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Precise Point Positioning (PPP) requires precise products, including high-accuracy satellite orbit and clock parameters. It is impossible to obtain an orbit solution that is sufficiently accurate for PPP services with a regional tracking network; therefore, satellite orbits are usually estimated by a global tracking network with a large number of ground stations. However, it is expensive to build globally distributed stations. Fortunately, BeiDou-3 satellites carry an Inter-Satellite Link (ISL) payload, which can track the whole arc of the BeiDou-3 satellites and enhance the orbit determination accuracy with regional ground stations. In this contribution, a novel orbit determination strategy for BeiDou-3 PPP is proposed, in which the BeiDou-3 satellite orbits are enhanced by the ISL. First, the generation of precise satellite products is demonstrated in detail. In addition, the products are assessed by satellite laser ranging (SLR) residuals and overlap comparisons. Moreover, the products are used for receivers in mainland China to carry out the static and kinematic modes to research the PPP performance of BeiDou-3′s 3IGSO/24MEO constellation. The SLR validations of the satellite orbits demonstrate an accuracy better than 0.1 m in the radial component, and the orbit overlap comparisons show accuracies of 0.016 m in the radial component, 0.088 m in the along-track component and 0.087 m in the cross-track component. The Standard Deviation (STD) in the differences in overlapping arcs for the estimated satellite clocks is approximately 0.10 ns. The static PPP results demonstrate that the error in both the horizontal and vertical components is smaller than 10 cm after 30 minutes of convergence. After 24 hours of convergence, the errors are 0.70 cm, 0.63 cm and 1.99 cm for the north, east and up components, respectively. The kinematic PPP experiment illustrates that the Root Mean Square (RMS) position errors in the north, east and up components are approximately 3.23 cm, 5.27 cm and 8.64 cm, respectively, after convergence. The obtainable positioning and convergence performances are comparable to those using products generated by global tracking networks.

Satellite attitude modes and antenna phase center variations have a great influence on the Precise Orbit Determination (POD) of Low Earth Orbit satellites (LEOs). Inaccurate information about spacecraft attitude, phase center offsets and variations in the POD leads to orbital error. The Jason-3 satellite experienced complex attitude modes which are fixed, sinusoidal, ramp-up/down and yaw-flip. Therefore, it is necessary to properly construct the attitude model in the process of POD especially when there is no external attitude data. For the antenna phase center correction, the PCO which is the deviation between Antenna Reference Point (ARP) and Mean Antenna Phase Center (MAPC) usually can be calibrated on the ground accurately, but the PCV which is the deviation between Instantaneous Antenna Phase Center (IAPC) and Mean Antenna Phase Center (MAPC) will change greatly with the change of space environment. Residual approach can be used to estimate the receiver PCV map. In this paper, we collected the on-board GPS data of Jason-3 satellite from January 2019 and analyzed the impacts of PCV and spacecraft attitude on the orbit accuracy by performing the reduced-dynamic POD. Compared with the reference orbit released by the Centre National d’Études Spatiales (CNES), using the PCV map can reduce the Root Mean Square (RMS) of orbit differences in the Radial (R), Along-track (T), Cross-track (N) and 3D direction about 0.3, 1.0, 0.9, and 1.4 mm. Based on the estimated PCV map, the orbit accuracy in R, T, N and 3D direction is 1.24, 2.81, 1.17, and 3.29 cm respectively by using the measured attitude data. When using the attitude model, the orbit accuracy in R, T, N and 3D directions is 1.60, 3.54, 1.33, and 4.13 cm, respectively. The results showed that the combination of measured attitude data and modeled PCV map can obtain the better orbit solution. It is essential to build a corresponding model in high-precision orbit determination, when there is no attitude data and PCV map.

The next-generation satellite-based augmentation system (SBAS) will follow the dual-frequency multi-constellation (DFMC) protocol and broadcast satellite clock-ephemeris corrections and integrity information via GPS L5-like signals to improve the accuracy and integrity for GNSS dual-frequency users. BeiDou Navigation Satellite System (BDS)-3 B1C/B2a dual-frequency users will obtain a higher positioning accuracy using DFMC clock-ephemeris corrections. This paper focuses on an approach for the generation of DFMC SBAS corrections and its preliminary results. Analyzing the signal-in-space ranging error characteristics of BDS-3 satellites reveals that it is impossible to obtain orbits that are more accurate than the broadcast orbits using regionally distributed SBAS monitoring stations. Therefore, a novel DFMC SBAS correction generation approach for BDS-3 satellites is proposed in which only clock offset corrections are calculated. The effectiveness of the proposed approach is validated using measurements from mainland China. By using clock corrections only, B1C/B2a dual-frequency users can obtain the best accuracy. The results of the BDS-3 B1C/B2a dual-frequency positioning experiment show that the user equivalent ranging error is reduced from 0.59 m to 0.37 m with clock corrections but is reduced to only 0.43 m with the addition of clock-ephemeris corrections. With clock corrections only, the 95% positioning errors are reduced from 3.57 m to 1.53 m and from 3.79 m to 2.24 m in the horizontal and vertical directions, respectively, indicating a 48% reduction in positioning errors compared to users without SBAS corrections; however, the error reduction is only 40% with clock-ephemeris corrections.

