Dynamic Orbit Determination Research Articles

LEO Satellite Navigation Based on Optical Measurements of a Cooperative Constellation

Autonomous, anti-jamming, and high-precision satellite navigation are of great importance to current and future space technologies. This paper proposes a cooperative constellation navigation system for low Earth orbit (LEO) satellites that use only the optical measurements of cooperative satellites. Based on photometry, an optical transmission link model of the system is built. With the pixel coordinates of the cooperative satellites on the optical images, the line of sight (LoS) vectors of the cooperative satellites with respect to the LEO spacecraft are first calculated, and a single-point positioning method based on the LoS vectors’ inner products is proposed. The single-point positioning results are then fed into a least square batch filter to estimate a high-precision spacecraft orbit. Simulations are conducted to evaluate the potential navigation accuracy. With a cooperative satellite ephemeris error of 100 m and an optical measurement noise level of 5 arcsecs, position accuracies of single-point positioning and dynamic orbit determination in the order of hundreds of meters and eight meters, respectively, are realized. In addition, the influences of the orbital altitude of the cooperative constellation, the ephemeris error of the cooperative satellite, the noise level of the optical measurements, and the Earth’s gravitational model on navigation accuracy are investigated via comparative simulations.

Calibration and validation of a space electrostatic accelerometer onboard Tianzhou-1 cargo spacecraft using GNSS and attitude data

The first Chinese cargo spacecraft, named Tianzhou-1, provides a very quiet and stable environment to test space accelerometers. In this study, the high-precision electrostatic accelerometer with a resolution of 3×10−10m/s2/Hz1/2 onboard Tianzhou-1 is calibrated and validated by in-orbit measurements. In our analysis, we employ 14.5 hours of accelerometer, Global Navigations Satellite Systems (GNSS), and attitude measurements. Non-gravitational linear accelerations of the spacecraft are estimated from GNSS observables by reduced dynamic orbit determination, and centrifugal accelerations are estimated from the spacecraft attitude data and the center of mass offset. The spacecraft microgravity reaches a level of 1×10−6m/s2/Hz1/2 within the bandwidth of 1×10−4 to 1×10−2 Hz revealed from accelerometer measurements, which agrees well with our estimation of the non-gravitational and centrifugal accelerations. The results show that the centrifugal forces are the dominant signal at the frequencies above 3 cycle per revolution (cpr, 1 cpr ≈1.8×10−4 Hz) while non-gravitational forces occupy the lower frequency band. Furthermore, the bias and scale factor of the accelerometer are obtained by calibration with the estimated non-gravitational and centrifugal accelerations, using the method of least-squares linear fit. Based on the data covering the whole test period (00:33:20-15:02:43, 3 June, 2017, Beijing time), the estimated biases are −(5.31±0.04)×10−5, −(1.75±0.02)×10−6 and (2.65±0.01)×10−6m/s2 for the x, y and z axes, respectively, and the estimated scale factors are 1.001±0.008, 0.999±0.003 and 1.018±0.003 for the x, y and z axes, respectively.

Orbit determination of BeiDou navigation satellite system maneuvered satellites based on instantaneous velocity pulses parameters

The BeiDou navigation satellite system (BDS) comprises geostationary earth orbit (GEO) satellites as well as inclined geosynchronous orbit (IGSO) and medium earth orbit (MEO) satellites. Owing to their special orbital characteristics, GEO satellites require frequent orbital maneuvers to ensure that they operate in a specific orbital window. The availability of the entire system is affected during the maneuver period because service cannot be provided before the ephemeris is restored. In this study, based on the conventional dynamic orbit determination method for navigation satellites, multiple sets of instantaneous velocity pulses parameters which belong to one of pseudo-stochastic parameters were used to simulate the orbital maneuver process in the orbital maneuver arc and establish the observed and predicted orbits of the maneuvered and non-maneuvered satellites of BeiDou regional navigation satellite system (BDS-2) and BeiDou global navigation satellite system (BDS-3). Finally, the single point positioning (SPP) technology was used to verify the accuracy of the observed and predicted orbits. The orbit determination accuracy of maneuvered satellites can be greatly improved by using the orbit determination method proposed in this paper. The overlapping orbit determination accuracy of maneuvered GEO satellites of BDS-2 and BDS-3 can improve 2–3 orders of magnitude. Among them, the radial orbit determination accuracy of each maneuvered satellite is basically better than 1 m. simultaneously, the combined orbit determination of the maneuvered and non-maneuvered satellites does not have a great impact on the orbit determination accuracy of the non-maneuvered satellites. Compared with the multi GNSS products (indicated by GBM) from the German Research Centre for Geosciences (GFZ), the impact of adding the maneuvered satellites on the orbit determination accuracy of BDS-2 satellites is less than 9 %. Furthermore, the orbital recovery time and the service availability period are significantly improved. When the node of the predicted orbit is traversed approximately 3 h after the maneuver, the accuracy of the predicted orbit of the maneuvered satellite can reach that of the observed orbit. The SPP results for the BDS reached a normal level when the node of the predicted orbit was 2 h after the maneuver.

