Hu XiaoGong

Orbit determination for Chang'E-2 lunar probe and evaluation of lunar gravity models

The Unified S-Band (USB) ranging/Doppler system and the Very Long Baseline Interferometry (VLBI) system as the ground tracking system jointly supported the lunar orbit capture of both Chang’E-2 (CE-2) and Chang’E-1 (CE-1) missions. The tracking system is also responsible for providing precise orbits for scientific data processing. New VLBI equipment and data processing strategies have been proposed based on CE-1 experiences and implemented for CE-2. In this work the role VLBI tracking data played was reassessed through precision orbit determination (POD) experiments for CE-2. Significant improvement in terms of both VLBI delay and delay rate data accuracy was achieved with the noise level of X-band band-width synthesis delay data reaching 0.2–0.3 ns. Short-arc orbit determination experiments showed that the combination of only 15 min’s range and VLBI data was able to improve the accuracy of 3 h’s orbit using range data only by a 1–1.5 order of magnitude, confirming a similar conclusion for CE-1. Moreover, because of the accuracy improvement, VLBI data was able to contribute to CE-2’s long-arc POD especially in the along-track and orbital normal directions. Orbital accuracy was assessed through the orbital overlapping analysis (2 h arc overlapping for 18 h POD arc). Compared with about 100 m position error of CE-1’s 200 km×200 km lunar orbit, for CE-2’s 100 km×100 km lunar orbit, the position errors were better than 31 and 6 m in the radial direction, and for CE-2’s 15 km×100 km orbit, the position errors were better than 45 and 12 m in the radial direction. In addition, in trying to analyze the Delta Differential One-Way Ranging (ΔDOR) experiments data we concluded that the accuracy of ΔDOR delay was dramatically improved with the noise level better than 0.1 ns and systematic errors better calibrated, and the Short-arc POD tests with ΔDOR data showed excellent results. Although unable to support the development of an independent lunar gravity model, the tracking data of CE-2 provided evaluations of different lunar gravity models through POD. It is found that for the 100 km×100 km lunar orbit, with a degree and order expansion up to 165, JPL’s gravity model LP165P did not show noticeable improvement over Japan’s SGM series models (100×100), but for the 15 km×100 km lunar orbit, a higher degree-order model can significantly improve the orbit accuracy.

Centralized autonomous orbit determination of Beidou navigation satellites with inter-satellite link measurements: preliminary results

Autonomous orbit determination is the process by which the orbit parameters of navigation satellites are estimated onboard using Inter-Satellite Link (ISL) measurements. In this contribution, autonomous orbit determination experiments using ISL measurements in a centralized mode of the new-generation Beidou navigation satellites are conducted. The mathematical formulation and the processing method of the dual one-way measurements are addressed as well as the main feathers of the ISL measurements are introduced. It is concluded that the ISL ranging data are high-precision measurements. The centralized autonomous orbit determination is processed in a batch mode. The average value of ISL measurements residuals is within 1.0 cm, standard deviation of ISL measurements residuals is within 10.0 cm and the standard deviation of the estimated ISL hardware delays is within 0.2 ns. The orbital accuracy is assessed by overlap comparison, User Equivalent Ranging Error and Satellite Laser Ranging (SLR) residuals. The radial overlap differences of the autonomous orbits are less than 6.0 cm and 24 h predicted orbital radial overlap differences less than 10.0 cm. The User Equivalent Ranging Error of 24 h predicted autonomous orbits is about 0.43 m and is better than the 24 h predicted L-band orbits at the 0.76 m level. The SLR residuals for the autonomous orbits are less than 10.0 cm. The ground anchor station which observes the constellation with ISL is important to maintain the Earth-Fixed-Frame and avoid the uncertainties of the entire constellation orientation. The influence of the ground station observation time span on autonomous orbit accuracy is also discussed. Even if the cutoff elevation of the ground anchor station is less than 60°, the radial accuracy of the autonomous orbits and 24 h predicted orbits is still better than 10.0 cm and three-dimensional orbit accuracy better than 1.5 m.