To satisfy the demands of civil aviation organizations and other users of satellite navigation systems for high-precision and high-integrity service performance, many countries and regions have established satellite-based augmentation systems (SBAS) referring to the Radio Technical Commission for Aeronautics (RTCA) service standards and agreements. The BeiDou SBAS (BDSBAS) provides both single-frequency service, which augments Global Positioning System (GPS) L1 C/A signal, and dual-frequency multi-constellation (DFMC) service, which augments BeiDou Navigation Satellite System (BDS) B1C and B2a dual frequency signals presently, meeting the requirements of the RTCA DO-229D protocol and the SBAS L5 DFMC protocol requirements, respectively. As one of the main error sources, the pseudorange bias errors of BDSBAS monitoring receivers were estimated and their effect on the performance of the BDSBAS service was analyzed. Based on the user algorithms of SBAS differential corrections and integrity information, the service accuracy, integrity, and availability of the BDSBAS were evaluated using real observation data. The results show that the maximum of monitoring receiver pseudorange bias errors between L1P and L1P/L2P can reach 1.57 m, which become the most important errors affecting the performance of the BDSBAS service. In addition, the results show that the pseudorange bias of GPS BlockIII is the smallest, while that of GPS BlockIIR is the largest. Compared with the positioning accuracy of the open service of the core constellation, the positioning accuracy of the BDSBAS service can be improved by approximately 47% and 36% for the RTCA service and DFMC service, respectively. For RTCA services, the protection limit (PL) calculated with the integrity information can 100% envelop the positioning error (PE) and no integrity risk event is detected. The service availability of BDSBAS for APV-I approach is approximately 98.8%, which is mainly affected by the availability of ionospheric grid corrections in the service marginal area. For DFMC service, the integrity risk is not detected either. The service availability for CAT-I approach is 100%. Improving the availability of ionospheric grid corrections is one of the important factors to improve service performance of BDSBAS RTCA service.

The Ka-band dual one-way measurements from Inter-Satellite Link (ISL) devices equipped on the third-generation Beidou Navigation Satellite System (BDS3) follow a time division multiple access (TDMA) structure and can calculate inter-satellite and satellite-ground clock offsets. L-band two-way satellite time and frequency transfer (TWSTFT) is also applied for time synchronization between satellites and ground master. We focus on a full-ISL clock offset estimation and prediction algorithm that estimates all satellite clock parameters simultaneously utilizing ISL clock observations and also synchronizes the constellation to the system time in Beidou Time (BDT) using Ka-band satellite-ground clock observations. We discuss the applications of this algorithm by assessing the clock performance of all BDS3 satellites equipped with a passive hydrogen maser (PHM) or rubidium atomic clock. After investigating the proper prediction model for each satellite, we use the full-ISL algorithm for 24-h clock predictions. The constant hardware delays in the ISL measurements are calibrated by comparing the derived clock parameters with TWSTFT measurements; the full-ISL clock products show high accuracy and continuity. The BDS3 PHMs and rubidium clocks both have a small clock rate drift of 10–20 s/s2. The frequency stability of the BDS3 PHMs and some rubidium clocks is approximately 6–9 × 10–15 at 1-day intervals. A linear model is suitable for these small-drift clocks, while a quadratic model is essential for the other rubidium clocks. Applying the full-ISL clock prediction method improves the RMS of the 24 h prediction error from 0.88 to 0.75 ns for PHMs and from 2.62 to 1.64 ns for rubidium clocks. The estimated ISL hardware delay STDs are less than 0.2 ns, and the prediction errors evaluated with TWSTFT clock observations are similar to those evaluated with Ka-band clock observations.

