Dynamic Precise Orbit Determination Research Articles

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.

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.

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.

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.

Precise orbit determination for Jason-1 satellite using on-board GPS data with cm-level accuracy

The joint US/French Jason-1 satellite altimeter mission, launched from the Vandenberg Air Force Base on December 7, 2001, continues the time series of centimeter-level ocean topography observations as the follow-on to the highly successful T/P radar altimeter satellite. Orbit error especially the radial orbit error is a major component in the overall budget of all altimeter satellite missions, in order to continue the T/P standard of observations. Jason-1 has a radial orbit error budget requirement of 2.5 cm. In this work, two cycles (December 19, 2002 to January 7, 2003) of the Jason-1 on-board GPS data were processed using the zero-difference (ZD) dynamic precise orbit determination (POD) technique. The resulting Jason-1 orbit accuracy was assessed by comparison with the precise orbit ephemeris (POE) produced by JPL, orbit overlaps and SLR residuals. These evaluations indicate that the RMS radial accuracy is in the range of 1–2 cm.

Efficient LEO Dynamic Orbit Determination with Triple Differenced GPS Carrier Phases

The dynamic precise orbit determination of a Low Earth Orbit satellite using triple differenced GPS phases is presented in this study. The atmospheric drag parameters are estimated to compensate the incomplete atmosphere model for better precision of the orbit solution. In addition, the empirical force parameters, especially once- and twice-per-revolution components, along with the new IERS Conventions and models to compute the perturbing forces are introduced to absorb the remaining unmodelled forces. The optimal arc length for the parameterization and the data processing strategy are also tested and analyzed for the best orbit solutions. The triple differencing technique enables fast and efficient orbit estimation, because no ambiguity resolution and cycle slip detection are required. With the triple differenced ion-free GPS phase observables, the orbit and the velocity solutions for 24 hours of CHAMP are calculated; they compare with the published Rapid Science Orbit with the accuracy of 8 cm and 0·12 mm/s in 3D RMS for the orbit and the velocity, respectively, and are statistically consistent with the RSO when it is not better than 4 cm in terms of an absolute accuracy. The approach presented here provides an efficient and simple, but robust, alternative approach, while the solution's accuracy is still comparable to the double-difference results.

Pseudo-Stochastic Orbit Modeling Techniques for Low-Earth Orbiters

The Earth’s non-spherical mass distribution and atmospheric drag cause the strongest perturbations on very low-Earth orbiting satellites (LEOs). Models of gravitational and non-gravitational accelerations are utilized in dynamic precise orbit determination (POD) with GPS data, but it is also possible to derive LEO positions based on GPS precise point positioning without dynamical information. We use the reduced-dynamic technique for LEO POD, which combines the geometric strength of the GPS observations with the force models, and investigate the performance of different pseudo-stochastic orbit parametrizations, such as instantaneous velocity changes (pulses), piecewise constant accelerations, and continuous piecewise linear accelerations. The estimation of such empirical orbit parameters in a standard least-squares adjustment process of GPS observations, together with other relevant parameters, strives for the highest precision in the computation of LEO trajectories. We used the procedures for the CHAMP satellite and found that the orbits may be validated by means of independent SLR measurements at the level of 3.2 cm RMS. Validations with independent accelerometer data revealed correlations at the level of 95% in the along-track direction. As expected, the empirical parameters compensate to a certain extent for deficiencies in the dynamic models. We analyzed the capability of pseudo-stochastic parameters for deriving information about the mismodeled part of the force field and found evidence that the resulting orbits may be used to recover force field parameters, if the number of pseudo-stochastic parameters is large enough. Results based on simulations showed a significantly better performance of acceleration-based orbits for gravity field recovery than for pulse-based orbits, with a quality comparable to a direct estimation if unconstrained accelerations are set up every 30 s.

Satellite dynamics of the CHAMP and GRACE leos as revealed from space- and ground-based tracking

The Low Earth Orbiters (LEOs) CHAMP and GRACE are precisely and continuously tracked by means of space-borne GPS. In case of the GRACE mission the distance between the twin satellites is also measured by a micrometer-precision ranging system. Thus the satellite dynamics are densely recorded and show up in the tracking residuals of the various data types in a dynamic Precise Orbit Determination (POD) solution. The signatures in the residuals time series are mainly caused by mis-modeling of the gravity field because the non-conservative forces such as atmospheric drag are taken care of by the on-board accelerometers. In addition all satellites carry laser retro-reflectors for centimeter accuracy range measurements from the ground. Examples of gravity signals in the residuals are displayed and discussed in view of the gravity field recovery and the POD tasks.