the day-boundary epoch. The differences between the GPS satellite orbits derived based on a 26-station network and the official IGS products decrease from 37.5 to 23.9 mm (34% improvement) in 1D-mean RMS when adding seven LEOs. Both the number of the space-based observations and the LEO orbit geometry affect the GPS satellite orbits derived in the integrated processing. In this study, the latter one is proved to be more critical. By including three LEOs in three different orbital planes, the GPS satellite orbits improve more than from adding seven well-selected additional stations to the network. Experiments with a ten-station and regional network show an improvement of the GPS satellite orbits from about 25 cm to less than five centimeters in 1D-mean RMS after integrating the seven LEOs.

Precise Orbit Determination for GNSS Maneuvering Satellite with the Constraint of a Predicted Clock

Precise orbit products are essential and a prerequisite for global navigation satellite system (GNSS) applications, which, however, are unavailable or unusable when satellites are undertaking maneuvers. We propose a clock-constrained reverse precise point positioning (RPPP) method to generate the rather precise orbits for GNSS maneuvering satellites. In this method, the precise clock estimates generated by the dynamic precise orbit determination (POD) processing before maneuvering are modeled and predicted to the maneuvering periods and they constrain the RPPP POD during maneuvering. The prediction model is developed according to different clock types, of which the 2-h prediction error is 0.31 ns and 1.07 ns for global positioning system (GPS) Rubidium (Rb) and Cesium (Cs) clocks, and 0.45 ns and 0.60 ns for the Beidou navigation satellite system (BDS) geostationary orbit (GEO) and inclined geosynchronous orbit (IGSO)/Median Earth orbit (MEO) satellite clocks, respectively. The performance of this proposed method is first evaluated using the normal observations without maneuvers. Experiment results show that, without clock-constraint, the average root mean square (RMS) of RPPP orbit solutions in the radial, cross-track and along-track directions is 69.3 cm, 5.4 cm and 5.7 cm for GPS satellites and 153.9 cm, 12.8 cm and 10.0 cm for BDS satellites. When the constraint of predicted satellite clocks is introduced, the average RMS is dramatically reduced in the radial direction by a factor of 7–11, with the value of 9.7 cm and 13.4 cm for GPS and BDS satellites. At last, the proposed method is further tested on the actual GPS and BDS maneuver events. The clock-constrained RPPP POD solution is compared to the forward and backward integration orbits of the dynamic POD solution. The resulting orbit differences are less than 20 cm in all three directions for GPS satellite, and less than 30 cm in the radial and cross-track directions and up to 100 cm in the along-track direction for BDS satellites. From the orbit differences, the maneuver start and end time is detected, which reveals that the maneuver duration of GPS satellites is less than 2 min, and the maneuver events last from 22.5 min to 107 min for different BDS satellites.

Impact of GPS receiver antenna GRAPHIC residual variations on single-frequency orbit determination of LEO satellites

Single-frequency (SF) precise orbit determination (POD) using space-borne Global Positioning System (GPS) measurements is a prerequisite for the success of many low-cost small/micro low Earth orbit (LEO) satellite missions. The first-order ionospheric effects are usually eliminated by group and phase ionospheric correction (GRAPHIC) combinations. GPS receiver antenna GRAPHIC residual variations (GRVs) are important systematic error sources in SF orbit determination. Azimuth and elevation dependent GRVs are estimated and obtained based on the GRAPHIC combination residuals in an in-flight calibration. One month of data from GRACE-A, GRACE-B, CHAMP and HY-2A satellites is used to assess the potential of receiver antenna GRVs in SF orbit determination. It is the first time to study the impact of receiver antenna GRVs on SF orbit determination for different LEO satellites, which exhibit different altitudes and data qualities. The impact of receiver antenna GRVs on SF orbit determination is significant. The use of in-flight determined receiver antenna GRVs leads to a better consistency between SF and dual-frequency POD solutions. The improvements are more obvious for GRACE-A and CHAMP satellites, whose receiver antenna GRV patterns demonstrate clear characteristics of systematic deviations. After correcting the receiver antenna GRVs, the root-mean-square of satellite laser ranging validation residuals are 3.11 cm, 2.31 cm, 2.86 cm and 5.29 cm for GRACE-A, GRACE-B, CHAMP and HY-2A satellites, respectively, which are reduced by 11.1%, 4.6%, 14.6% and 4.7%, respectively. At last, a set of a priori GDV corrections of GPS transmitter antennas are used in SF orbit determination and its effects on receiver antenna GRVs estimation and SF orbit determination are analyzed. Applying these corrections can slightly improve the SF orbit quality of GRACE-A satellite.

