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For real-time (RT) precise point positioning (PPP), the state space representation (SSR) information is often delayed due to possible communication delays and specific broadcast intervals. In this case, the positioning results will diverge and re-converge due to the increase of SSR products extrapolation errors. In addition, RT orbit and clock offset accuracy, as well as their extrapolation errors, will vary in different systems and satellites. We propose a PPP with ambiguity resolution (PPP-AR) method that combines a time-differenced carrier phase (TDCP) model, in which the characteristics of the orbit and clock are considered. Under normal communication, the PPP-AR solution is obtained by fixing satellites with small SSR product errors. When the communication is abnormal, the TDCP model is utilized to extrapolate user coordinates by considering different extrapolation error characteristics of satellites. The experimental results show that GPS and Galileo SSR products have better accuracy than BDS, with signal-in-space user ranger errors (SISREs) of 2.7, 2.2, and 8.6 cm, respectively. Optimizing the PPP stochastic model based on SISREs can effectively reduce the convergence time. Under 5 min SSR delay, SISREs caused by clock and orbit extrapolation for GPS/Galileo/BDS are 3.5, 1.4, and 2.6 cm, respectively. After optimizing the TDCP stochastic model based on extrapolation errors, the horizontal and vertical positioning accuracies can be maintained at 0.7 cm and 5.0 cm. For multi-GNSS, the combination of the TDCP and PPP-AR can overcome the influence of short delay. After optimizing the stochastic model, the GPS/Galileo/BDS positioning accuracy can be maintained at about 2.4 cm under 3 min delay, showing an accuracy improvement rate of 59.3% compared with the traditional method using only PPP. Additionally, the rapid PPP convergence results can be obtained by inheriting previous filter state information when the communication recovers normally. [ABSTRACT FROM AUTHOR]

The orbit maneuver detection is crucial in Global Navigation Satellite System (GNSS) precise orbit determination, which is necessary for adjusting data processing strategies. The frequency of orbit maneuvers for the BeiDou Navigation System is significantly higher than that of other navigation systems, especially for geosynchronous orbit (GEO) and inclined geosynchronous orbit (IGSO) satellites. We propose a novel real-time and postprocessing method for detecting orbit maneuvers for BeiDou satellites based on the orbit differences between the epoch-updated orbit estimated using square root information (SRIF) and the predicted orbit according to the precise orbit estimated during non-maneuver period, as well as the orbital state difference during maneuver and non-maneuver periods. This method has significant advantages over using observation residuals and it is not affected by observation outliers, thus improving the accuracy and timeliness of orbit maneuver detection. We demonstrated that 32 orbit maneuver events of BeiDou satellites were successfully detected in 2022, of which 1 was for medium Earth orbit (MEO), 7 were for IGSO with an average detected maneuvering time of 7–8 min, and 24 were for GEO satellites with an average detected time of 4–5 min. Moreover, our method can be easily integrated into current real-time filter-based precise orbit determination (POD) processing without any extra task line, which simplifies the overall data processing. The data used in this method can be accessed easily, including GNSS observation data, broadcast ephemeris, and other open-source information files. [ABSTRACT FROM AUTHOR]

Real-time satellite clock offset is a crucial element for real-time precise point positioning (RT-PPP). However, the elapsed time for undifferenced (UD) multi-global navigation satellite system (GNSS) real-time satellite clock offset estimation at each epoch is increased with the growth of stations, which may fall short of real-time application requirements. Therefore, a rapid estimation method for UD multi-GNSS real-time satellite clock offset is proposed to improve the computation efficiency, in which both the dimension of the normal equation (NEQ) and the number of redundant observations are calculated before adjustment; if these two values are larger than the predefined thresholds, the elevation mask is gradually increased until they are less than the predefined thresholds. Then, the clock offset estimation is conducted; this method is called clock offset estimation using partial observations. Totals of 50, 60, 70 and 80 stations are applied to perform experiments. Compared to clock offset estimation using all observations, the elapsed times of clock offset estimation using partial observations can be reduced from 6.80 to 3.10 s, 7.93 to 2.97 s, 12.04 to 3.14 s for 60, 70 and 80 stations, respectively. By using the proposed method, the elapsed time of the clock offset estimation at each epoch is less than 5 s. The estimated clock offset accuracy for GPS, BDS-3, Galileo and GLONASS satellites are better than 0.04, 0.05, 0.03 and 0.16 ns when using the partial observations to estimate clock offset with 50, 60, 70 and 80 stations, respectively. For the multi-GNSS kinematic PPP using the estimated clock offset from 50, 60, 70 and 80 stations with partial observations, the positioning accuracy at 95% confidence level in the east, north and up direction are better than 2.70, 2.20 and 5.60 cm, respectively. [ABSTRACT FROM AUTHOR]