The third generation of the BeiDou navigation satellite system (BDS-3) is a global navigation system, and is expected to be in full operation by 2020. High-precision orbits are a precondition for BDS-3 to provide a highly accurate service, which needs a global tracking and monitoring capability for the operational satellites. However, it is difficult for BDS to construct global ground monitoring stations. Fortunately, Ka-band Inter-Satellite Link (ISL) antennae fitted to the BDS-3 satellites can be used to extend the visible arc of the Medium Earth Orbit (MEO) satellites and to enhance the ground stations for orbit determination. This paper analyses the ISL-enhanced orbit determination for eight BDS-3 satellites, using the data from ten Chinese domestic stations and 13 international Global Navigation Satellite System (GNSS) Monitoring and Assessment System (iGMAS) overseas stations. The results show that the Three-Dimensional (3D) position Root Mean Square (RMS) error of the Overlapping Orbit Differences (OODs) is approximately 1 m when only ten regional stations are used. When the ISL measurements are added, the 3D position RMS error is decreased to 0·5 m, and the accuracy of the 24-hour orbit prediction can also be improved from 2 m to 0·7 m, which is even better than that of the orbits determined using globally distributed stations. It can be expected that with the subsequent launch of BDS-3 satellites and the increasing number of ISLs, the advantage of the ISL enhanced orbit determination will become more significant.

The Chinese BeiDou Navigation Satellite System (BDS) is accelerating its development and has been applied in various fields. Compared with other satellite navigation systems in the world, BDS has many unique features such as multiservices integrated with Radio Determination Satellite Service (RDSS), Radio Navigation Satellite Service (RNSS), and Satellite-Based Augmentation Service (SBAS), a mixed-orbit satellite constellation, and flexible navigation messages, etc. This paper presents the distinctive innovative designs as well as processing strategies in BDS. First, this paper introduces the characteristics of BeiDou navigation messages broadcast by the hybrid constellation of satellites in Geostationary Earth Orbit (GEO), Inclined Geo-Synchronization Orbit (IGSO), and Medium Earth Orbit (MEO). Next, the innovative design and operation of the control segment are discussed. Finally, highlights of the unique usage algorithm of the BDS navigation message information are presented, such as the BDS satellite clock correction and TGD parameters, satellite ephemeris and almanac, and ionospheric delay parameters.

The Tianping-1B is a 20-kg low earth orbit nanosatellite with a commercial multi-GNSS receiver based on a microelectromechanical system. This receiver collects concurrent code and phase dual-frequency measurements from the global positioning system (GPS) and the second and third generations of the BeiDou Global Navigation Satellite System (i.e., BDS-2 and BDS-3). However, BDS-3 signals with pseudorandom noise code numbers greater than 32 cannot be received. In this study, onboard GPS and BDS measurements from Tianping-1B are collected for days 133–147 of 2019. The performance of the onboard BDS-3 measurements is analyzed, and the potential of the BDS-3-based precise orbit determination (POD) for Tianping-1B is assessed. The carrier-to-noise-density ratio of the BDS-3 is higher than that of the BDS-2 and approaches that of the GPS. The BDS-3 has a smaller code multipath error than the BDS-2 and the GPS and therefore a higher quality of code measurements. The results of the overlap comparison show a GPS-based orbit consistency below 3.5 cm in three dimensions (3D) and below 1.2 cm in the radial direction. The mean of satellite laser ranging validation residual RMS is 1.7 cm. The orbit obtained using onboard BDS measurements is assessed using the GPS-based orbit as a reference: The mean 3D root mean square (RMS) difference between the BDS-3-only-based POD and the reference orbit is 4.57 cm. Thus, a sub-dm-level orbit can be achieved using only onboard BDS-3 measurements. A POD with slightly higher precision than the BDS-3-only-based POD is obtained using both BDS-3 and BDS-2 measurements, using higher weights for the BDS-3 data than the BDS-2 data. Then, the combined BDS-3/GPS POD is performed: The RMS difference between this joint orbit and the GPS-based orbit is 1 cm in 3D. This study can be used as a reference for the development of BDS-3 based POD, which will approve in accuracy and precision upon completion of BDS-3.

On December 27, 2018, the basic system of the third-generation BeiDou navigation satellite system (BDS-3) completed the deployment of its constellation of 18 MEO networking satellites as well as the construction of the operation control system (OCS) and began to provide basic navigation services to users worldwide. Compared with BDS-2, BDS-3 aims to offer users better navigation signals and higher precision with a series of new technologies. For example, the spaceborne atomic clock of BDS-3 is upgraded for higher performance, the Ka-band inter-satellite link is adopted for inter-satellite ranging and communication, and new B1C and B2a signals are broadcast in addition to B1I and B3I signals (compatible with BDS-2). In addition, a 9-parameter model based on a spherical harmonic function is employed for ionospheric delay corrections. Using the observation data from 18 satellites of the basic system, this paper conducts a comprehensive evaluation of the pseudorange measurement characteristics, signal-in-space (SIS) accuracy of navigation messages and global service capability of BDS-3. The results indicate that the pseudorange measurement multipath effect and observation noise of BDS-3 satellites are better than those of BDS-2; additionally, with the support of inter-satellite links, the user range error (URE) of the BDS-3 satellite broadcast ephemeris is better than 10 cm, the precision of the broadcast clock parameter is better than 1.5 ns, and the SIS accuracy is better than 0.6 m overall. Different from the traditional Klobuchar model, the BeiDou global broadcast ionospheric delay correction model (BDGIM) can provide ionospheric delay corrections better than 70% for worldwide single-frequency users. The service capability evaluation of the basic system consists mainly of the accuracy improvement of the B1I and B3I signals according to BDS-2 as well as the global positioning accuracy of the new signals. These results prove that the BDS-3 basic system has achieved the design goal; that is, both the horizontal and the vertical global positioning accuracies are better than 10 m (95%). In the future, 6 MEO satellites as well as 3 GEO satellites and 3 IGSO satellites for regional enhancement purposes will be deployed for full operation; consequently, BDS-3 will definitely provide a higher SIS accuracy and better service capability.