BDS near real-time maneuver detection based on triple-differenced phase observations

The BeiDou Navigation Satellite System (BDS) geostationary earth orbit (GEO) and inclined geosynchronous orbit (IGSO) satellites need frequent orbital maneuvers to keep them in position due to various perturbations. However, common users cannot obtain the exact maneuver times, which may yield a decline in the real-time service performance of the BDS. To solve this problem, we presented a near real-time maneuver detection method for BDS based on triple-differenced phase observations, which can automatically detect the exact start and end times of satellite orbital maneuvers. In this method, the carrier-phase triple-differences residuals are firstly computed using the precise station coordinates, broadcast ephemeris and dual-frequency observations of ground tracking stations. Afterward, the residuals are be modeled using linear regression to identify maneuver times. The observations from the BDS Experimental Tracking Stations (BETS) and the reference time announced by the Beijing Satellite Navigation Center (BSNC) from Day of year (DOY) 100 to DOY 300, 2017 are used to evaluate the performance of the proposed method. The detected maneuver periods are consistent with the announced ones, except the detected start times lag 42 min and end times advance 23 min on average. Then, the detected times are further validated by dynamic precise orbit determination (POD) after the maneuver. The phase residuals and 3D RMS of the orbit differences of maneuvered satellites proved that the accuracy of detected maneuver times is better than 5-minute. At last, the kinematic precise point positioning (PPP) validation is implemented to evaluate the effect of more accurate GEO and IGSO satellites to BDS positioning. Results show that both the convergence and accuracy of BDS PPP are improved by adding one satellite that has ended maneuvering.

In-flight performance analysis of the navigation augmentation payload on LEO communication satellite: a preliminary study on WT01 mission

ABSTRACT With the development of the Low Earth Orbit (LEO) communication constellations, it has become a hot area of research to provide additional navigation augmentation services. Limited by volume, weight, power consumption, and running time, the in-flight performance of navigation augmentation payload remains to be investigated. In this paper, we analyze the data quality of on-board GNSS observation and evaluate the precision of short-arc dynamic Precise Orbit Determination (POD) performance based on the WangTong-01 (WT01) mission. Furthermore, the downlink navigation measurement data of WT01 satellites are analyzed and compared with the GNSS observations. The results show that the average multipath errors of the WT01 on-board GPS L1, L2 and BeiDou Satellite Navigation System (BDS) B1, B2 code observation are 0.54, 0.74, 0.65, and 0.58 m, respectively. The short-arc dynamic POD three-dimensional (3D) overlapping accuracy is 7.1 cm. The average multipath errors of downlink navigation signal Z1 and Z2 are 0.81 and 0.80 m, respectively, which at the same order of magnitude as GNSS signals. The maximum Carrier-to-Noise Ratio (C/N0) value of WT01 downlink measurement data can reach 60 dB Hz, which is much stronger than GNSS and indicates the navigation signals of LEO satellites can meet the basic requirement of navigation augmentation.

