BDS Satellite Clock Prediction Considering Periodic Variations

The periodic noise exists in BeiDou navigation satellite system (BDS) clock offsets. As a commonly used satellite clock prediction model, the spectral analysis model (SAM) typically detects and identifies the periodic terms by the Fast Fourier transform (FFT) according to long-term clock offset series. The FFT makes an aggregate assessment in frequency domain but cannot characterize the periodic noise in a time domain. Due to space environment changes, temperature variations, and various disturbances, the periodic noise is time-varying, and the spectral peaks vary over time, which will affect the prediction accuracy of the SAM. In this paper, we investigate the periodic noise and its variations present in BDS clock offsets, and improve the clock prediction model by considering the periodic variations. The periodic noise and its variations over time are analyzed and quantified by short time Fourier transform (STFT). The results show that both the amplitude and frequency of the main periodic term in BDS clock offsets vary with time. To minimize the impact of periodic variations on clock prediction, a time frequency analysis model (TFAM) based on STFT is constructed, in which the periodic term can be quantified and compensated accurately. The experiment results show that both the fitting and prediction accuracy of TFAM are better than SAM. Compared with SAM, the average improvement of the prediction accuracy using TFAM of the 6 h, 12 h, 18 h and 24 h is in the range of 6.4% to 10% for the GNSS Research Center of Wuhan University (WHU) clock offsets, and 11.1% to 14.4% for the Geo Forschungs Zentrum (GFZ) clock offsets. For the satellites C06, C14, and C32 with marked periodic variations, the prediction accuracy is improved by 26.7%, 16.2%, and 16.3% for WHU clock offsets, and 29.8%, 16.0%, 21.0%, and 9.0% of C06, C14, C28, and C32 for GFZ clock offsets.

Characteristics and Performance Evaluation of QZSS Onboard Satellite Clocks

In the Global Navigation Satellite System (GNSS) community, the Quasi-Zenith Satellite System (QZSS) is an augmentation system for users in the Asia-Pacific region. However, the characteristics and performance of four QZSS satellite clocks in a long-term scale are unknown at present. However, it is crucial to the positioning, navigation and timing (PNT) services of users, especially in Asia-Pacific region. In this study, the characteristics and performance variation of four QZSS satellite clocks, which including the phase, frequency, frequency drift, fitting residuals, frequency accuracy, periodic terms, frequency stability and short-term clock prediction, are revealed in detail for the first time based on the precise satellite clock offset products of nearly 1000 days. The important contributions are as follows: (1) It is detected that the times of phase and frequency jump are 2.25 and 1.5 for every QZSS satellite clock in one year. The magnitude of the frequency drift is about 10−18. The periodic oscillation of frequency drift of J01 and J02 satellite clocks is found. The clock offset model precision of QZSS is 0.33 ns. (2) The two main periods of QZSS satellite clock are 24 and 12 hours, which is the influence of the satellite orbit; (3) The frequency stability of 100, 1000 and 10,000 s are 1.98 × 10−13, 6.59 × 10−14 and 5.39 × 10−14 for QZSS satellite clock, respectively. The visible “bump” is found at about 400 s for J02 and J03 satellite clocks. The short-term clock prediction accuracy of is 0.12 ns. This study provides a reference for the state monitoring and performance variation of the QZSS satellite clock.

Improving Clock Prediction Algorithm for BDS-2/3 Satellites Based on LS-SVM Method

The satellite clock prediction is crucial to support real-time global satellite precise positioning services. Currently, the clock prediction for the Chinese BeiDou navigation satellite system (BDS) is still challenging to satisfy the precise positioning applications. Based on the exploration of existing prediction models, an improved model combing the spectrum analysis model (SAM) and the least-squares support-vector machine (LS-SVM) is proposed especially for BDS-2/3 satellites. Considering satellite-specific characteristics, the parameters of the LS-SVM method are optimized satellite by satellite, including input length, regularization and kernel parameters. The improved model is evaluated by comparing the predicted clocks of existing methods and the improved model. The bias of the predicted clock offsets are within ±1.0 ns for most medium Earth orbits (MEOs) over three hours employing the improved model, which is better than that of the existing methods and can be applied for several real-time precise positioning applications. The predicted clock offsets are further evaluated by applying clock corrections to precise point positioning (PPP) in both static and kinematic modes for 10 international GNSS service (IGS) Multi-GNSS Experiment (MGEX) stations, including five stations in the Asia-Pacific region. According to the practical engineering experience, 2 dm and 5 dm are defined for static and kinematic PPP, respectively, as a convergence threshold. Then, in the static PPP, the improved model is demonstrated to be effective, and positioning accuracies of some stations obtain more than 15% improvements on average for each direction, which enables them to get sub-decimeter positioning, especially in the Asia-Pacific region. In the kinematic PPP, the improved model performs much better than the others in terms of both the convergence time and the positioning accuracy. The convergence time can be shortened from 1.0 h to below 0.5 h, while the positioning accuracies are enhanced by 16.3%, 10.8%, and 18.9% on average in east, north, and up direction, respectively.