• Provide a simplified joint orbit determination (JOD) method that employs kinematic approach to determine the LEO satellites orbit. • The comparative analysis between proposed method and traditional method is analyzed based on the real data from LEO onboard GNSS receiver. • Simplified JOD method demonstrates a significant decrease in computation time and is nearly unaffected by orbital maneuvers of LEO satellites. • The proposed method is prospective to be an efficient JOD mode for future LEO navigation enhancement system. Joint orbit determination (JOD) of Global Navigation Satellite Systems (GNSS) satellites and low Earth orbit (LEO) satellites has been substantiated as an efficacious approach to compensate for the ground station geometry. In the traditional JOD, the precise orbit determination (POD) of LEO satellite is mainly processed by the reduced-dynamic approach, however, this approach involves complex calculations and the credibility of the determined positions diminishes when LEO satellites undergo orbital maneuvers. Therefore, a simplified JOD method is designed that employs kinematic approach to determine the LEO satellites orbit. To verify the effectiveness of the proposed method, the orbit of GPS satellites and LEO satellites are jointly estimated utilizing the regional and global networks. 8 LEO satellites, including GRACE-C/D, SWARM-A/B/C, SENTINEL-3A/B, and JASON-3, are chosen for JOD. The comparative analysis between the proposed method and traditional method are achieved in terms of GPS orbit accuracy, LEO orbit accuracy, computation time and the JOD performance during LEO maneuvers. Under regional station scenario, the GPS orbit accuracy determined using the proposed method and the traditional method is 3.64 cm and 2.52 cm, respectively. In the case of global station scenario, the accuracies are 1.71 cm and 1.64 cm. Additionally, the traditional method yields superior enhancement and higher accuracy of the LEO orbits. However, it exhibits a noticeable increase in computation time compared to the proposed method and the performance of JOD declines significantly when LEO satellites undergo orbital maneuvers. Alternatively, although the accuracy of the LEO orbits using the proposed method is comparatively lower, it offers a substantial reduction in the overall network computation time compared to traditional method. Moreover, the proposed method based on LEO kinematic precise orbit determination (KPOD) is nearly unaffected by orbital maneuvers of LEO satellites, presenting unique advantages in practical data processing. [ABSTRACT FROM AUTHOR]

The quality of real-time satellite clock offsets products is one of the key elements for real-time satellite clock performance monitoring and real-time precise point positioning (PPP). However, impacted by the station location, environment, communication equipment, receiver performance, network delay, temporary modem failure or other reasons, the observation data of clock offset datum receiver occasionally outage, resulting in all satellite clocks offset cannot be estimated. In this contribution, an efficient clock offset datum switching compensation method for BDS real-time satellite clock offset estimation is proposed. One hundred stations distributed around the world, from day of year (DOY) 074 to 075 in 2019 are used to estimate BDS real-time satellite clock offset. Four schemes: clock offset datum switching without compensation (S1), clock offset datum switching with satellite clock offset jump compensation (S2), clock offset datum switching with satellite clock offset jump and receiver clock drift compensation (S3, the proposed method), clock offset datum without switching (S4), are used to validate the proposed method. By using the proposed method, the satellite clock offset jump can be eliminated and the satellite clock offset consistency can be maintained. The satellite clock offsets STD for S1, S2, S3 and S4 are 0.184, 0.183, 0.183 and 0.150 ns, respectively. The fitting precision of S1, S2, S3 and S4 are 70907.344, 0.731, 0.502 and 0.543 ns, respectively. The frequency stability of S3 shows the best performance among S2, S3 and S4 when the averaging interval time is 10,000 and 20,000 s, which can be attributed to the effectiveness of proposed method and frequency stability difference of clock offset datum receiver. The fitting precision and frequency stability cannot be reflected correctly by clock offset due to the satellite clock offset jump in S1. For precise point positioning (PPP), the coordinates jump and re-convergence can be eliminated by using the proposed method. Thus, this method can provide a reference for obtaining real-time, continuous and reliable BDS satellite clock offset products. [ABSTRACT FROM AUTHOR]