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 0.25 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 0.5 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 10.0 cm, and the standard deviation of the estimated ISL hardware delays is within 0.2 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 15.0 cm for the inclined geosynchronous orbit (IGSO) satellites and less than 10.0 cm for the MEO satellites. The SLR residuals are approximately 15.0 cm for the IGSO satellites and approximately 10.0 cm for the MEO satellites, representing an improvement over the L-band orbits.

Autonomous satellite navigation is based on the ability of a Global Navigation Satellite System (GNSS), such as Beidou, to estimate orbits and clock parameters onboard satellites using Inter-Satellite Link (ISL) measurements instead of tracking data from a ground monitoring network. This paper focuses on the time synchronization of new-generation Beidou Navigation Satellite System (BDS) satellites equipped with an ISL payload. Two modes of Ka-band ISL measurements, Time Division Multiple Access (TDMA) mode and the continuous link mode, were used onboard these BDS satellites. Using a mathematical formulation for each measurement mode along with a derivation of the satellite clock offsets, geometric ranges from the dual one-way measurements were introduced. Then, pseudoranges and clock offsets were evaluated for the new-generation BDS satellites. The evaluation shows that the ranging accuracies of TDMA ISL and the continuous link are approximately 4 cm and 1 cm (root mean square, RMS), respectively. Both lead to ISL clock offset residuals of less than 0.3 ns (RMS). For further validation, time synchronization between these satellites to a ground control station keeping the systematic time in BDT was conducted using L-band Two-way Satellite Time Frequency Transfer (TWSTFT). System errors in the ISL measurements were calibrated by comparing the derived clock offsets with the TWSTFT. The standard deviations of the estimated ISL system errors are less than 0.3 ns, and the calibrated ISL clock parameters are consistent with that of the L-band TWSTFT. For the regional BDS network, the addition of ISL measurements for medium orbit (MEO) BDS satellites increased the clock tracking coverage by more than 40% for each orbital revolution. As a result, the clock predicting error for the satellite M1S was improved from 3.59 to 0.86 ns (RMS), and the predicting error of the satellite M2S was improved from 1.94 to 0.57 ns (RMS), which is a significant improvement by a factor of 3–4.

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.

Beidou-2 satellite navigation system adopts China Geodetic Coordinate System 2000 (CGCS2000), which can’t meet the requirements of Beidou-3 global service and timely update. This paper discusses two approaches to build BeiDou Terrestrial Reference Frame (BTRF), one is precise point position (PPP) and the other is net-solution with MGEXs. We only relied on BDS observations to determine precise coordinates of each BDS monitoring station under ITRF and verify the two approaches. Especially, we analyzed the improvement for the accuracy of Beidou satellites orbit determination (OD) with regional tracking network after refining and updating the coordinates of tracking stations by means of net-solution. Initial results show that repeatability of PPP for the horizontal and vertical components of a BDS monitoring receiver is better than 2.3 cm and 3.4 cm, respectively, which may be reduced to 0.8 cm and 2.2 cm for net-solution. After the refinement, the OD accuracy of IGSOs 3D overlap increase by 15.4%, while MEOs increase by 25.9%. We also evaluate BDS satellite orbit with SLR measurements, results reveal that SLR residuals of BD-2 satellites reduce from 0.39 m to 0.24 m, the accuracy increases by 38%, the residuals of BD-3 satellites reduce from 0.25 m to 0.18 m, the accuracy increases by 28%.

An atomic clock is one of the most important payloads in navigation satellites. It is in charge of generating and maintaining the satellite time. The performance and on-orbit adaptability of a 23-kg passive hydrogen maser (PHM) have been verified using the experimental satellite of the third-generation Beidou satellite navigation system (BDS-3). The clock offset of the PHM is less than 1 ns per day. In BDS-3, PHMs operate as the master clocks in the GEO, IGSO, and MEO satellites; therefore, they are important in the system operation. Herein, we present the design and performance evaluation of the PHM and compare the hydrogen maser, rubidium atomic clock, and cesium atomic clock. Using the satellite-ground time-difference data, we analyze the frequency stability and time prediction accuracy. Furthermore, we perform a preliminary analysis of the operating status and aging trend based on the satellite telemetry data.

