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1
Wang, Hu, Pengyuan Li, Jiexian Wang, Hongyang Ma, Yangfei Hou, and Yingying Ren. "Analysis of BDS-3 Real-Time Satellite Clock Offset Estimated in Global and Asia-Pacific and the Corresponding PPP Performances." Remote Sensing 14, no. 24 (December 7, 2022): 6206. http://dx.doi.org/10.3390/rs14246206.
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The quality of satellite clock offset affects the performances of positioning, navigation and timing services, and thus it is essential to the Global Navigation Satellite System (GNSS). This research focuses on the estimation of BeiDou Navigation Satellite System (BDS) real-time precise satellite clock offset by using GNSS stations located in the Global and Asia-Pacific region based on the mixed-difference model. The precision of the estimated BDS clock corrections is then analyzed with the classification of the orbit types, satellite generations, and atomic clock types. The results show that the precision of the BDS clock offset estimated in the Asia-Pacific for Geosynchronous Earth Orbit (GEO), Inclined Geosynchronous Satellite Orbit (IGSO) and Medium Earth Orbit (MEO) satellites are 0.204 ns, 0.077 ns and 0.085 ns, respectively, as compared to those of clock offsets estimated in globally distributed stations. The average precision of the BDS-3 satellites clock offset estimated in global region is 0.074 ns, which is much better than the 0.130 ns of BDS-2. Furthermore, analyzing the characteristics of the corresponding atomic clocks can explain the performance of the estimated satellite clock offset, and the stability and accuracy of various parameters of the Passive Hydrogen Maser (PHM) atomic clocks are better than those of Rubidium (Rb) atomic clocks. In the positioning domain, the real-time clocks estimated in the global/Asia-Pacific have been applied to BDS kinematic Precise Point Positioning (PPP) in different regions. The Root Mean Square (RMS) of positioning results in global real-time kinematic PPP is within 4 cm in the horizontal direction and about 6 cm in the vertical direction. Hence, the BDS real-time clock offset can supply the centimeter-level positioning demand around the world.
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Gu, Shengfeng, Feiyu Mao, Xiaopeng Gong, Yidong Lou, Xueyong Xu, and Ye Zhou. "Evaluation of BDS-2 and BDS-3 Satellite Atomic Clock Products and Their Effects on Positioning." Remote Sensing 13, no. 24 (December 11, 2021): 5041. http://dx.doi.org/10.3390/rs13245041.
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The BeiDou Navigation Satellite System (BDS) has completed third phase construction and currently provides global services, with a mixed constellation of BDS-2 and BDS-3. The newly launched BDS-3 satellites are equipped with rubidium and passive hydrogen maser (PHM) atomic clocks. The performance of atomic clocks is one of the cores of satellite navigation system, which will affect the performance of positioning, navigation and timing (PNT). In this paper, we systematically analyze the characteristics of BDS-2 and BDS-3 atomic clocks, based on more than one year of precise satellite clock products and broadcast ephemeris. Firstly, the results of overlapping Allan variations demonstrate that BDS-3 Rb and PHM clocks improve better in stability than BDS-2 Rb clock and are comparable to GPS IIF Rb and Galileo PHM clocks. Accordingly, the STDs of BDS-3 broadcast satellite clock are better than GPS and BDS-2, which are at the same level with that of Galileo. Secondly, the inter-system bias (ISB) between BDS-2 and BDS-3 is analyzed by satellite clock datum comparison and precise point positioning (PPP). Surprisingly, the discrepancy between BDS-2 and BDS-3 satellite clock datum has a great difference between products that could reach up to about 10 ns for WHU satellite clock products and broadcast ephemeris. Moreover, the ISBs between BDS-2 and BDS-3 satellite clocks are quite stable over one-year periods. Thirdly, due to the improved stability of BDS-3 atomic clock, the 68% positioning accuracy is better than 0.65 m at 10 min for BDS-3 PPP, based on broadcast ephemeris. Besides, the non-negligible bias between BDS-2 and BDS-3 will greatly affect the BDS precise data processing. The accuracy of positioning is greatly improved when considering the ISB.
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Geng, Tao, Rui Jiang, Yifei Lv, and Xin Xie. "Analysis of BDS-3 Onboard Clocks Based on GFZ Precise Clock Products." Remote Sensing 14, no. 6 (March 13, 2022): 1389. http://dx.doi.org/10.3390/rs14061389.