Optimization of ground tracking stations for BDS-3 satellite orbit determination

Abstract A precise satellite orbit is the basis for high-precision services for users, and the determination of high-precision satellite orbits depends on the reasonable distribution and volume of ground tracking stations (GTSs). In July 2020, the BeiDou global navigation satellite system (BDS-3) was completed and began to be operated globally. Based on the principle of dynamic orbit determination, we first developed an algorithm to determine the optimal distribution and number of GTSs for accurate satellite orbit determination. Subsequently, based on 10 GTSs located in China, the optimal distribution and number of GTSs with and without inter-satellite link (ISL) ranging observations were determined. Finally, real measurements of GTS and ISL ranging observation data were used to validate the GTS results yielded by the algorithm. Using 18 BDS-3 satellites, and based on non-ISL observations and 10 Chinese regional GTSs, we found that GTSs distributed near the equator contributed significantly to the accuracy of orbit determination for these satellites compared to other GTSs. Orbit determination results obtained from the measured data of the optimal GTSs were more accurate than those obtained from the measured data of uniformly distributed global GTSs. Upon the addition of 55 uniformly distributed GTSs worldwide, the orbit determination accuracy for BDS-3 satellites tended to plateau. Moreover, following the addition of ISL, although the distribution and number of GTSs was optimized using the proposed algorithm, the orbit determination results from the measured data revealed that a change in the distribution and number of GTSs had a limited effect on the BDS-3 orbit determination results.

GRACE-FO Antenna Phase Center Modeling and Precise Orbit Determination with Single Receiver Ambiguity Resolution

Precise knowledge of the phase center location of the global navigation satellite system (GNSS) antenna is a prerequisite for precise orbit determination (POD) of the low Earth orbit (LEO) satellite. The phase center offset (PCO) and phase center variation (PCV) values for the LEO antenna obtained from ground calibration cannot reflect the error sources encountered in the actual spacecraft environment. PCV corrections are estimated by ionosphere free (IF) carrier phase post-fit residuals of reduced dynamic orbit determination. Ambiguity resolution (AR) plays a crucial role in achieving the best orbit accuracy. The single receiver AR concept is realized using wide-lane (WL) and narrow-lane (NL) bias products. Single difference (SD) observations between satellites are applied to remove the receiver dependent phase bias. SD AR and traditional double difference (DD) AR methods are applied to fix the ambiguities. The recovered SD and DD IF ambiguities are taken as pseudo-observations to constrain the undifferenced IF ambiguity parameters in the POD process. The LEO orbits based on float ambiguity (FA), SD, AR, and DD AR are investigated. One year’s data collected by the Gravity Recovery And Climate Experiment Follow-On (GRACE-FO) mission and GPS precise products provided by the Center for Orbit Determination in Europe (CODE) were analyzed. Precise orbit generated by the Jet Propulsion Laboratory (JPL), independent satellite laser ranging (SLR), and K-band ranging (KBR) measurements were utilized to assess the orbit accuracy. More than 98% of SD WL and 95% of SD NL ambiguities are fixed, which confirms the good quality of the bias products and correctness of the SD AR method. With PCV corrections, the average phase residuals of DD and SD AR solutions are 0.13 and 0.41 mm, which indicates improved consistency between applied models and observations. Compared with JPL’s orbit, the SD AR orbits achieve the accuracy of 6.0, 6.2, and 5.1 mm in along-track, cross-track, and radial directions. The SD AR solutions show an average improvement of 18.3% related to the FA orbits while 6.3% is gained by the DD AR approach. The root mean squares (RMSs) of SLR residuals for FA, DD AR, and SD AR solutions are 11.5, 10.2, and 9.6 mm, which validate the positive effect of AR on POD. Standard deviation (STD) of KBR residuals for SD AR orbits is 1.8 mm while 0.9 mm is achieved by the DD AR method. The explanation is that the phase bias products used for SD AR are not free of errors and the errors may degrade the KBR validation. In-flight PCV calibration and ambiguity resolution improve the LEO orbit accuracy effectively.

Precise orbit determination of BDS-3 satellites using B1C and B2a dual-frequency measurements