Abstract Transmission link disturbances and device failure cause global navigation satellite system (GNSS) receivers to miss observations, leading to poor accuracy in real-time kinematic (RTK) positioning. Previously described solutions for this problem are influenced by the length of the prediction period, or are unable to account for changes in receiver state because they use information from previous epochs to make predictions. We propose an algorithm for predicting double difference (DD) observations of obstructed BeiDou navigation system (BDS) GEO satellites. Our approach adopts the first-degree polynomial function for predicting missing observations. We introduce a Douglas-Peucker algorithm to judge the state of the rover receiver to reduce the impact of predictive biases. Static and kinematic experiments were carried out on BDS observations to evaluate the proposed algorithm. The results of our navigation experiment demonstrate that RTK positioning accuracy is improved from meter to decimeter level with fixed ambiguity (horizontal < 2 cm, vertical < 18 cm). Horizontal accuracy is improved by over 50%, and the vertical accuracies of the results of the static and kinematic experiments are increased by 47% and 27% respectively, compared with the results produced by the classical approach. Though as the baseline becomes longer, the accuracy is weakened, our predictive algorithm is an improvement over existing approaches to overcome the issue of missing data. [ABSTRACT FROM AUTHOR]

Abstract The information of the satellite clock switching and performance variations on-orbit of Chinese BeiDou-2 Navigation System (BDS) is not available for the public. In order to detect the BDS satellite clock switching and performances variation, we analyzed the precise clock offset products with a total duration of 5 years every BDS satellite equipped four atomic clocks from four different manufactures from January 2013 to October 2017. Three important contributions are concluded as follows. (1) It is found that the average time of on-orbit operation for BDS satellite clocks is about 1–2 years. There have been 22 times of clock switching for BDS satellites, of which the C05 and C08 satellites have been switched to the fourth (last) atomic clock. (2) There are frequent phase adjustments for BDS on-orbit satellite clocks, and the frequency series is relatively stable. Furthermore, there are semi-annual sinusoid cycles in the frequency drift series of C06 and C09 satellites. (3) The performances of MEO satellite clocks perform better than the IGSO and GEO satellite clocks. The average ten-thousand frequency stability of BDS satellite clocks is about 1E-13, which is worse than that of GPS and Galileo but better than that of GLONASS. [ABSTRACT FROM AUTHOR]

• A new evaluation method considering periodic errors for GNSS atomic clocks on board is proposed. • The correlation relationship between the sun elevation and orbit radial error, fitting precision, frequency stability, amplitude is revealed. • The evaluation results of GPS satellite clocks in orbit that more approach to the real performance are obtained. The performance of the atomic clock in orbit is of terrific significance for the Global Navigation Satellite System (GNSS). With the rapid development of satellite navigation and atomic clock technology, the periodic error of satellite clocks caused by the environment is more prominent. This paper focuses on the analysis and quantification of the systematic periodic error in the clock offset and proposes a more accurate evaluation method for GPS satellite clocks. The fact that the J2 relativistic effect and orbit radial error are the main sources of the systematic periodic term has been revealed. Then, the Fast Fourier Transform (FFT) is employed using the sliding window to investigate the periodic influence caused by satellite orbit and the J2 relativistic effect on clock offset through six GPS satellites with different orbital planes, these satellites also cover all four types of GPS satellite blocks. The results show that there is an obvious relationship between the sun elevation and orbit radial error, clock offset fitting precision, frequency stability and amplitude. The different geometric configurations of the satellite and the varying environment make this relationship different. Based on the clock offset provided by European Space Agency (ESA), the period of clock offset is extracted and quantized, with the period of 24 h, 12 h, 8 h, 6 h, 4 h, and 3 h. According to the daily extraction results of the time-varying periodic terms, the two most noticeable terms correction on satellite clock offset has been proven to be effective in eliminating periodic errors. Compared to those without periodic correction, the fitting precision and frequency stability can improve by 48.5% and 42.6%, respectively. In addition, all GPS satellite clocks in orbit are evaluated by this periodic correction method, and the results are more approach to the actual performance of the satellite clock. Furthermore, this method can also be adapted to evaluate satellite clocks of other GNSS systems. Therefore, when we evaluate the high-precision atomic clock flying on board GNSS satellites and compare them with the manufacturers' specifications, the periodic error cannot be neglected. [ABSTRACT FROM AUTHOR]

