Five new-generation BeiDou-3 experimental satellites, called BeiDou-3e, have been launched into inclined geosynchronous orbit (IGSO) and medium orbit (MEO) since March 2015. In addition to newly designed signals and intersatellite links, different satellite buses, updated rubidium atomic frequency standards (RAFSs), and new passive hydrogen masers (PHMs) have been used. Using 15 stations, mainly in the Asia–Pacific region, we determined orbits and clock for both the BeiDou-3e and the regional BeiDou-2 satellites using the Extend CODE (Center for Orbit Determination in Europe) Orbit Model (ECOM). The orbit consistency, indicated by 3D orbit boundary discontinuity, is 50–70 and 40–60 cm for BeiDou-3e IGSO and MEO satellites, respectively, and better than 15 cm in radial component. Satellite laser ranging (SLR) validation gives about 17 and 10 cm for BeiDou-3e IGSO and MEO satellites. The BeiDou-3e satellites orbits show slightly better performance than the BeiDou-2 satellites as indicated by SLR. However, errors depending on the sun elongation angle were identified in SLR residuals for the BeiDou-3e IGSO C32 satellite, while such errors did not exist for BeiDou-2 IGSO/MEO and BeiDou-3e MEO satellites. No orbit accuracy degeneration for BeiDou-3e IGSO and MEO satellites was observed when the elevation angle (β angle) of the sun above the orbital plane was between − 4° and + 4°. In that case, the BeiDou-2 IGSO and MEO satellites are in orbit normal (ON) mode. An analysis of the yaw attitude identified that BeiDou-3e satellites did not use the ON mode, but experienced midnight- and noon-point maneuvers when the β angle is approximately between − 3° and + 3°. Compared with BeiDou-2 satellites, the onboard clocks of the BeiDou-3e IGSO satellites showed dramatic improved performance. The stability of BeiDou-3e IGSO satellites can be compared to the latest type of RAFSs employed onboard the GPS IIF satellites as well as the PHMs used onboard the Galileo satellites.

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Precise orbit and clock determination for BeiDou-3 experimental satellites with yaw attitude analysis

The BDS-3 preliminary system was declared functional on December 27, 2018. It enables positioning service on a global scale. This study conducts a comprehensive investigation of the BDS-3 global service from the perspective of positioning, including satellite ephemeris, benefits of the new BDS-3 satellites, and the new signal effect on three positioning modes: single-point positioning (SPP), precise-point positioning (PPP) and real-time kinematic (RTK). First, the broadcast and precise ephemeris availabilities of 18 BDS-3 Medium Earth orbit (MEO) satellites from January to June 2019 are investigated. Due to the shorter operational timespans of BDS-3 satellites, their broadcast and precise ephemeris files retrieved from Multi-GNSS Experiment (MGEX) have 1.2–19.4% and 10.9–13.77% discontinuities, respectively, while the discontinuities of BDS-2 satellite broadcast and precise ephemeris are only 0.1 and 2.1%. Second, the BDS-3 satellite orbit accuracies and clock precisions are significantly improved, i.e., below 0.5 m and 1.82 ns compared to 2 m and 2.91 ns for BDS-2 because of the inter-satellite links of BDS-3 satellites. Third, an average of 4.4–5.7 BDS satellites can be observed at stations located in North/South America, and 8.9 for the European station FFMJ located in Germany after the BDS-3 global system announcement. As a result, continuous positioning is feasible in these regions. As to four Asia–Pacific stations, their SPP accuracies are improved by 12.1–60.2% compared to those of the BDS-2-only solution. Meanwhile, the PPP and RTK convergence times of Asia–Pacific stations are also shortened. Last but not least, the new B1C signal does not bring convincing improvement to PPP and RTK positioning accuracies in this study, due to the limited number of available B1C new signals at this time.

Assessment of BDS-3 global positioning service: ephemeris, SPP, PPP, RTK, and new signal

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

Since November 2017, eight BeiDou global navigation system (BDS-3) satellites equipped with Ka-band inter-satellite link (ISL) payloads have been launched into medium earth orbit. We present the precise orbit determination (POD) for BDS-3 satellites using both L-band satellite-ground and Ka-band ISL observations. The satellite-ground tracking data are collected from the international GNSS Monitoring and Assessment System stations. The data period is DOY (day of year) 127---156, 2018. The BDS-3 ISL measurements are described by a dual one-way observation model. After transforming the dual one-way observations to the same epoch, clock-free and geometry-free observables can be obtained by the addition and subtraction of dual one-way observations. Using the geometry-free observables, the ISL measurement noise is analyzed and confirmed to be less than 10?cm. Using the clock-free observables and ground tracking data, the precise orbits are determined together with combined ISL hardware delays. For the estimates of hardware delays, the mean STD is 0.08?ns. For the satellite orbits, the ground-only POD solutions are also computed for comparison. When using 16 globally distributed ground stations, the addition of the ISLs improves the POD performance. For example, the 3D RMS of orbit overlap differences is reduced from 15.9?cm to 9.2?cm, yielding an improvement of 42% compared to ground-only POD. When only 6 stations in China are used for POD, the addition of ISLs enables the 3D RMS to be reduced from 85.4?cm to 14.8?cm with a greater improvement of 83%.

Precise orbit determination for BDS-3 satellites using satellite-ground and inter-satellite link observations

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.