The contribution of intersatellite links to BDS ‐3 orbit determination: Model refinement and comparisons

By end-2018, the Chinese BeiDou satellite system (BDS) has entered its third phase of global scale coverage (BDS-3). This study presents and validates a modified modeling aspect concerning an intersatellite link (ISL) hardware delay estimation. The precise orbit determination (POD) results of BDS-3 demonstrate this aspect along with calibrated phase center offsets (PCOs) of the ISL terminal to help improve the orbit accuracy. After onboarding the ISL data, two additional sets of POD solutions using regional and global ground stations are conducted. About a 40% improvement can be achieved for regional cases and 20% for global cases after ISL data were used for POD. The best POD performance solution is obtained with observations from both the global ground stations and ISL when the averaged 3D root mean squares of the orbit overlapping differences can reach around 20 cm and the signal-in-space range errors (SISREs) obtained by 6-hour predicted clock and orbit solutions show an average value of 25 cm.

Improving multi-GNSS ultra-rapid orbit determination for real-time precise point positioning

Currently, with the rapid development of multi-constellation Global Navigation Satellite Systems (GNSS), the real-time positioning and navigation are undergoing dramatic changes with potential for a better performance. To provide more precise and reliable ultra-rapid orbits is critical for multi-GNSS real-time positioning, especially for the three merging constellations Beidou, Galileo and QZSS which are still under construction. In this contribution, we present a five-system precise orbit determination (POD) strategy to fully exploit the GPS $$+$$ GLONASS $$+$$ BDS $$+$$ Galileo $$+$$ QZSS observations from CDDIS $$+$$ IGN $$+$$ BKG archives for the realization of hourly five-constellation ultra-rapid orbit update. After adopting the optimized 2-day POD solution (updated every hour), the predicted orbit accuracy can be obviously improved for all the five satellite systems in comparison to the conventional 1-day POD solution (updated every 3 h). The orbit accuracy for the BDS IGSO satellites can be improved by about 80, 45 and 50% in the radial, cross and along directions, respectively, while the corresponding accuracy improvement for the BDS MEO satellites reaches about 50, 20 and 50% in the three directions, respectively. Furthermore, the multi-GNSS real-time precise point positioning (PPP) ambiguity resolution has been performed by using the improved precise satellite orbits. Numerous results indicate that combined GPS $$+$$ BDS $$+$$ GLONASS $$+$$ Galileo (GCRE) kinematic PPP ambiguity resolution (AR) solutions can achieve the shortest time to first fix (TTFF) and highest positioning accuracy in all coordinate components. With the addition of the BDS, GLONASS and Galileo observations to the GPS-only processing, the GCRE PPP AR solution achieves the shortest average TTFF of 11 min with $$7{^{\circ }}$$ cutoff elevation, while the TTFF of GPS-only, GR, GE and GC PPP AR solution is 28, 15, 20 and 17 min, respectively. As the cutoff elevation increases, the reliability and accuracy of GPS-only PPP AR solutions decrease dramatically, but there is no evident decrease for the accuracy of GCRE fixed solutions which can still achieve an accuracy of a few centimeters in the east and north components.

