Developing an Innovative High-precision Approach to Predict Medium-term and Long-term Satellite Clock Bias

A new prediction method based on the nonlinear autoregressive model is proposed to improve the accuracy of medium-term and long-term predictions of Satellite Clock Bias(SCB).Forecast experiments for three time periods were implemented based on the precision SCB published on the International GNSS Server(IGS)server.The results show that the medium-term and long-term prediction accuracy of the proposed approach is significantly better compared to other traditional models,with the training time being much shorter than the wavelet neural network model.

Proposal for a realtime Einstein-synchronization-defined satellite virtual clock

Realization of high performance satellite onboard clock is vital for various positioning, navigation, and timing applications. For further improvement of the synchronization-based satellite time and frequency references, we propose a geosynchronous(GEO) satellite virtual clock concept based on ground–satellite synchronization and present a beacon transponder structure for its implementation(scheduled for launch in 2025), which does not require atomic clocks to be mounted on the satellite. Its high performance relies only on minor modifications to the existing transponder structure of GEO satellites. We carefully model the carrier phase link and analyze the factors causing link asymmetry within the special relativity. Considering that performance of such synchronization-based satellite clocks is primarily limited by the link's random phase noise, which cannot be adequately modeled, we design a closed-loop experiment based on commercial GEO satellites for pre-evaluation. This experiment aims at extracting the zero-means random part of the ground-satellite Ku-band carrier phase via a feedback loop. Ultimately, we obtain a 1σ value of 0.633 ps(two-way link), following the Gaussian distribution. From this result, we conclude that the proposed real-time Einstein-synchronization-defined satellite virtual clock can achieve picosecond-level replication of onboard time and frequency.

Real‑time service performances of BDS‑3 and Galileo constellations with a linear satellite clock correction models

In order to facilitate high-precision and real-time Precise Point Positioning(PPP),the International GNSS(Global Navigation Satellite System)Service(IGS),BDS-3(BeiDou-3 Navigation Satellite System),and Galileo navigation satellite system(Galileo)have provided real-time satellite clock correction,which is updated at a high-frequency.However,the frequent updates pose the challenges of increasing the computational burden and compromising the timeliness of these correction parameters.To address this issue,an improved Real-Time Service(RTS)method is developed using an extrapolation algorithm and a linear model.The results indicate that a 1 h arc length of the satellite clock correction series is optimal for fitting a linear model of the RTS.With this approach,the 1 h extrapolation results for BDS-3 and Galileo are superior to 0.09 ns.Moreover,when these model coefficients are transmitted and updated at the intervals of 1,2,5,and 10 min,the corresponding PPP can converge at the centimeter-level.It is evident that these improved RTS methods outperform the current approach with high-frequency interval transmission,as they effectively mitigate the challenges associated with maintaining the timeliness of correction parameters.

Impact of Sampling Rate of IGS Satellite Clock on Precise Point Positioning

Both static and kinematic testings are investigated by using IGS 5rain, 30s and 5s-interval precise satellite clock prod- ucts in precise point positioning （PPP） solution. Test results show that the sampling rate oflGS satellite clock has very little effect on the static PPP solution. All the three types of sampling intervals of precise satellite clock can satisfy mm-cm level of positioning accuracy; higher sampling rate has no significant improvement for PPP solution. However, sampling rate of satellite clock has a significant impact on the PPP solution in kinematic PPP. The higher the interval of satellite clock, the better the accuracy achieved. The accuracy of kinematic PPP achieved by using 30s-interval precise satellite clock is improved by nearly 30-50 percent with re- spect to the solution by using 5min-interval precise satellite clock, but using 5s and 30s-interval satellite clock can almost produce the same accuracy of kinematic solution. Moreover, the use of precise satellite clock products from different analysis centers may also produce more or less effect on the PPP solution.

