Autonomous orbit determination is the ability of navigation satellites to estimate the orbit parameters on-board using inter-satellite link (ISL) measurements This study mainly focuses on data processing of the ISL measurements as a new measurement type and its application on the centralized autonomous orbit determination of the new-generation Beidou navigation satellite system satellites for the first time The ISL measurements are dual one-way measurements that follow a time division multiple access (TDMA) structure The ranging error of the ISL measurements is less than 025 ns This paper proposes a derivation approach to the satellite clock offsets and the geometric distances from TDMA dual one-way measurements without a loss of accuracy The derived clock offsets are used for time synchronization, and the derived geometry distances are used for autonomous orbit determination The clock offsets from the ISL measurements are consistent with the L-band two-way satellite, and time–frequency transfer clock measurements and the detrended residuals vary within 05 ns The centralized autonomous orbit determination is conducted in a batch mode on a ground-capable server for the feasibility study Constant hardware delays are present in the geometric distances and become the largest source of error in the autonomous orbit determination Therefore, the hardware delays are estimated simultaneously with the satellite orbits To avoid uncertainties in the constellation orientation, a ground anchor station that “observes” the satellites with on-board ISL payloads is introduced into the orbit determination The root-mean-square values of orbit determination residuals are within 100 cm, and the standard deviation of the estimated ISL hardware delays is within 02 ns The accuracy of the autonomous orbits is evaluated by analysis of overlap comparison and the satellite laser ranging (SLR) residuals and is compared with the accuracy of the L-band orbits The results indicate that the radial overlap differences between the autonomous orbits are less than 150 cm for the inclined geosynchronous orbit (IGSO) satellites and less than 100 cm for the MEO satellites The SLR residuals are approximately 150 cm for the IGSO satellites and approximately 100 cm for the MEO satellites, representing an improvement over the L-band orbits

Initial results of centralized autonomous orbit determination of the new-generation BDS satellites with inter-satellite link measurements

Various types of onboard atomic clocks such as rubidium, cesium and hydrogen have different frequency accuracies and frequency drift rate characteristics. A passive hydrogen maser (PHM) has the advantage of low-frequency drift over a long period, which is suitable for long-term autonomous satellite time keeping. The third generation of Beidou Satellite Navigation System (BDS3) is equipped with PHMs which have been independently developed by China for their IGSO and MEO experimental satellites. Including Galileo, it is the second global satellite navigation system that uses PHM as a frequency standard for navigation signals. We briefly introduce the PHM design at the Shanghai Astronomical Observatory (SHAO) and detailed performance evaluation of in-orbit PHMs. Using the high-precision clock values obtained by satellite-ground and inter-satellite measurement and communication systems, we analyze the frequency stability, clock prediction accuracy and clock rate variation characteristics of the BDS3 experimental satellites. The results show that the in-orbit PHM frequency stability of the BDS3 is approximately 6 × 10−15 at 1-day intervals, which is better than those of other types of onboard atomic clocks. The BDS3 PHM 2-, 10-h and 7-day clock prediction precision values are 0.26, 0.4 and 2.2 ns, respectively, which are better than those of the BDS3 rubidium clock and most of the GPS Block IIF and Galileo clocks. The BDS3 PHM 15-day clock rate variation is − 1.83 × 10−14 s/s, which indicates an extremely small frequency drift. The 15-day long-term stability results show that the BDS3 PHM in-orbit stability is roughly the same as the ground performance test. The PHM is expected to provide a highly stable time and frequency standard in the autonomous navigation case.

Performance of the BDS3 experimental satellite passive hydrogen maser

Time synchronization of new-generation BDS satellites using inter-satellite link measurements

A major outstanding problem for many quantum clock synchronization protocols is the hidden assumption of a common phase reference between the parties to be synchronized. In general, the definition of the quantum states between two parties do not have consistent phase definitions, which can lead to an unknown systematic error. We show that despite prior arguments to the contrary, it is possible to remove this unknown phase via entanglement purification. This closes the loophole for entanglement based quantum clock synchronization protocols, which is a non-local approach to synchronize two clocks independent of the properties of the intervening medium. Starting with noisy Bell pairs, we show that the scheme produces a singlet state for any combination of (i) differing basis conventions for Alice and Bob; (ii) an overall time offset in the execution of the purification algorithm; and (iii) the presence of a noisy channel. Error estimates reveal that better performance than existing classical Einstein synchronization protocols should be achievable using current technology. Quantum mechanics can be used to synchronise the clocks of two distant parties by using the non-local properties of entanglement. It was shown in 2000 that, if two parties share entangled qubit pairs, performing coordinated quantum operations allows them to detect systematic errors in their measurements of time. Unfortunately, performing the correct manipulations already implicitly requires some degree of synchronisation. Ebubechukwu Ilo-Okeke and colleagues from New York University Shanghai and Louisiana State University show that this can be resolved using quantum purification, which concentrates the entanglement from many qubits into states with higher entanglement. They demonstrate that when the parties are out of sync the purification generates states that account for the discrepancy and then can be used for synchronisation. If fully developed, the quantum synchronization scheme could outperform existing classical methods.