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

The BeiDou Navigation Satellite System is expected to provide a global positioning and navigation service by 2020. To achieve this goal, the new-generation navigation satellites that have been launched since March 2015 are equipped with inter-satellite links (ISLs), with the objective of testing new navigation signals and the ISLs themselves. Using these new-generation navigation satellites and several ground facilities in China, a combined orbit determination experiment was carried out during August 2016. The orbit mechanical model, orbit determination method, and accuracy evaluation method used in this experiment are presented here. The accuracy of the combined orbit determination method is evaluated, and the performance-related improvements resulting from the ISLs are analyzed. The performance of orbit determination has been increased about 37–76% for different satellites in orbit-only signal-in-space range error (orbit-only SISRE).

Globalization highlight: orbit determination using BeiDou inter-satellite ranging measurements

Inter-satellite links improve the performance of global navigation satellite systems (GNSSs) via communication and ranging. When there are limited facilities and links, a key challenge involves assigning links for the downlink of telemetry data in time and effective ranging. We describe this problem and propose a corresponding link scheduling method consisting of three steps. A genetic algorithm was used to identify optimal downlink routes for all non-visible satellites in the first step. The optimization of minimizing timeslot delays usually has multiple optimal routes. The optimal routes were selected to expand to a superframe’s length, which constituted a downlink route scheme for the superframe. The position dilution of precision (PDOP) of ranging links was limited through satellite selection in the second step. Four visible satellites with minimal PDOP were selected and scheduled with idle timeslots. The PDOP decreased with increasing links, and its upper limit was therefore determined by the selected satellites. The final step was to schedule idle timeslots for visible satellites unless the requested link number was met. To test the feasibility of the proposed method, the link assignment was implemented for 10,080 superframes of a typical GNSS constellation. The final link assignment enabled all satellites to transmit telemetry data back to the facility with a delay of no more than 4 timeslots (with one ground facility tracking), and more than 10 links were obtained with PDOPs approaching the minimum. These scheduling results confirm the utility of the method.

Inter-satellite communication and ranging link assignment for navigation satellite systems

The introduction of an intersatellite link, also called a crosslink, is considered a promising technique for improving the reliability and integrity of a global navigation satellite system. As one of the most rapidly developing satellite navigation systems, the BeiDou system launched from March 2015 to February 2016 an in-orbit validation constellation that includes two inclined geosynchronous orbit satellites and three medium earth orbit satellites equipped with an intersatellite link in the Ka band. We modeled the intersatellite measurements of BeiDou and evaluated the ranging performance of the intersatellite link based on the analysis of in-orbit measurement data. We used both residual analysis and external data comparison to assess the data. The results show that the ranging precision of the BeiDou intersatellite link is within 10 cm and is determined mainly by the thermal noise of the receiver. Moreover, the drift rate of the group delay of the transceiver channel is within 1 cm per day.

In-orbit performance assessment of BeiDou intersatellite link ranging

The number and scope of space applications of global navigation satellite systems have grown significantly. However, the availability and the navigation performance for a spacecraft operating within and beyond the space services volume are different from those of terrestrial service volume users. To effectively evaluate the space service performance of navigation satellite systems, we present the calculation method of signal-in-space ranging error for space users. Considering the geometric visibility and the constraints of the lowest carrier-to-noise ratio, we analyze the feasibility of receiving the signal transmitted from the different off-nadir angles and obtain the coverage area of navigation satellite. Then, the relationship between the weighting factors of ephemeris errors and the orbital height of the user spacecraft is analyzed. Finally, the statistics characteristic of signal-in-space ranging error of typical navigation satellites is presented. The results show that the signal-in-space ranging error increases first and then decreases as the orbital height of the user increases. Generally, when the user's orbital height is slightly higher than the orbital height of the navigation satellite, the signal-in-space ranging error reaches a maximum. In particular, due to the significant horizontal orbit error, global signal-in-space ranging error of the Beidou geostationary orbits satellites increase significantly compared with the user located on the ground. Therefore, the impact of user height changes on the statistical properties of signal-in-space ranging error cannot be ignored when evaluating the navigation performance of the space user.

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Statistical Characterization of GNSS Signal-in- Space Ranging Errors for the User Within and Beyond Space Service Volume

The invention discloses a method for building a satellite navigation system test verification and test assessment mathematic model. The method comprises the steps of S1: driven by function and performance verification/assessment of verification, design, construction and application stages of a satellite navigation system, determining a verification/test and assessment project of the satellite navigation system, and forming a verification/test and assessment method for a to-be-tested item; S2: according to driving data, determining a satellite navigation physical system or entity generating the driving data; performing abstraction on a satellite navigation physical system entity/function to form a system level simulation model, wherein the model is a basis of a satellite navigation system test verification and test assessment mathematic model system; and S3: after a satellite navigation system verification/test and assessment model and the system level simulation model are built, performing self-closing verification, and performing abstraction on self-closing verification item and method to form a self-closing verification model. The method has the advantages of simple principle, easy realization, good effect and the like.

Yifan Zhou

Papers

Globalization highlight: orbit determination using BeiDou inter-satellite ranging measurements

Inter-satellite communication and ranging link assignment for navigation satellite systems

In-orbit performance assessment of BeiDou intersatellite link ranging

Statistical Characterization of GNSS Signal-in- Space Ranging Errors for the User Within and Beyond Space Service Volume

Method for building satellite navigation system test verification and test assessment mathematic model