Orbit determination and time synchronizationfor new-generation Beidou satellites: Preliminary results

Five new-generation Beidou Satellite Navigation System (BDS) satellites, including two satellites in the Inclined Geostationary Orbit (IGSO) and three satellites in the Medium Orbit (MEO), have completed deployment on 1st February 2016. The mission of the five new-generation satellites is to validate the new system designs and the new technologies that will successfully expand BDS’s Positioning, Navigation and Timing (PNT) services from regional to global. Responsible to keep time and frequency standards that are used to generate navigation signals, atomic clocks are important payloads onboard BDS satellites. Using data from BDS’ two-way satellite time and frequency transfer system, this paper evaluates performance of those new generation atomic clocks (Hydrogen Maser and Rubidium). Compared to the regional operational satellites onboard atomic clocks, the prediction accuracy of the new-generation onboard atomic clocks is improved. The short-term prediction error of IGSO satellites drops from 0.65 to 0.30 ns, the short-term prediction error of MEO satellites drops from 0.78 to 0.32 ns, and the media-term prediction error of IGSO and MEO satellites drops from 2.50 to 1.50 ns. Inter-Satellite Links (ISL) with measurement and data communication capabilities is one of the most important ingredient for global BDS system design. With ISL data collected for the five new-generation satellites, this paper compares differences in space signal accuracy, or orbits and clocks in broadcast navigation messages, with or without ISL contribution. Our finding confirms ISL contributes a great deal to the space signal accuracy, in particular when the satellites are not tracked by a regional network. With ISL measurements, the prediction error of MEO broadcast satellite clock parameters drops from 3 ns to within 1 ns when the MEO satellites go into the visual field once more. When ISL measurements join orbit determination as additional observation to L Band code and phase measurements, the orbit determination and prediction accuracy is greatly improved: the radial orbit overlap difference is better than 0.1 m, three-dimensional overlap difference better than 0.5 m and 24 h prediction radial orbit overlap difference is better than 0.2 m, three-dimensional overlap difference better than 1.0 m. Furthermore, with clock measurements obtained with ISL, clock estimates may be decoupled from orbital estimates during orbit determination process for better solutions. A new strategy is proposed in this paper, in which the variation of the satellite clock offsets is constrained and kept as known in orbit determination. With the new strategy, the 4 h prediction UERE drops from 1.04 to 0.82 m.

A new autonomous orbit determination algorithm based on inter-satellite ranging measurements

Due to the limitation of onboard computers relatively low storage and processing ability, current autonomous orbit determination (OD) algorithms mostly adopt sequential and distributed method for navigation satellite. Such algorithms can save computing resources, however have met the problem of filter divergence and rapid accuracy decline especially under the condition of less inter-satellite links (ISLs). This paper proposes a new rapid and stable centralized algorithm based on powerful high frequency inter-satellite measurement capability under the space/time-division multiple access (STDMA) system. This approach describes the difference between the real and long term forecasting orbit as the simple higher order polynomials, which needs no complex dynamic modeling, trajectory integration and the state transition matrix calculation, thus greatly saves computing resources. Meanwhile, this paper advances to make full use of the longitude of the ascending node information of forecast orbit so as to reduce the dependence on ground support system. Finally, we simulate the Beidou global constellation structure and ISL measurements, demonstrate the impact of the number of ISL, the noise of ISL on the performance of autonomous OD, and analyze the total amount of computation theoretically. The simulation results show that the algorithm with high stability has no error accumulation, and can run normally even with 3 ISLs, and under the condition of no less than 5 ISLs, the orbit user orbit error (URE) is about 0.9 m after 60 days autonomous operation. The total amount of calculation of the new method is theoretically one-seventh of the distributed extended Kalman filter algorithm.

Comparison between CNMC and hatch filter& its precision analysis for

Phase smoothing Pseudorange can effectively suppress the multipath effect on pseudorange, and there is no ambiguity problem, which has been widely studied and applied in the field of GNSS data processing. This paper made a systematic analysis and comparison of mathematical models for Hatch filter and CNMC phase smoothing pseudorange method. The ionsphere free combination of single frequency pseudorange through CNMC algorithm is proved equivalence with dual frequency hatch filter. On the assumption that there exists only random errors and the various measurements are independent, the accuracy expression of the CNMC method for smoothing pseudorange is deduced. Dual band hatch filter in the initialization period observation noise is bigger than CNMC smoothed pseudorange, but after a bit more than ten minutes, observation noise gradually gets better than CNMC smoothed pseudorange. BDS navigation system is qualified with serious and low-frequency characteristic for multipath errors through the comparison of OMC of double difference observation for real BDS short baseline, the conclusion that the phase smoothing pseudorange algorithm can greatly weaken the random error of original pseudorange, however, cant improve the system error is drawn. The system error of pseudorange smoothed by CNMC is at the save level with the original pseudorange, but the system error of pseudorange smoothed by double frequency hatch filter is increased. At last, relative positioning is carried through using the different kinds of phase smoothed pseudorange of that short baseline. The positioning results show that the positioning precision is improved from 0.797 m to 0.541 m using pseudorange smoothed by CNMC and the positioning precision is decreased to 1.160 m using pseudorange smoothed by hatch filter.