Precise orbit determination of the Sentinel-3A altimetry satellite using ambiguity-fixed GPS carrier phase observations

The Sentinel-3 mission takes routine measurements of sea surface heights and depends crucially on accurate and precise knowledge of the spacecraft. Orbit determination with a targeted uncertainty of less than 2 cm in radial direction is supported through an onboard Global Positioning System (GPS) receiver, a Doppler Orbitography and Radiopositioning Integrated by Satellite instrument, and a complementary laser retroreflector for satellite laser ranging. Within this study, the potential of ambiguity fixing for GPS-only precise orbit determination (POD) of the Sentinel-3 spacecraft is assessed. A refined strategy for carrier phase generation out of low-level measurements is employed to cope with half-cycle ambiguities in the tracking of the Sentinel-3 GPS receiver that have so far inhibited ambiguity-fixed POD solutions. Rather than explicitly fixing double-difference phase ambiguities with respect to a network of terrestrial reference stations, a single-receiver ambiguity resolution concept is employed that builds on dedicated GPS orbit, clock, and wide-lane bias products provided by the CNES/CLS (Centre National d’Etudes Spatiales/Collecte Localisation Satellites) analysis center of the International GNSS Service. Compared to float ambiguity solutions, a notably improved precision can be inferred from laser ranging residuals. These decrease from roughly 9 mm down to 5 mm standard deviation for high-grade stations on average over low and high elevations. Furthermore, the ambiguity-fixed orbits offer a substantially improved cross-track accuracy and help to identify lateral offsets in the GPS antenna or center-of-mass (CoM) location. With respect to altimetry, the improved orbit precision also benefits the global consistency of sea surface measurements. However, modeling of the absolute height continues to rely on proper dynamical models for the spacecraft motion as well as ground calibrations for the relative position of the altimeter reference point and the CoM.

Improving GLONASS Precise Orbit Determination through Data Connection.

In order to improve the precision of GLONASS orbits, this paper presents a method to connect the data segments of a single station-satellite pair to increase the observation continuity and, consequently, the strength of the precise orbit determination (POD) solution. In this method, for each GLONASS station-satellite pair, the wide-lane ambiguities derived from the Melbourne–Wübbena combination are statistically tested and corrected for phase integer offsets and then the same is carried out for the narrow-lane ambiguities calculated from the POD solution. An experimental validation was carried out using one-month GNSS data of a global network with 175 IGS stations. The result shows that, on average, 27.1% of the GLONASS station-satellite pairs with multiple data segments could be connected to a single long observation arc and, thus, only one ambiguity parameter was estimated. Using the connected data, the GLONASS orbit overlapping RMS at the day boundaries could be reduced by 19.2% in ideal cases with an averaged reduction of about 6.3%.

Quality assessment of onboard GPS receiver and its combination with DORIS and SLR for Haiyang 2A precise orbit determination

The GPS, DORIS, and SLR instruments are installed on Haiyang 2A (HY2A) altimetry satellite for Precise Orbit Determination (POD). Among these instruments, the codeless GPS receiver is the state-of-art Chinese indigenous onboard receiver, and it is the first one successfully used for Low Earth Orbit (LEO) satellite. Firstly, the contribution assesses the performance of the receiver through an analysis of data integrity, numbers of all tracked and valid measurements as well as multipath errors. The receiver generally shows good performance and quality despite a few flaws. For example, L2 observations are often missing in low elevations, particularly during the ascent of GPS satellites, and the multipath errors of P1 show a slightly abnormal pattern. Secondly, the PCO (Phase Center Offset) and PCV (Phase Center Variation) of the antenna of the GPS receiver are determined in this contribution. A significant leap for Z-component of PCO up to −1.2 cm has been found on 10 October 2011. Thirdly, the obtained PCO and PCV maps are used for GPS only POD solutions. The post-fit residuals of ionosphere-free phase combinations reduce almost 50%, and the radial orbit differences with respect to CNES (Centre National d’Etudes Spatiales) Precise Orbit Ephemeris (POEs) improve about 13.9%. The orbits are validated using the SLR data, and the RMS of SLR Observed minus Computed (O-C) residuals reduces from 17.5 to 15.9 mm. These improvements are with respect to the orbits determined without PCO and PCV. Fourthly, six types of solutions are determined for HY2A satellite using different combinations of GPS, DORIS, and SLR data. Statistics of SLR O-C residuals and cross-comparison of orbits obtained in the contribution and the CNES POEs indicate that the radial accuracy of these orbits is at the 1.0 cm level for HY2A orbit solutions, which is much better than the scientific requirements of this mission. It is noticed that the GPS observations dominate the achievable accuracy of POD, and the combination of multiple types of observations can reduce orbit errors caused by data gaps and maintain more stable and continuous orbits.