Compared to the BeiDou regional navigation satellite system (BDS-2), the BeiDou global navigation satellite system (BDS-3) includes the newly designed B1C and B2a signals, which are compatible with the L1 and L5 frequencies of the global positioning system (GPS). Considering that the precise orbit determination (POD) of the BDS-3 constellation is currently restricted to the legacy B1I and B3I signals, we reported the POD performance of BDS-3 satellites using B1C and B2a dual-frequency measurements. Nine globally distributed Multi-GNSS Experiment (MGEX) stations were selected to determine the orbits of BDS-3 satellites during the period of July 2019. The results show that B1C/B2a-based POD enables an average three-dimensional root-mean-square error (3D RMS) of 24.2 cm, and the precision is better than 6 cm in the radial component in a comparison of two-day overlapping arcs. Satellite laser ranging (SLR) validation achieves an overall precision of 6.8 cm in RMS differences. Compared to the B1I/B3I-based POD results, the quality of B1C/B2a-based orbits is improved by approximately 9% across the whole BDS-3 constellation, indicating that the new B1C/B2a signals can be employed for the superior POD performance of BDS-3 satellites. Moreover, we investigated the behavior of the solar radiation pressure (SRP), which is generally considered one of the primary error sources in BDS-3 medium earth orbit (MEO) dynamic orbit determination. The ECOM7 SRP model has a better POD performance in continuous yaw steering (CYS) mode than the ECOM5 and ECOM9 SRP models. The results also show that there is no degradation in the orbit precision of BDS-3 MEO satellites when the elevation angle of the sun above the orbital plane (β angle) varies within the range of − 4° to + 4°.

Extended Kalman filter based statistical orbit determination for geostationary and geosynchronous satellite orbits in BeiDou constellation

BeiDou Navigation Satellite System (BDS) is composed of satellites in geostationary Earth orbit (GEO), medium Earth orbit (MEO) and inclined geosynchronous orbit (IGSO). However, the orbit determination of geostationary Earth orbits and of geosynchronous orbits (GSO) with small inclination angle and small eccentricity is a challenging task that is addressed in this paper using Extended Kalman Filter (EKF). The satellite positions were predicted in Earth-centred inertial (ECI) reference frame when propagated through Keplerian model and perturbation force model for different values of right ascension of ascending node (RAAN). Root mean square (RMS) errors of 9.61 cm, 6.73 cm and 11.46 cm were observed in ECI X, Y and Z satellite position coordinates of GSO respectively, whereas, the RMS errors for GEO satellite were 8.89 cm, 7.92 cm, and 0.93 cm respectively in ECI X, Y and Z coordinates; for perturbation force model with maximum value of RAAN when compared with dynamic orbit determination model. Kolmogorov-Smirnov test for EKF reported a p-value > 0.05, indicating a good fit of perturbation force model for orbit propagation. Orbit determination using EKF with perturbation force model were compared with that using EKF with Kepler's model. Wilcoxon Rank Sum test was used to compare the residuals from EKF algorithm through Kepler's model and perturbation force model. EKF with Perturbation force model showed improvement in predicting the satellite positions as compared to Kepler's model. EKF with Perturbation force model was further applied to International GNSS Service (IGS) station data and kilometre level accuracy was achieved. RMS errors of 0.75 km, 2.53 km and 1.91 km were observed in ECI X, Y and Z satellite position coordinates of GSO, respectively, whereas, the RMS errors for GEO satellite were 3.89 km, 4.20 km and 6.66 km respectively in ECI X, Y and Z coordinates for perturbation force model.

Assessment of single-difference and track-to-track ambiguity resolution in LEO precise orbit determination

Single-difference (SD) ambiguity resolution (AR) and track-to-track (T2T) AR are two typical AR methods in precise orbit determination (POD) for Low Earth Orbit (LEO) satellites, which could improve the accuracy of orbits greatly. In this study, SD AR and T2T AR methods are introduced and analyzed. The performance of these two methods is assessed by three months of GPS observations from the Gravity Recovery and Climate Experiment Follow On (GRACE-FO) twin satellites. Results show that T2T AR is highly dependent on the stability of receiver hardware delays, while SD AR requires Fractional Cycle Bias (FCB) or Integer Recovery Clock (IRC) products. We find that these two methods have comparable performance in Reduced Dynamic Precise Orbit Determination (RDPOD), while SD AR slightly outperforms T2T AR in Kinematic Precise Orbit Determination (KPOD). We also find that SD AR has a higher AR success rate than T2T AR. Therefore, we recommend SD AR as the top choice in LEO orbit determination, and T2T AR can be a good alternative when FCB or IRC products are not available.

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.