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The characteristics and performance of satellite clocks are important to the positioning, navigation, and timing (PNT) services of Global Navigation Satellite System (GNSS) users. Although China’s BeiDou-3 Navigation Satellite System (BDS-3) has been fully operational for more than one year, there is still a lack of comprehensive research on the onboard clocks of the entire BDS-3 constellation. In this study, the precise clock products of GeoForschungsZentrum (GFZ) from day-of-year (DOY) 1, 2021 to DOY 300, 2021 were used to analyze the characteristics and performance of BDS-3 onboard clocks from the following aspects: clock bias, frequency, drift rate, fitting residuals, periodicity, and frequency stability. Compared with BDS-2, the clock quality of BDS-3 satellites has been greatly improved, but there are still jumps in the clock offsets and frequency series of BDS-3 clocks. The drift rate of BDS-3 clocks varies within the range between −2×10−18 and 2×10−18 s/s2. The daily model fitting residuals of passive hydrogen masers (PHM) on BDS-3 medium Earth orbit (MEO), inclined geosynchronous orbit (IGSO), and geostationary (GEO) satellites are 0.15, 0.28, and 0.46 ns, respectively. The overlapping Allan deviation (OADEV) of BDS-3 MEO clocks is 4.0 × 10−14 s/s at a time interval of 1000 s. The PHMs on BDS-3 MEO satellites exhibit fewer periodic signals than those of Rb clocks. In addition, the precise clock offsets of the BDS-3 PHMs carried on the MEO, IGSO, and GEO satellites show different periodicities, which are similar to those of the corresponding types of BDS-2 satellites.
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Kudrys, Jacek, Dominik Prochniewicz, Fang Zhang, Mateusz Jakubiak, and Kamil Maciuk. "Identification of BDS Satellite Clock Periodic Signals Based on Lomb-Scargle Power Spectrum and Continuous Wavelet Transform." Energies 14, no. 21 (November 1, 2021): 7155. http://dx.doi.org/10.3390/en14217155.
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Onboard satellite clocks are the basis of Global Navigation Satellite Systems (GNSS) operation, and their revolution periods are at the level of 2 per day (about 12 h) in the case of the Medium Earth Orbit (MEO) satellites. In this work, the authors analysed the entire BeiDou Navigation Satellite System (BDS) space segment (BDS-2 and BDS-3) in terms of the occurrence of periodic, repetitive signals in the clock products, and checked if they coincide with the orbital periods or their multiples. The Lomb-Scargle (L-S) power spectrum was used as a tool to determine the periods present in the BDS clock products, allowing for analyses based on incomplete input data; in this case, the incomplete data were the phase data with jumps and outliers removed. In addition, continuous wavelet transform (CWT) was used to produce a time−frequency representation showing the more complex behaviour of the satellite clock products. As shown in the case of geostationary and geosynchronous inclined orbit satellites, the main period was 23.935 h, while for the Medium Earth Orbit it was 12.887 h, with the BDS satellite orbital period being 12 h 53 m (12.883 h). Some effects connected with reference clock swapping are also visible in the power spectrum. The conducted analyses showed that the BDS-2 satellite clocks have much higher noise than the BDS-3 satellite clocks, meaning that the number of designated periods is greater, but their reliability is significantly lower. BDS-3 satellites have only been in operation for a very short time, thus this is the first analysis to include this type of data. Moreover, such a wide and complex analysis has not been carried out to date.
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Xie, Wei, Guanwen Huang, Bobin Cui, Pingli Li, Yu Cao, Haohao Wang, Zi Chen, and Bo Shao. "Characteristics and Performance Evaluation of QZSS Onboard Satellite Clocks." Sensors 19, no. 23 (November 24, 2019): 5147. http://dx.doi.org/10.3390/s19235147.
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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.
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Lv, Yifei, Tao Geng, Qile Zhao, and Jingnan Liu. "Characteristics of BeiDou-3 Experimental Satellite Clocks." Remote Sensing 10, no. 11 (November 22, 2018): 1847. http://dx.doi.org/10.3390/rs10111847.
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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.
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Dai, Xiaolei, Yidong Lou, Zhiqiang Dai, Caibo Hu, Yaquan Peng, Jing Qiao, and Chuang Shi. "Precise Orbit Determination for GNSS Maneuvering Satellite with the Constraint of a Predicted Clock." Remote Sensing 11, no. 16 (August 20, 2019): 1949. http://dx.doi.org/10.3390/rs11161949.