System error calibration for time division multiple access inter-satellite payload of new-generation Beidou satellites

The new-generation Beidou satellites constellation consists of 2 inclined geosynchronous orbit (IGSO) satellites and 3 medium orbit (MEO) satellites. The inter-satellite ranging payloads onboard provide the constellation with autonomous navigation capability. Each satellite navigates using the rest of the satellites in the constellation. The satellites perform two-way time division multiple access (TDMA) inter-satellite link (ISL) ranging using pseudo random codes. For some reasons, the global system of Beidou navigation satellite system (BDS) will still depend on its regional station net, which is not able to observe medium orbit satellites for the whole section. The ISL ranges also make it possible for BDS to obtain clock and orbit observables when the satellites cannot be seen by its limited regional stations. While ranging, the system errors of TDMA payloads on new-generation Beidou satellites must be considered, which are hard to calibrate on the ground and will affect the accuracy of inter-satellite time synchronization and orbit determination. In this paper, a calibration method of inter-satellite system error is proposed, and the application of ISL ranges on satellite-ground time synchronization is discussed. Firstly, the using strategy of ISL clock offset is discussed. The satellite-ground part obtained by L-band two-way satellite time frequency transfer (TWSTFT) is introduced and the satellite-satellite part obtained by inter-satellite link is modeled to obtain the clock and orbit observables. Broadcast ephemeris is used to decouple the inter-satellite clock offset and inter-satellite range, and the observation equations are provided. Secondly, the L-Band clock offset is used to calibrate the combined system error of each inter-satellite payload. By comparing inter-satellite clock offsets of a pair of satellites obtained by ISL with satellite-ground clock offsets of the same two satellites obtained by TWSTFT, a combination of signal transmitting delay and signal receiving delay is calibrated using least-squares estimation. The combined system error of one inter-satellite payload is fixed to solve the rank lack problem. The corrected clock offsets of ISL are then combined with clock offsets of TWSTFT to determine the satellite-ground clock offsets and calculate the predicting clock offset parameters while the satellites are out of the regional station net. The result shows that the accuracy of ISL clock offsets can reach 0.25 ns while the accuracy of TWSTFT clock offsets is 0.5 ns. The proposed method can calibrate the combined system errors and improve the accuracy of inter-satellite time synchronization. The standard deviations of a 14-day time series of combined inter-satellite system errors are less than 0.3 ns. And the calibrated ISL clock parameters are consistent with that of the L-band TWSTFT. The results of medium orbit satellite are quite remarkable: the monitoring section length increase more than 40% of the whole section length. At the beginning of the regional station net section, predicting error of satellite M1S is improved from 3.59 to 0.86 ns (RMS), predicting error of satellite M2S is improved from 1.94 to 0.57 ns (RMS). Taking into account all these results, we may reasonably come to the conclusion that inter-satellite link is a high accuracy measurement and it can improve the accuracy of clock offset prediction.

Real-time orbit determination for transfer orbit and lunar orbit of the CE-5T1 probe

In order to meet the needs of autonomous capability for the lunar exploration, an analysis of real-time orbit determination is proposed in this paper for the CE-5T1 probe by using extended Kalman filter. For the lunar-Earth transfer orbit, compared with the least squares method, the accuracy of orbit determination result using 2.5 h satellite-based GNSS data is about 30 m in position, and 1 cm/s in velocity by using EKF method, as well as the velocity of convergence is better than 1 h. For the lunar orbit, the result shows that the EKF method is able to achieve the same level accuracy to the least squares method, furthermore, through a better orbit forecast algorithm design, the Earth-based observation gap caused by the shelter of the moon has little influence to the filter accuracy of the following observation arc.

The application of the seam beam VLBI techniquefor the orbit determination of CE-5 in the rendezvous and dockingphase

CE-5 will be launched in 2017 – 2018, and it is a lunar sampling return mission. It is the first time for China to carry out the rendezvous and docking in the Moon. How to achieve rendezvous and docking successfully in the Moon is very important for CE-5 project. When the ascender is about 70 km farther away from the orbiter, the ground based tracking technique including range, Doppler and VLBI will be used to track the orbiter and the ascender. Later the ascender will approach the orbiter automatically. Here the application of the same beam VLBI for the orbit determination of the orbiter and the ascender in the long range of the rendezvous and docking phase is discussed. The same beam VLBI technique can be used to track the orbiter and the ascender simultaneously when they are in the same beam. Delta delay of the two probes can be derived, and the measurement accuracy is much higher than that of the traditional VLBI data because of the cancelation of common errors. Theoretically it can result in a more accurate relative orbit between the two probes. The simulation results show that the relative position accuracy of the orbiter and ascender can reach about 1 m in CE-5 project with delta delay data of 10 ps.