[Display omitted] • The long-term performance of GLONASS satellite clocks were revealed for the first time. • The periodic terms existed in the clock are detected. • The comparison between GLONASS and other GNSS satellite clock is conducted. The cesium atomic clock installed on the GLObal NAvigation Satellite System (GLONASS) is a key piece of equipment. However, its performance is easily affected by the external environment and its physical characteristics. Therefore, it is essential to evaluate the long-term performance of the clock. In this study, using eight years of continuous GLONASS precise satellite clock offset products, the long-term performance of GLONASS satellite clocks is revealed for the first time. The results showed that the mean number of phase and frequency jumps for one satellite clock in one year were 0.29 and 0.19, respectively. The fitting precision, which is the standard deviation of the fitting residuals, was 0.88 nanoseconds (ns). Except for the R06 satellite clock, the first or second period was 11.24 h in the clock offset. In terms of clock stability, the short-term clock offset prediction accuracy was 0.52 ns, the frequency stability at 1000 and 10000 s was 4.03 × 10-13 and 1.01 × 10-13, respectively. Both the short-term clock offset prediction accuracy and frequency stability were inferior to those of the rubidium atomic clock of the Global Positioning System (GPS) Block IIF satellites, the second-generation BeiDou Navigation Satellite System (BDS-2), Quasi-Zenith Satellite System (QZSS), and Galileo Passive Hydrogen Maser (PHM). The mean switching number for each GLONASS satellite clock was 0.27 per year. Furthermore, the R15 satellite clock, maybe owing to its hardware noise, delivered the poorest performance among those of all the GLONASS satellite clocks. [ABSTRACT FROM AUTHOR]

The positioning, navigation, and timing (PNT) service of the Global Navigation Satellite System (GNSS) is developing in the direction of real time and high precision. However, there are some problems that restrict the development of real-time and high-precision PNT technology. Satellite orbit maneuvering is one of the factors that reduce the reliability of real-time navigation products, especially the high-frequency orbit maneuvering of geostationary earth orbit (GEO) and inclined geosynchronous orbit (IGSO) satellites. The BeiDou Navigation Satellite System (BDS) constellation is designed to contain GEO, IGSO, and medium earth orbit (MEO). These orbit maneuvers bring certain difficulties for data processing, especially for BeiDou satellites, such as decreased real-time service performance, which results in real-time navigation products including unusable maneuvered satellites. Additionally, the performance of real-time navigation products will decrease because the orbit maneuvers could not be known in advance, which diminishes the real-time PNT service performance of BDS for users. Common users cannot obtain maneuvering times and strategies owing to confidentiality, which can lead to a decline in the BDS real-time service performance. Thus, we propose a method to predict orbit maneuvers. BDS data from the broadcast ephemeris were analyzed to verify the availability of the proposed method. In addition, the results of real-time positioning were analyzed by using ultra-rapid orbit products, demonstrating that their reliability is improved by removing maneuvered satellites in advance. This is vital to improve the reliability of real-time navigation products and BDS service performance. [ABSTRACT FROM AUTHOR]