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Precise orbit products are essential and a prerequisite for global navigation satellite system (GNSS) applications, which, however, are unavailable or unusable when satellites are undertaking maneuvers. We propose a clock-constrained reverse precise point positioning (RPPP) method to generate the rather precise orbits for GNSS maneuvering satellites. In this method, the precise clock estimates generated by the dynamic precise orbit determination (POD) processing before maneuvering are modeled and predicted to the maneuvering periods and they constrain the RPPP POD during maneuvering. The prediction model is developed according to different clock types, of which the 2-h prediction error is 0.31 ns and 1.07 ns for global positioning system (GPS) Rubidium (Rb) and Cesium (Cs) clocks, and 0.45 ns and 0.60 ns for the Beidou navigation satellite system (BDS) geostationary orbit (GEO) and inclined geosynchronous orbit (IGSO)/Median Earth orbit (MEO) satellite clocks, respectively. The performance of this proposed method is first evaluated using the normal observations without maneuvers. Experiment results show that, without clock-constraint, the average root mean square (RMS) of RPPP orbit solutions in the radial, cross-track and along-track directions is 69.3 cm, 5.4 cm and 5.7 cm for GPS satellites and 153.9 cm, 12.8 cm and 10.0 cm for BDS satellites. When the constraint of predicted satellite clocks is introduced, the average RMS is dramatically reduced in the radial direction by a factor of 7–11, with the value of 9.7 cm and 13.4 cm for GPS and BDS satellites. At last, the proposed method is further tested on the actual GPS and BDS maneuver events. The clock-constrained RPPP POD solution is compared to the forward and backward integration orbits of the dynamic POD solution. The resulting orbit differences are less than 20 cm in all three directions for GPS satellite, and less than 30 cm in the radial and cross-track directions and up to 100 cm in the along-track direction for BDS satellites. From the orbit differences, the maneuver start and end time is detected, which reveals that the maneuver duration of GPS satellites is less than 2 min, and the maneuver events last from 22.5 min to 107 min for different BDS satellites.
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Yang, Zhixin, Hui Liu, Chuang Qian, Bao Shu, Linjie Zhang, Xintong Xu, Yi Zhang, and Yidong Lou. "Real-Time Estimation of Low Earth Orbit (LEO) Satellite Clock Based on Ground Tracking Stations." Remote Sensing 12, no. 12 (June 25, 2020): 2050. http://dx.doi.org/10.3390/rs12122050.
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The rapid movement of low Earth orbit (LEO) satellite can improve geometric diversity, which contributes to the rapid convergence of Global Navigation Satellite System (GNSS) precise point positioning (PPP). However, the LEO onboard receiver clock cannot be used directly by PPP users as the LEO satellite clock because the LEO onboard receiver clock and LEO satellite clock absorb different code delays when receiving and transmitting signals. In this study, a real-time estimation approach for the LEO satellite clock based on ground tracking stations was proposed for the first time. The feasibility for the rapid convergence of the LEO satellite clock was analyzed using the satellite time dilution of precision (TDOP) that one satellite is relative to multiple ground tracking stations. The LEO constellation of 168 satellites and observations for 15 ground tracking stations were simulated to verify the proposed method. The experiment results showed that the average convergence time was 31.21 min for the Global Positioning System (GPS) satellite clock, whereas the value for the LEO satellite clock was only 2.86 min. The average root mean square (RMS) and standard deviation (STD) values after convergence were 0.71 and 0.39 ns for the LEO satellite clock, whereas the values were 0.31 and 0.13 ns for the GPS satellite clock. The average weekly satellite TDOP for the LEO satellite was much smaller than that for the GPS satellite. The average satellite TDOPs for all LEO and GPS satellites were 19.13 and 1294.70, respectively. However, the average delta TDOPs caused by satellite motion for all LEO and GPS satellites were both 0.10. Therefore, the rapid convergence of the LEO satellite clock resulted from the better geometric distribution of the LEO satellite relative to ground stations. Despite errors and the convergence time of the LEO satellite clock, the convergence time and positioning accuracy for LEO-augmented GPS and BeiDou Navigation Satellite System (BDS) PPP with the real-time estimated LEO satellite clock can still reach 10.63 min, 1.94 cm, 1.44 cm, and 4.18 cm in the east, north, and up components, respectively. The improvements caused by LEO satellite for GPS/BDS PPP were 59%, 30%, 31%, and 33%, respectively.
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Meng, Fan Qin, Xu Hai Yang, Ji Kun Ou, and Pei Wei. "Method of Determining Satellite Clock Error by Using Observation Data of Satellite-Ground and Inter-Satellite." Advanced Materials Research 718-720 (July 2013): 474–79. http://dx.doi.org/10.4028/www.scientific.net/amr.718-720.474.