The signal-in-space ranging error (SISRE) is a major factor that affects the accuracy of positioning and timing. It describes the projection of the satellite-broadcast ephemeris error and clock difference error in the average direction from satellites to stations. In this study, the size and characteristics of the broadcast ephemeris user range error (URE), clock difference error, and SISRE are evaluated with respect to GPS, Galileo, and BDS-3. The results indicate that the SISREs of Galileo, GPS, and BDS-3 are 0.14, 0.49, and 0.35 m, respectively, the broadcast ephemeris UREs of Galileo, GPS, and BDS-3 are 0.14, 0.27, and 0.09 m, respectively, and the clock difference errors of Galileo, GPS, and BDS-3 are 0.14, 0.41, and 0.35 m, respectively. In case of Galileo, the radial orbit error and the clock difference error exhibit strong correlation. Both these errors cancel each other, and the SISRE associated with Galileo can be effectively reduced. Further, obvious differences can be observed with respect to the clock difference error and SISRE in case of different types of GPS satellites. The clock difference error and SISRE of GPS will gradually decrease with the upgradation of satellites. The SISRE of BDS-3 exhibits different characteristics when compared with those exhibited by the SISREs of GPS and Galileo. First, the radial error of BDS-3 is less correlated with the clock difference error, which exhibits poor self-consistency. Second, the BDS-3 satellite-broadcast ephemeris URE is small, whereas the clock difference error is large. Furthermore, the broadcast ephemeris URE associated with BDS-3 is lower than those associated with Galileo and GPS. However, the contribution of the clock difference error associated with BDS-3 to SISRE is considerably greater than those of the clock difference errors associated with GPS and Galileo to SISRE. In this study, the sizes and characteristics of the SISRE of BDS-3, Galileo, and GPS are compared, indicating that signal-in-space accuracy of BDS-3 can be improved by reducing the clock difference error.

The Beidou Navigation Satellite System (BDS) manages to estimate simultaneously the orbits and clock offsets of navigation satellites, using code and carrier phase measurements of a regional network within China. The satellite clock offsets are also directly measured with Two-way Satellite Time Frequency Transfer (TWSTFT). Satellite laser ranging (SLR) residuals and comparisons with the precise ephemeris indicate that the radial error of GEO satellites is much larger than that of IGSO and MEO satellites and that the BDS orbit accuracy is worse than GPS. In order to improve the orbit determination accuracy for BDS, a new orbit determination strategy is proposed, in which the satellite clock measurements from TWSTFT are fixed as known values, and only the orbits of the satellites are solved. However, a constant systematic error at the nanosecond level can be found in the clock measurements, which is obtained and then corrected by differencing the clock measurements and the clock estimates from orbit determination. The effectiveness of the new strategy is verified by a GPS regional network orbit determination experiment. With the IGS final clock products fixed, the orbit determination and prediction accuracy for GPS satellites improve by more than 50% and the 12-h prediction User Range Error (URE) is better than 0.12 m. By processing a 25-day of measurement from the BDS regional network, an optimal strategy for the satellite-clock-fixed orbit determination is identified. User Equivalent Ranging Error is reduced by 27.6% for GEO satellites, but no apparent reduction is found for IGSO/MEO satellites. The SLR residuals exhibit reductions by 59% and 32% for IGSO satellites but no reductions for GEO and MEO satellites.

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.

Satellite-station two-way time comparison is a typical design in Beidou System (BDS) which is significantly different from other satellite navigation systems. As a type of two-way time comparison method, BDS time synchronization is hardly influenced by satellite orbit error, atmosphere delay, tracking station coordinate error and measurement model error. Meanwhile, single-way time comparison can be realized through the method of Multi-satellite Precision Orbit Determination (MPOD) with pseudo-range and carrier phase of monitor receiver. It is proved in the constellation of 3GEO/2IGSO that the radial orbit error can be reflected in the difference between two-way time comparison and single-way time comparison, and that may lead to a substitute for orbit evaluation by SLR. In this article, the relation between orbit error and difference of two-way and single-way time comparison is illustrated based on the whole constellation of BDS. Considering the all-weather and real-time operation mode of two-way time comparison, the orbit error could be quantifiably monitored in a real-time mode through comparing two-way and single-way time synchronization. In addition, the orbit error can be predicted and corrected in a short time based on its periodic characteristic. It is described in the experiments of GEO and IGSO that the prediction accuracy of space signal can be obviously improved when the prediction orbit error is sent to the users through navigation message, and then the UERE including terminal error can be reduced from 0.1 m to 0.4 m while the average accuracy can be improved more than 27%. Though it is still hard to make accuracy improvement for Precision Orbit Determination (POD) and orbit prediction because of the confined tracking net and the difficulties in dynamic model optimization, in this paper, a practical method for orbit accuracy improvement is proposed based on two-way time comparison which can result in the reflection of orbit error.