Assessment of chosen GRACE-related gravity models based on the GOCE satellite precise science orbit

Eight selected geopotential models obtained through the International Center for Global Earth Models were used in the dynamic orbit determination process of the satellite of the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) mission. For the estimation of various GOCE orbital arc variants, the following gravity models were taken into account: HUST-GRACE2016S, ITU_GRACE16, ITSG-GRACE2014S, ITSG-GRACE2014K, TONGJI-GRACE01, EIGEN-51C, EIGEN5S, EGM2008. The official kinematic and reduced-dynamic precise science orbit (PSO) of the GOCE satellite received via the European Space Agency was adopted as the reference orbit. Cartesian coordinates of the GOCE satellite in this orbit were treated as pseudo-observations in the estimation process using the classical least-squares method. The estimated orbital arcs were fitted to the corresponding arcs of the reference orbit. This allowed the values of 3D root-mean-square (RMS) of the distance between the estimated and reference arcs to be computed. The averages for these 3D RMS values, computed for ten and fifty orbital arcs, made it possible to compare the orbital performance of selected gravity models. Additionally, the fit to both types of the GOCE PSO, i.e., the kinematic orbit and the reduced-dynamic orbit made it possible to compare their quality. Investigation of the gravity model performance was also the opportunity to describe the effectiveness of dynamic orbit determination solutions, depending on the estimated arc lengths, type of reference orbit and the use (or not) of the background models.

Assessment of Earth Gravity Field Models in the Medium to High Frequency Spectrum Based on GRACE and GOCE Dynamic Orbit Analysis

An analysis of current static and time-variable gravity field models is presented focusing on the medium to high frequencies of the geopotential as expressed by the spherical harmonic coefficients. A validation scheme of the gravity field models is implemented based on dynamic orbit determination that is applied in a degree-wise cumulative sense of the individual spherical harmonics. The approach is applied to real data of the Gravity Field and Steady-State Ocean Circulation (GOCE) and Gravity Recovery and Climate Experiment (GRACE) satellite missions, as well as to GRACE inter-satellite K-band ranging (KBR) data. Since the proposed scheme aims at capturing gravitational discrepancies, we consider a few deterministic empirical parameters in order to avoid absorbing part of the gravity signal that may be included in the monitored orbit residuals. The present contribution aims at a band-limited analysis for identifying characteristic degree ranges and thresholds of the various GRACE- and GOCE-based gravity field models. The degree range 100–180 is investigated based on the degree-wise cumulative approach. The identified degree thresholds have values of 130 and 160 based on the GRACE KBR data and the GOCE orbit analysis, respectively.

Near real-time BDS GEO satellite orbit determination and maneuver analysis with reversed point positioning

The Geostationary Earth Orbit (GEO) satellite is a crucial part of the BeiDou Navigation Satellite System (BDS) constellation. However, due to various perturbation forces acting on the GEO satellite, it drifts gradually over time. Thus, frequent orbit maneuvers are required to maintain the satellite at its designed position. During the orbit maneuver and recovery periods, the orbit quality of the maneuvered satellite computed with broadcast navigation ephemeris will be significantly degraded. Furthermore, the conventional dynamic Precise Orbit Determination (POD) approach may not work well, because of a lack of publicly available satellite information for modeling the thrust forces. In this paper, a near real-time approach free of thrust forces modeling is proposed for BDS GEO satellite orbit determination and maneuver analysis based on the Reversed Point Positioning (RPP). First, the station coordinates and receiver clock offsets are estimated by GPS/BDS combined Single Point Positioning (SPP) with single-frequency phase-smoothed pseudorange observations. Then, with the fixed station coordinates and receiver clock offsets, the RPP method can be conducted to determine the GEO satellite orbits. When no orbit maneuvers occur, the proposed method can obtain orbit accuracies of 0.92, 2.74, and 8.30 m in the radial, along-track, and cross-track directions, respectively. The average orbit-only Signal-In-Space Range Error (SISRE) is 1.23 m, which is slightly poorer than that of the broadcast navigation ephemeris. Using four days of GEO maneuvered datasets, it is further demonstrated that the derived orbits can be employed to characterize the behaviors of GEO satellite maneuvers, such as the time span of the maneuver as well as the satellite thrusting accelerations. These results prove the efficiency of the proposed method for near real-time GEO satellite orbit determination during maneuvers.

Reduced dynamic and kinematic precise orbit determination for the Swarm mission from 4 years of GPS tracking

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.