BDS satellite clock offset prediction based on a semiparametric adjustment model considering model errors

In view of the influence of model errors in conventional BeiDou prediction models for clock offsets,a semiparametric adjustment model for BeiDou Navigation Satellite System(BDS)clock offset prediction that considers model errors is proposed in this paper.First,the model errors of the conventional BeiDou clock offset prediction model are analyzed.Additionally,the relationship among the polynomial model,polynomial model with additional periodic term correction,and its periodic correction terms is explored in detail.Second,considering the model errors,combined with the physical relationship between phase,frequency,frequency drift,and its period in the clock sequence,the conventional clock offset prediction model is improved.Using kernel estimation and comprehensive least squares,the corresponding parameter solutions of the prediction model and the estimation of its model error are derived,and the dynamic error correction of the clock sequence model is realized.Finally,the BDS satellite precision clock data provided by the IGS Center of Wuhan University with a sampling interval of 5 min are used to compare the proposed prediction method with commonly used methods.Experimental results show that the proposed prediction method can better correct the model errors of BDS satellite clock offsets,and it can effectively overcome the inaccuracies of clock offset correction.The average forecast accuracies of the BeiDou satellites at 6,12,and 24 h are 27.13%,37.71%,and 45.08%higher than those of the conventional BeiDou clock offset forecast models;the average model improvement rates are 16.92%,20.96%,and 28.48%,respectively.In addition,the proposed method enhances the existing BDS satellite prediction method for clock offsets to a certain extent.

Review of satellite disciplined clock system

Satellite disciplined clock system(SDCS)composed of satellite timing receiver and local frequency synthesis is widely applied for its high accuracy and low cost.This paper provides a review of SDCS.Key technologies such as phase difference measurement,pulse noise process and frequency calibration are surveyed in detail.Disciplined clock model based on PI controller is built and disciplined process is analyzed.The methods of realizing the disciplined clock circuit are classified and summarized.A prototype based on FPGA is proposed.At last development trend of SDCS is discussed.

Consistency of MGEX Orbit and Clock Products

The analysis centers of the Multi-GNSS Pilot Project of the International GNSS Service provide orbit and clock products for the global navigation satellite systems(GNSSs)Global Positioning System(GPS),GLONASS,Galileo,and BeiDou,as well as for the Japanese regional Quasi-Zenith Satellite System(QZSS).Due to improved solar radiation pressure modeling and other more sophisticated models,the consistency of these products has improved in recent years.The current orbit consistency between different analysis centers is on the level of a few centimeters for GPS,around one decimeter for GLONASS and Galileo,a few decimeters for BeiDou-2,and several decimeters for QZSS.The clock consistency is about 2 cm for GPS,5 cm for GLONASS and Galileo,and 10 cm for BeiDou-2.In terms of carrier phase modeling error for precise point positioning,the various products exhibit consistencies of 2–3 cm for GPS,6–14 cm for GLONASS,3–10 cm for Galileo,and 10–17 cm for BeiDou-2.

Satellite Autonomous Integrity Monitoring of BDS and Onboard Performance Evaluation

With the development of satellite navigation technology,the user demands for the integrity of Global Navigation Satellite System(GNSS)have increased more and more.A ground-based monitoring system can hardly report an alarm message to GNSS users during the valid alarming period due to the satellite-Earth propagation delay.It is beneficial to monitor abnormal events and report the corresponding alarms from orbit.Adopting this approach,which is an important feature for future GNSS integrity monitoring,the time needed to provide an alarm is shorter and the system integrity capability is strengthened.The BeiDou Navigation Satellite System(BDS)new generation satellites have the capabilities of satellite autonomous integrity monitoring(SAIM).This paper presents the technical scheme of SAIM,and proposes the integrity monitoring method of both navigation signals and the clocks onboard.The proposed method was verified through the onboard test on the BDS satellites.In addition,we analyzed the integrity telemetry data from the new generation of BDS satellite,including signal delay,power,carrier phase measurement,correlation peak,consistency of pseudo-code and carrier phase,clock phase and frequency step.The analysis results indicated that the quality of the data on orbit met the requirements,and SAIM could monitor effectively any abnormal change of satellite clocks and navigation signal,generate rapidly an alarm message,and transmit it to the user.The alarm time was less than 6 s through the message,and 2 s through non-standard code(NSC).Finally,we present future opportunities for improving the SAIM technology of BDS.