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.

In order to evaluate the orbit accuracy of regional network of Chinese BeiDou Satellite Navigation System (BDS), we compare the orbits determined by regional network consisting of ground stations within the border of China and orbits provided by global Multi-GNSS Experiment (MGEX) covering 2-year time span from 2013 to 2014. The results show that, for GEO/IGSO/MEO, mean radial accuracies of regional network orbits are around 0.4, 0.3, and 0.2 m, respectively. The orbit accuracy degenerates significantly during eclipse and IGSO/MEO yaw-fixing season. IGSO/MEO orbit accuracies present possible quasi-periodic oscillation, but show week correlation with sun’s elevations above the orbital plane. Assessment of regional network orbits by satellite laser ranging (SLR) shows, for GEO/IGSO/MEO, that the RMS values of station–satellite distance are around 0.6, 0.3, and 0.2 m, respectively, which match the orbit radial errors fairly well but contain significant systematic offsets. The characteristics presented in BeiDou satellites are quite different from those in GPS/Galileo. The dynamic modeling accuracy and orbit processing strategy on BeiDou satellites need further enhancement.

Satellite clock bias (SCB) is provided by the in orbit atomic clock, which is the key to satellite navigation system. First, the time reference of the satellite navigation system is realized by the SCB, and the SCB prediction accuracy will also affect the positioning accuracy of real-time navigation users. With the development of our Beidou satellite navigation system (BDS), the performance requirement of the satellite clock and accuracy requirement of the SCB prediction are higher and higher. This paper will study on performance evaluation of BDS atomic clock and the prediction analysis of SCB series exclusively. In order to show the results objectively and effectively, we select two data processing centers of the GeoForschungsZentrum Potsdam (GBM), and SHAO Analysis Center (SHA), to obtain the same time BDS clock bias sequence as the base data, for a comparative analysis. First, the performance of the atomic clock is evaluated by statistics of the Allen variance. Meanwhile, we establish the model for each SCB sequence according to the characteristic of the atomic clock, by using a combined method of least squares and autoregressive model (LS+AR), to predict and assess the SCB with root mean square error (RMS). Results show that the performance of BDS in orbit atomic clock is stable, with the day stability in the order of 10−14; And the atomic clock performance is related to the SCB prediction accuracy, that is shown as better performance with higher prediction accuracy; Mean while the LS+AR model predict SCB series based on the performance of different atomic clocks, which can improve the SCB prediction accuracy effectively.

Determined to become a new member of the well-established GNSS family, COMPASS (or BeiDou-2) is developing its capabilities to provide high accuracy positioning services. Two positioning modes are investigated in this study to assess the positioning accuracy of COMPASS’ 4GEO/5IGSO/2MEO constellation. Precise Point Positioning (PPP) for geodetic users and real-time positioning for common navigation users are utilized. To evaluate PPP accuracy, coordinate time series repeatability and discrepancies with GPS’ precise positioning are computed. Experiments show that COMPASS PPP repeatability for the east, north and up components of a receiver within mainland China is better than 2 cm, 2 cm and 5 cm, respectively. Apparent systematic offsets of several centimeters exist between COMPASS precise positioning and GPS precise positioning, indicating errors remaining in the treatments of COMPASS measurement and dynamic models and reference frame differences existing between two systems. For common positioning users, COMPASS provides both open and authorized services with rapid differential corrections and integrity information available to authorized users. Our assessment shows that in open service positioning accuracy of dual-frequency and single-frequency users is about 5 m and 6 m (RMS), respectively, which may be improved to about 3 m and 4 m (RMS) with the addition of differential corrections. Less accurate Signal In Space User Ranging Error (SIS URE) and Geometric Dilution of Precision (GDOP) contribute to the relatively inferior accuracy of COMPASS as compared to GPS. Since the deployment of the remaining 1 GEO and 2 MEO is not able to significantly improve GDOP, the performance gap could only be overcome either by the use of differential corrections or improvement of the SIS URE, or both.

The regional satellite navigation system of COMPASS (Phase I) provides both open services and authorized services. Authorized services offer differential corrections and integrity information to users to support higher positioning, navigation and timing precision. Experimenting with real data, positioning accuracy is estimated with a 3GEO/4IGSO COMPASS constellation. The results show that with dual-frequency and single-frequency pseudo-range measurements, the positioning errors are respectively 8 and 10 m (RMS) for open service users, while for authorized users, the errors are 4 and 5 m (RMS), respectively. The COMPASS constellation geometry may cause large error to occur in the height component by 7–9 m for dual-or single-frequency users, which can be effectively reduced with the differential corrections supplied by the authorized services. Multipath errors are identified and corrected for COMPASS, resulting in 25% positioning accuracy improvement for dual-frequency users and 10% improvement for single-frequency users.