Comparison of accelerometer data calibration methods used in thermospheric neutral density estimation

Abstract. Ultra-sensitive space-borne accelerometers on board of low Earth orbit (LEO) satellites are used to measure non-gravitational forces acting on the surface of these satellites. These forces consist of the Earth radiation pressure, the solar radiation pressure and the atmospheric drag, where the first two are caused by the radiation emitted from the Earth and the Sun, respectively, and the latter is related to the thermospheric density. On-board accelerometer measurements contain systematic errors, which need to be mitigated by applying a calibration before their use in gravity recovery or thermospheric neutral density estimations. Therefore, we improve, apply and compare three calibration procedures: (1) a multi-step numerical estimation approach, which is based on the numerical differentiation of the kinematic orbits of LEO satellites; (2) a calibration of accelerometer observations within the dynamic precise orbit determination procedure and (3) a comparison of observed to modeled forces acting on the surface of LEO satellites. Here, accelerometer measurements obtained by the Gravity Recovery And Climate Experiment (GRACE) are used. Time series of bias and scale factor derived from the three calibration procedures are found to be different in timescales of a few days to months. Results are more similar (statistically significant) when considering longer timescales, from which the results of approach (1) and (2) show better agreement to those of approach (3) during medium and high solar activity. Calibrated accelerometer observations are then applied to estimate thermospheric neutral densities. Differences between accelerometer-based density estimations and those from empirical neutral density models, e.g., NRLMSISE-00, are observed to be significant during quiet periods, on average 22 % of the simulated densities (during low solar activity), and up to 28 % during high solar activity. Therefore, daily corrections are estimated for neutral densities derived from NRLMSISE-00. Our results indicate that these corrections improve model-based density simulations in order to provide density estimates at locations outside the vicinity of the GRACE satellites, in particular during the period of high solar/magnetic activity, e.g., during the St. Patrick's Day storm on 17 March 2015.

Satellite orbit determination using quantum correlation technology

After the presentation of second-order correlation ranging principles with quantum entanglement, the concept of quantum measurement is introduced to dynamic satellite precise orbit determination. Based on the application of traditional orbit determination models for correcting the systematic errors within the satellite, corresponding models for quantum orbit determination (QOD) are established. This paper experiments on QOD with the BeiDou Navigation Satellite System (BDS) by first simulating quantum observations of 1 day arc-length. Then the satellite orbits are resolved and compared with the reference precise ephemerides. Subsequently, some related factors influencing the accuracy of QOD are discussed. Furthermore, the accuracy for GEO, IGSO and MEO satellites increase about 20, 30 and 10 times, respectively, compared with the results from the resolution by measured data. Therefore, it can be expected that quantum technology may also bring delightful surprises to satellite orbit determination as have already emerged in other fields.

Comparison of precise orbit determination methods of zero-difference kinematic, dynamic and reduced-dynamic of GRACE-A satellite using SHORDE software

Abstract Zero-difference kinematic, dynamic and reduced-dynamic precise orbit determination (POD) are three methods to obtain the precise orbits of Low Earth Orbit satellites (LEOs) by using the on-board GPS observations. Comparing the differences between those methods have great significance to establish the mathematical model and is usefull for us to select a suitable method to determine the orbit of the satellite. Based on the zero-difference GPS carrier-phase measurements, Shanghai Astronomical Observatory (SHAO) has improved the early version of SHORDE and then developed it as an integrated software system, which can perform the POD of LEOs by using the above three methods. In order to introduce the function of the software, we take the Gravity Recovery And Climate Experiment (GRACE) on-board GPS observations in January 2008 as example, then we compute the corresponding orbits of GRACE by using the SHORDE software. In order to evaluate the accuracy, we compare the orbits with the precise orbits provided by Jet Propulsion Laboratory (JPL). The results show that: (1) If we use the dynamic POD method, and the force models are used to represent the non-conservative forces, the average accuracy of the GRACE orbit is 2.40cm, 3.91cm, 2.34cm and 5.17cm in radial (R), along-track (T), cross-track (N) and 3D directions respectively; If we use the accelerometer observation instead of non-conservative perturbation model, the average accuracy of the orbit is 1.82cm, 2.51cm, 3.48cm and 4.68cm in R, T, N and 3D directions respectively. The result shows that if we use accelerometer observation instead of the non-conservative perturbation model, the accuracy of orbit is better. (2) When we use the reduced-dynamic POD method to get the orbits, the average accuracy of the orbit is 0.80cm, 1.36cm, 2.38cm and 2.87cm in R, T, N and 3D directions respectively. This method is carried out by setting up the pseudo-stochastic pulses to absorb the errors of atmospheric drag and other perturbations. (3) If we use the kinematic POD method, the accuracy of the GRACE orbit is 2.92cm, 2.48cm, 2.76cm and 4.75cm in R, T, N and 3D directions respectively. In conclusion, it can be seen that the POD of GRACE satellite is practicable by using different strategies and methods. The orbit solution is well and stable, they all can obtain the GRACE orbits with centimeter-level precision.