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Remote quantum clock synchronization without synchronized clocks

We derive orbit and clock errors for BeiDou satellites from March 1, 2013, to September 30, 2016 by comparing broadcast ephemerides with the precise ephemerides produced by Wuhan University. The broadcast ephemerides are pre-processed to filter out the “data-logging” errors, and a robust estimation is subsequently implemented for removing the time-varying common timescale bias between the broadcast and precise clocks. To obtain the nominal SISEs (Signal-In-Space Errors), the SIS (Signal-In-Space) outliers are excluded according to the standard of SIS integrity. The long-term satellite clock behavior reveals that for GEO, IGSO and MEO satellites, each category of satellites has its inter-category clock consistency, and the clocks of MEO as well as the clocks of IGSO satellites have better inter-category consistency than that of GEO satellites. Between different categories, GEO satellite clocks have been more divergent from IGSO satellite clocks since May 2014. The larger orbit errors, resulting in approximately 1–2 m orbit-only UREs (User Range Errors), periodically occur for all satellites every half year when the satellites are in eclipse period. For the GEO and IGSO satellites, several larger orbit errors may be caused by the effect of satellite maneuvering, resulting in 2–3 m orbit-only UREs. Most satellite clocks have a nonzero mean, and all MEO satellite clocks have a positive mean of approximately 1.0 m, whereas the IGSO satellite clocks have a negative mean at the same level. For the GEO satellites, the various means indicate that the clocks are divergent from one to another. The clock standard deviation of 1 m is achieved by all satellites except for C03. Near-zero means are obtained in along-track, cross-track and radial errors for the IGSO and MEO satellites but not for the GEO satellites. The average RMSs (Root Mean Square) of approximately 0.8, 1.7 and 2.0 m are obtained for the orbit-only UREs, global-average UREs and worst-UREs, respectively, for the constellation as a whole. The RMSs of clock errors for GEO, IGSO and MEO are 1.8, 1.4 and 1.3 m, respectively. Due to a nearly-static observation geometry, the GEO satellites always have the worst SISE performance, and as a result, they degrade the overall SISE statistical characterization. The analysis of URE and broadcast URA (User Range Accuracy) indicates that the broadcast URA of 2.0 m throughout is slightly optimistic. The unchanging URA of 2.0 m may not be able to describe adequately the accuracy of UREs. Instead, the upper-bound URA of 2.4 m is recommended to users. The cross-correlation analysis results show that there is a significant positive correlation between along-track errors and radial errors, whereas radial errors are not evidently correlated to clock errors as they are with GPS.

Long-term behavior and statistical characterization of BeiDou signal-in-space errors

A two-way satellite time and frequency transfer (TWSTFT) device equipped in the BeiDou navigation satellite system (BDS) can calculate clock error between satellite and ground master clock. TWSTFT is a real-time method with high accuracy because most system errors such as orbital error, station position error, and tropospheric and ionospheric delay error can be eliminated by calculating the two-way pseudorange difference. Another method, the multi-satellite precision orbit determination (MPOD) method, can be applied to estimate satellite clock errors. By comparison with MPOD clock estimations, this paper discusses the applications of the BDS TWSTFT clock observations in satellite clock measurement, satellite clock prediction, navigation system time monitor, and satellite clock performance assessment in orbit. The results show that with TWSTFT clock observations, the accuracy of satellite clock prediction is higher than MPOD. Five continuous weeks of comparisons with three international GNSS Service (IGS) analysis centers (ACs) show that the reference time difference between BeiDou time (BDT) and golbal positoning system (GPS) time (GPST) realized IGS ACs is in the tens of nanoseconds. Applying the TWSTFT clock error observations may obtain more accurate satellite clock performance evaluation in the 104 s interval because the accuracy of the MPOD clock estimation is not sufficiently high. By comparing the BDS and GPS satellite clock performance, we found that the BDS clock stability at the 103 s interval is approximately 10−12, which is similar to the GPS IIR.

XiuQiang Gong

Papers

Applications of two-way satellite time and frequency transfer in the BeiDou navigation satellite system