Self-consistent treatment of tidal variations in the geocenter for precise orbit determination

We show that the current levels of accuracy being achieved for the precise orbit determination (POD) of low-Earth orbiters demonstrate the need for the self-consistent treatment of tidal variations in the geocenter. Our study uses as an example the POD of the OSTM/Jason-2 satellite altimeter mission based upon Global Positioning System (GPS) tracking data. Current GPS-based POD solutions are demonstrating root-mean-square (RMS) radial orbit accuracy and precision of \({<}1\) cm and 1 mm, respectively. Meanwhile, we show that the RMS of three-dimensional tidal geocenter variations is \({<}6\) mm, but can be as large as 15 mm, with the largest component along the Earth’s spin axis. Our results demonstrate that GPS-based POD of Earth orbiters is best performed using GPS satellite orbit positions that are defined in a reference frame whose origin is at the center of mass of the entire Earth system, including the ocean tides. Errors in the GPS-based POD solutions for OSTM/Jason-2 of \({<}4\) mm (3D RMS) and \({<}2\) mm (radial RMS) are introduced when tidal geocenter variations are not treated consistently. Nevertheless, inconsistent treatment is measurable in the OSTM/Jason-2 POD solutions and manifests through degraded post-fit tracking data residuals, orbit precision, and relative orbit accuracy. For the latter metric, sea surface height crossover variance is higher by \(6~\hbox {mm}^{2}\) when tidal geocenter variations are treated inconsistently.

Measuring atmospheric density using GPS–LEO tracking data

We present a method to estimate the total neutral atmospheric density from precise orbit determination of Low Earth Orbit (LEO) satellites. We derive the total atmospheric density by determining the drag force acting on the LEOs through centimeter-level reduced-dynamic precise orbit determination (POD) using onboard Global Positioning System (GPS) tracking data. The precision of the estimated drag accelerations is assessed using various metrics, including differences between estimated along-track accelerations from consecutive 30-h POD solutions which overlap by 6h, comparison of the resulting accelerations with accelerometer measurements, and comparison against an existing atmospheric density model, DTM-2000. We apply the method to GPS tracking data from CHAMP, GRACE, SAC-C, Jason-2, TerraSAR-X and COSMIC satellites, spanning 12years (2001–2012) and covering orbital heights from 400km to 1300km. Errors in the estimates, including those introduced by deficiencies in other modeled forces (such as solar radiation pressure and Earth radiation pressure), are evaluated and the signal and noise levels for each satellite are analyzed. The estimated density data from CHAMP, GRACE, SAC-C and TerraSAR-X are identified as having high signal and low noise levels. These data all have high correlations with anominal atmospheric density model and show common features in relative residuals with respect to the nominal model in related parameter space. On the contrary, the estimated density data from COSMIC and Jason-2 show errors larger than the actual signal at corresponding altitudes thus having little practical value for this study. The results demonstrate that this method is applicable to data from a variety of missions and can provide useful total neutral density measurements for atmospheric study up to altitude as high as 715km, with precision and resolution between those derived from traditional special orbital perturbation analysis and those obtained from onboard accelerometers.