Orbit determination using real tracking data from FY3C-GNOS

China is currently developing the BeiDou Navigation Satellite System, also known as BDS. The nominal constellation of BDS (regional), which had been able to provide preliminary regional positioning and navigation functions, was composed of fourteen satellites, including 5 GEO, 5 IGSO and 4 MEO satellites, and was realized by the end of 2013. Global navigation satellite system occultation sounder (GNOS) on board the Fengyun3C (FY3C) satellite, which is the first BDS/GPS compatible radio occultation (RO) sounder in the world, was launched on 23 September 2013. The GNOS instrument is capable of tracking up to 6 BeiDou satellites and more than 8GPS satellites. We first present a quality analysis using 1-week onboard BDS/GPS measurements collected by GNOS. Satellite visibility, multipath combination and the ratio of cycle slips are analyzed. The analysis of satellite visibility shows that for one week the BDS receiver can track up to 6 healthy satellites. The analysis of multipath combinations (MPC) suggests more multipath present for BDS than GPS for the CA code (B1 MPC is 0.597m, L1 MPC is 0.326m), but less multipath for the P code (B2 MPC is 0.421m, L2 MPC is 0.673m). More cycle slips occur for the BDS than for the GPS receiver as shown by the ratio of total satellites/cycle slips observed over a 24h period. Both the maximum value and average of the ratio of cycle slips based on BDS measurements is 72/50.29, which is smaller than 368/278.71 based on GPS measurements. Second, the results of reduced dynamic orbit determination using BDS/GPS code and phase measurements, standalone BDS SPP (Single Point Positioning) kinematic solution and real-time orbit determination using BDS/GPS code measurements are presented and analyzed. Using an overlap analysis, the orbit consistency of FY3C-GNOS is about 3.80cm. The precision of BDS only solutions is about 22cm. The precision of FY3C-GNOS orbit with the Helmert variance component estimation are improved slightly after the BDS observations are added for one week (October 10–16, 2013). In the three-dimensional direction, the orbit precision is respectively improved by 0.31cm. BDS code observations already allow a standalone positioning with RMS accuracy of at least 22m using BDS broadcast ephemeris, while the accuracy is at least 5m using BDS precise ephemeris. The standard deviations of differences of real-time orbit determination with the Dynamic Model Compensation using BDS/GPS, GPS, and BDS code measurements are 1.24m, 1.27m and 6.67m in three-dimensional direction, respectively. It can slightly improve convergence time for real-time orbit determination by 17s after the BDS observations are added. And it can also slightly improve the accuracy of real-time orbit determination by 0.03m. The results obtained in this paper are already rather promising.

Assessment of numerical integration methods in the context of low Earth orbits and inter-satellite observation analysis

The integration of differential equations is a fundamental tool in the problem of orbit determination. In the present study, we focus on the accuracy assessment of numerical integrators in what refers to the categories of single-step and multistep methods. The investigation is performed in the frame of current satellite gravity missions i.e. Gravity Recovery and Climate Experiment (GRACE) and Gravity Field and steady-state Ocean Circulation Explorer (GOCE). Precise orbit determination is required at the level of a few cm in order to satisfy the primary missions’ scope which is the rigorous modelling of the Earth’s gravity field. Therefore, the orbit integration errors are critical for these low earth orbiters. As the result of different schemes of numerical integration is strongly affected by the forces acting on the satellites, various validation tests are performed for their accuracy assessment. The performance of the numerical methods is tested in the analysis of Keplerian orbits as well as in real dynamic orbit determination of GRACE and GOCE satellites by taking into account their sophisticated observation techniques and orbit design. Numerical investigation is performed in a wide range of the fundamental integrators’ parameters i.e. the integration step and the order of the multistep methods.