China’s COMPASS satellite navigation system relies on a regional tracking network to provide navigation services. Limited by its geographic border, the regional network is able to cover only 30% of the medium-earth-orbits (MEO). Accuracy of determined and predicted orbits is not able to satisfy system requirements if the tracking data processing strategy for global tracking network processing is used for the regional network. Two major error sources for orbital prediction are accuracy of initial orbital elements and dynamical modeling. To achieve better prediction accuracy, we propose a two-step orbit determination and prediction strategy. For step 1, only solar radiation pressure (SRP) parameters are estimated along with the orbital elements and other parameters; for step 2, all parameters are estimated but the SRP parameters are tightly constrained to their step 1 estimates. Experimenting with data from a regional GPS network, we conclude for orbital prediction using the proposed two-step strategy, the average user range error (URE) for 24-h prediction arcs is better than 0.6 m.

Geostationary (GEO) satellites form an indispensable component of the constellation of Beidou navigation system (BDS). The ephemerides, or predicted orbits of these GEO satellites(GEOs), are broadcast to positioning, navigation, and timing users. User equivalent ranging error (UERE) based on broadcast message is better than 1.5 m (root formal errors: RMS) for GEO satellites. However, monitoring of UERE indicates that the orbital prediction precision is significantly degraded when the Sun is close to the Earth's equatorial plane (or near spring or autumn Equinox). Error source analysis shows that the complicated solar radiation pressure on satellite buses and the simple box-wing model maybe the major contributor to the deterioration of orbital precision. With the aid of BDS' two-way frequency and time transfer between the GEOs and Beidou time (BDT, that is maintained at the master control station), we propose a new orbit determination strategy, namely three-step approach of the multi-satellite precise orbit determination (MPOD). Pseudo-range (carrier phase) data are transformed to geometric range (biased geometric range) data without clock offsets; and reasonable empirical acceleration parameters are estimated along with orbital elements to account for the error in solar radiation pressure modeling. Experiments with Beidou data show that using the proposed approach, the GEOs' UERE when near the autumn Equinox of 2012 can be improved to 1.3 m from 2.5 m (RMS), and the probability of user equivalent range error (UERE)

A good-quality Ce:YAG scintillation crystal with a diameter of 3 inches has been grown by temperature gradient technology (TGT) for the first time. The longitudinal distribution of cerium ions in the TGT-Ce:YAG crystal was measured by the ICP-AES method. The absorption spectrum in the range of 190–800 nm and the X-ray excited luminescence (XEL) of the as-grown Ce:YAG crystal were measured at the room temperature. The four typical absorption bands corresponding to internal 4f–5d transitions in Ce3+ ions, and the emission peak centered at 550 nm with the 2F5/2–2F7/2 ground state splitting were found in the absorption and XEL spectra. (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Broadcast ephemeris parameter is an important reflection of navigation system service performance. In hybrid constellation, GEO, IGSO and MEO satellites have different dynamic characteristics which lead to different fitting performances. In this article, the basic physical meaning of ephemeris parameters are analyzed, and the evaluation for the variation characteristics of fitting parameters is carried on. Several improved algorithms are proposed from the aspect of mathematical processing, which effectively eliminates the unsuitability in the parameter fitting of GEO. The fitting accuracy of 3 types of satellites are analyzed based on the 16-parameter model, and then the evaluation of fitting performance is completed. It is proved in the experiments: the high accuracy can be realized for the 3 types of satellites, and even the accuracy is prior to 1 cm for most time. For GEO, the accuracy can be sub-centimeter, while the accuracy can be millimeter for IGSO and MEO satellites. In summary, the 16-parameter model is enough to meet the centimeter level application requirement.

Real-time wide area differential corrections are provided to BeiDou authorized users to satisfy the need of high-accuracy navigation service. The algorithm of wide area differential corrections are studied based on independent two-way time synchronization system and the performance of two kinds of differential modes with one-dimensional (also the equivalent satellite clock correction introduced in BeiDou ICD file) or four-dimensional correction are comparatively analyzed. The results show that for the current one-dimensional mode, the correction accuracy will decrease when the orbital errors are large, especially for the situations such as quickly orbit determination recovery after satellite failure or maneuver. While for the four-dimensional mode, the stability and precision of the separation of ephemeris and satellite clock parameters are seriously limited by the regional monitoring network. Applying the two-way time synchronization observations, the high-precision separation of orbital and satellite clock errors is realized with kinematic method, and with actual observations, the processing results show that user differential range error may be minimized to decimeter level and the positioning accuracy is also improved by 40 % in the area lacked monitor stations. The four-dimensional mode may process in real-time and once be applied in BeiDou Wide Area Differential Augmentation System, the accuracy, continuity and availability of the system will all be improved.