The wide-area difference system for the regional satellite navigation system of COMPASS

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 dualor 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.

GNSS clock corrections densification at SHAO:from 5 min to 30 s

High frequency multi-GNSS zero-difference applications like Precise Orbit Determination （POD） for Low Earth Orbiters （LEO） and high frequency kinematic positioning require corresponding high-rate GNSS clock corrections. The determination of the GNSS clocks in the orbit determination process is time consuming, especially in tile combined GPS/GLONASS pro- cessing. At present, a large number of IGS Analysis Centers （AC） provide clock corrections in 5-rain sampling and only a few ACs provide clocks in 30-s sampling for both GPS and GLONASS. In this paper, an efficient epoch-difference GNSS clock determination algorithm is adopted based on the algorithm used by the Center for Orbit Determination in Europe （CODE）. The clock determination procedure of the GNSS Analysis Center at Shanghai Astronomical Observatory （SHAO） and the algorithm is described in detail. It is shown that the approach greatly speeds up the processing, and the densified 30-s clocks have the same quality as the 5-rain clocks estimated based on a zero-difference solution. Comparing the densified 30-s GNSS clocks provided by SHAO with that of IGS and its ACs, results show that our 30-s GNSS clocks are of the same quality as that of 1GS. Allan deviation also gives the same conclusion. Further validation of the SHAO 30-s clock product is performed in kine- matic PPP and LEO POD. Results indicate that the positions have the same accuracy when using SHAO 30-s GNSS clocks or IGS （and its AC） finals. The robustness of the algorithm and processing approach ensure its extension to provide clocks in 5-s or even higher frequencies. The implementation of the new approach is simple and it could be delivered as a black-box to the current scientific software packages.

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

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.

Estimation of fractional cycle bias for GPS/BDS-2/Galileo based on international GNSS monitoring and assessment system observations using the uncombined PPP model

The Fractional Cycle Bias(FCB)product is crucial for the Ambiguity Resolution(AR)in Precise Point Positioning(PPP).Different from the traditional method using the ionospheric-free ambiguity which is formed by the Wide Lane(WL)and Narrow Lane(NL)combinations,the uncombined PPP model is flexible and effective to generate the FCB prod-ucts.This study presents the FCB estimation method based on the multi-Global Navigation Satellite System(GNSS)precise satellite orbit and clock corrections from the international GNSS Monitoring and Assessment System(iGMAS)observations using the uncombined PPP model.The dual-frequency raw ambiguities are combined by the integer coefficients(4,−3)and(1,−1)to directly estimate the FCBs.The details of FCB estimation are described with the Global Positioning System(GPS),BeiDou-2 Navigation Satellite System(BDS-2)and Galileo Navigation Satellite System(Galileo).For the estimated FCBs,the Root Mean Squares(RMSs)of the posterior residuals are smaller than 0.1 cycles,which indicates a high consistency for the float ambiguities.The stability of the WL FCBs series is better than 0.02 cycles for the three GNSS systems,while the STandard Deviation(STD)of the NL FCBs for BDS-2 is larger than 0.139 cycles.The combined FCBs have better stability than the raw series.With the multi-GNSS FCB products,the PPP AR for GPS/BDS-2/Galileo is demonstrated using the raw observations.For hourly static positioning results,the performance of the PPP AR with the three-system observations is improved by 42.6%,but only 13.1%for kinematic positioning results.The results indicate that precise and reliable positioning can be achieved with the PPP AR of GPS/BDS-2/Galileo,supported by multi-GNSS satellite orbit,clock,and FCB products based on iGMAS.