A Practical Adaptive Clock Offset Prediction Model for the Beidou-2 System

The predicted navigation satellite clock offsets are crucial to support real-time global navigation satellite system (GNSS) precise positioning applications, especially for those applications difficult to access the real-time data stream, such as the low earth orbit (LEO) autonomous precise orbit determination. Currently, the clock prediction for the Chinese BeiDou system is still challenging to meet the precise positioning requirement. The onboard clocks of BeiDou satellites are provided by different manufacturers, and the clocks’ switch events are more frequent. Considering the satellite-specified and temporal variation of the BeiDou clocks characteristics, we intend to use an adaptive model for BeiDou clock prediction. During clock prediction, we identify different models for BeiDou clocks’ characteristics, and then address the optimal model with a cross-validation procedure. The model achieving the minimum variance in the cross-validation procedure is used for the final clock prediction. We compared the prediction results of our method with two well-recognized BeiDou ultra-rapid clock products, named GBU-P and ISU-P, respectively. The comparison results indicate that the adaptive model achieves about 1-ns precision for 3-h prediction, which corresponds to 47.3% and 32.1% precision improvement compared to the GBU-P and ISU-P products, respectively. The efficiency of the predicted clocks is further validated with the precise point positioning (PPP) data processing. The results indicate that the static PPP solution precision is improved by 21.6%–30.0% compared to the current predicted clock product. The precision improvement in kinematic PPP is even more significant, which reaches 46.7%–53.9% with respect to these GBU-P and ISU-P products. Therefore, the proposed adaptive model is a practical and an efficient way to improve the BeiDou clock prediction.

Improving Short Term Clock Prediction for BDS-2 Real-Time Precise Point Positioning

Although there are already several real-time precise positioning service providers, unfortunately, not all users can use the correction information due to either cost of the service and limitation of their equipment or out of the service coverage. An alternative way is to enhance the accuracy of the predicted satellite clocks for precise real-time positioning. Based on the study of existing prediction models, an improved model combing the spectrum analysis (SA) and the generalized regression neural network (GRNN) model is proposed especially for BeiDou satellite navigation system (BDS)-2 satellites. The periodic terms and GRNN-related parameters including length and interval of sample data, as well as a smooth factor, are optimized satellite by satellite to consider satellite-specific characteristics for all the fourteen BDS-2 satellites. The improved model is validated by comparing the predicted clocks of existing models and the improved model with precisely estimated ones. The bias of the predicted clock is within ±0.5 ns over three hours and better than that of the other models and can be used for several real-time precise applications. The clock prediction is further evaluated by applying clock corrections to precise point positioning (PPP) in both static and kinematic mode for eight IGS (International GNSS Service) MGEX (Multi-GNSS Experiment) stations in the Asia-Pacific region. In the static PPP, the improved model is validated to be effective, and position accuracies of some IGS MGEX stations achieve more than 30.0% improvements on average for each component, which enables us to obtain sub-decimeter positioning. In the kinematic PPP, the improved model performs much better than the others in terms of both the convergence time and the position accuracy. The convergence time can be shortened from 1–2 h to 0.5–1 h, while the position accuracy is enhanced by 15.4%, 21.6% and 19.3% on average in east, north and up component, respectively.

Characteristics of BeiDou-3 Experimental Satellite Clocks

The characteristics of the improved Atomic Frequency Standard (AFS) operated on the latest BeiDou-3 experimental satellites are analyzed from day-of-year (DOY) 254 to 281, of the year 2017, considering the following three aspects: stability, periodicity, and prediction precision. The two-step method of Precise Orbit Determination (POD) is used to obtain the precise clock offsets. We presented the stability of such new clocks and studied the influence of the uneven distribution of the ground stations on the stability performance of the clock. The results show that the orbit influence on the Medium Earth Orbit (MEO) clock offsets is the largest of three satellite types, especially from 3 × 10 3 s to 8.64 × 10 4 s. Considering this orbit influence, the analysis shows that the Passive Hydrogen Maser (PHM) clock carried on C32 is approximately 2.6 × 10 − 14 at an interval of 10 4 , and has the best stability for any averaging intervals among the BeiDou satellite clocks, which currently achieves a level comparable to that of the PHM clock of Galileo, and the rubidium (Rb) clocks of Global Positioning System (GPS) Block IIF. The stability of the improved Rb AFS on BeiDou-3 is also superior to that of BeiDou-2 from 3 × 10 2 s to 3 × 10 3 s, and comparable to that of Rb AFS on the Galileo. Moreover, the periodicity of the PHM clock and the improved Rb clock are presented. For the PHM clock, the amplitudes are obviously reduced, while the new Rb clocks did not show a visible improvement, which will need further analysis in the future. As expected, the precision of the short-term clock prediction is improved because of the better characteristics of AFS. The Root Mean Square (RMS) of 1-h clock prediction is less than 0.16 ns.