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.

As a highly accurate technique of satellite orbit tracking, a precise determination method of satellite orbit, and an independent way of external validation on the orbits obtained by other satellite precise orbit determination (POD) means, satellite laser ranging (SLR) has been applied in many international and Chinese satellite projects. In China’s BeiDou (Compass) Navigation Satellite System, as the cooperative targets of international SLR monitoring, multiple satellites have been equipped with on-board laser retro-reflector array, and high-quality observation data have been obtained from around 20 tracking stations distributed all over the world. In this work, we summarized the SLR tracking status on BeiDou satellites and determined the proper SLR dynamic POD strategy. Using SLR tracking data, we determined orbits of four BeiDou satellites, assessed SLR orbits’ accuracies by orbit overlap and orbit comparison with precise ephemeris produced from radio navigation bands, and analyzed characters and possible causes of orbit errors. The results demonstrated that SLR-derived orbits on BeiDou satellites are on the level of meter, and the precisions along radial direction can achieved decimeter level. For current BeiDou satellites in different types of orbits, and in the future construction and improvement of BeiDou Navigation Satellite System, SLR has already and will continue to play an important role in the process of POD and orbit validation.

Up to the end of October 2012, 14 COMPASS/Beidou-2 regional satellite navigation satellites are fully operational. Different with Global Positioning System (GPS), the space segment of COMPASS consists of Geostationary Earth Orbit (GEO) satellites, Inclined Geosynchronous Satellite Orbit (IGSO) satellites and Medium Earth Orbit (MEO) satellites, and navigation information is provided by monitoring stations limited in regional area. Besides, attitude control mode is different for each type of satellites. The predictability of satellite attitude will make broadcast ephemeris precisely predicted. In this study, satellite telemetry data are compared with nominal attitude to assess the accuracy of satellite attitude prediction. Experiments show that the accuracy is different for each type satellites, and overall prediction accuracy is better than 1°. The analyses of pseudo-range multipath noise for receivers from different manufacturers show that the random noise characteristics is significantly for the US and European manufacturers’ receivers, and the magnitude is larger than domestic manufacturers’, but strong daily repeatability of multipath noise characteristics is displayed for domestic receivers. The accuracy of precision orbit determination (OD) for COMPASS using regional and global monitoring stations data are compared to evaluate the impact of monitoring stations’ distribution on the accuracy of satellite OD. Satellite Leaser Range (SLR) residuals are adopted to assess the satellite orbit accuracy in station line-of-sight direction. The results show that the accuracy of satellite orbit overlap is about 0.2, 1.2 and 0.6 m in R/T/N direction for regional monitor network, the accuracy for MEO overlap is slightly worse than two other type satellites, and the SLR residual is better than 1 m. The two-way satellite time frequency transfer (TWSTFT) observations are adopted to evaluate the accuracy of satellite clock error estimations. Experiments show that the standard deviation of satellite clock estimations solved by OD is about 1.4 ns. Global monitoring stations can increase the depth of coverage for MEO satellites, and the accuracy of clock estimations may be improved by about 0.6 ns. The observations from multi-constellation GNSS receiver are adopted to realize the system timing service. The results show that the stability of time system for COMPASS is consistent with GPS, the standard deviation of comparison for COMPASS and GPS precise timing is about 1.5 ns, the real time timing is about 3 ns.

Ionospheric delay is one of the main error sources affecting the positioning and timing precision of satellite navigation system for single frequency users. China’s regional satellite navigation system uses ionospheric puncture point data of monitoring stations to fit the 8 parameters of klobuchar model in geographic coordinate system,and broadcasts them to users through the navigation message which is valid for 2 h. Long-term monitoring shows that this model can correct the ionospheric delay up to 74 % in service area around China. Due to the lack of ionospheric measured data in the southern hemisphere and high latitudes of the northern hemisphere, this model can not guarantee the correction accuracy in equatorial belt and high latitudes. This paper improves the klobuchar model expressed in the form of 9 parameters. Not only this model can keep the ionospheric double-peak characteristic but also ensure global fitting precision. In order to obtain real-time ionospheric data outside regional monitoring network, this paper examines the precision of forecasting model based on ionosphere spherical harmonic coefficient. According to the results of comparison,the model in this paper can correct the ionospheric delay for the next 24 h up to 72 % in China. Globally, the correction accuracy reaches 70 % in the north hemisphere, while 69 % in the south hemisphere. As a result, the correction precision of the model is better than the model broadcasted by GPS.

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.

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.