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We have done some simulate analysis on GPS data in this paper. The main research is method of determining satellite clock error by usining observation data of satellite-ground and inter-satellite under the condition of regional station arrangement. The research method is as follows: when the satellite in the visible area of regional observation network, we can get satellite clock error directly by satellite-ground time comparison, and predict the satellite clock error in invisible area. When the satellite in the invisible area of regional observation network, if this satellite can establish inter-satellite links with other satellites in the visible area, then the satellite clock error can be determined by time comparison of satellite-ground and inter-satellite; If there is no inter-satellite link between this satellite and other satellites in the visible area, then we can only predict the satellite clock error by given data. The simulation conditions of this paper are as follows: the system error of satellite-ground is 0.5 ns, the random error is 0.5 ns; the system error of inter-satellite is 1 ns, the random error is 0.5 ns. In this case, we can obtain the satellite clock error of PRN02 in an orbital period by method of this paper, and the accuracy is about 1.3 ns.
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Yuan, Zhimin, Changsheng Cai, Lin Pan, and Cuilin Kuang. "An Improved Multi-Satellite Method for Evaluating Real-Time BDS Satellite Clock Offset Products." Remote Sensing 12, no. 21 (November 5, 2020): 3638. http://dx.doi.org/10.3390/rs12213638.
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Two methods are widely used for evaluating the precision of satellite clock products, namely the single-satellite method (SSM) and the multi-satellite method (MSM). In the satellite clock product evaluation, an important issue is how to eliminate the timescale difference. The SSM selects a reference satellite to eliminate the timescale difference by between-satellite differencing, but its evaluation results are susceptible to the gross errors in the referenced satellite clock offsets. In the MSM, the timescale difference is first estimated and then removed. Unlike the GPS, the BeiDou Navigation Satellite System (BDS) consists of three types of satellites, namely geosynchronous earth orbit (GEO), inclined geosynchronous orbit (IGSO), and medium earth orbit (MEO) satellites. The three types of satellites have uneven orbital accuracy. In the generation of satellite clock products, the orbital errors are partly assimilated into the clock offsets. If neglecting the orbital accuracy difference of the three types of BeiDou satellites, the MSM will obtain biased estimates of the timescale difference and finally affect the clock product evaluation. In this study, an improved multi-satellite method (IMSM) is proposed for evaluating the real-time BDS clock products by removing the assimilated orbital errors of the three types of BDS satellites when estimating the timescale difference. Three real-time BDS clock products disseminated by three different International GNSS Service (IGS) analysis centers, namely CLK16, CLK20, and CLK93, over a period of two months are used to validate this method. The results indicate that the assimilated orbital errors have a significant impact on the estimation of the timescale difference. Subsequently, the IMSM is compared with the SSM in which the referenced satellite is rigorously chosen, and their RMS difference is only 0.08 ns, which suggests that the evaluation results obtained by the IMSM are accurate. Compared with the traditional MSM, the IMSM improves the RMS by 0.16, 0.11, and 0.07 ns for CLK16, CLK20, and CLK93, respectively. Finally, three real-time BDS clock products are evaluated using the proposed method, and results reveal a significant precision difference among them.
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Xu, Beizhen, Lei Wang, Wenju Fu, Ruizhi Chen, Tao Li, and Xinxin Zhang. "A Practical Adaptive Clock Offset Prediction Model for the Beidou-2 System." Remote Sensing 11, no. 16 (August 8, 2019): 1850. http://dx.doi.org/10.3390/rs11161850.
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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.
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Liu, Shuai, and Yunbin Yuan. "A Method to Accelerate the Convergence of Satellite Clock Offset Estimation Considering the Time-Varying Code Biases." Remote Sensing 13, no. 14 (July 9, 2021): 2714. http://dx.doi.org/10.3390/rs13142714.
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Continuous and stable precision satellite clock offsets are an important guarantee for real-time precise point positioning (PPP). However, in real-time PPP, the estimation of a satellite clock is often interrupted for various reasons such as network fluctuations, which leads to a long time for clocks to converge again. Typically, code biases are assumed to stay constant over time in clock estimation according to the current literature. In this contribution, it is shown that this assumption reduces the convergence speed of estimation, and the satellite clocks are still unstable for several hours after convergence. For this reason, we study the influence of different code bias extraction schemes, that is, taking code biases as constants, extracting satellite code biases (SCBs), extracting receiver code biases (RCBs) and simultaneously extracting SCBs and RCBs, on satellite clock estimation. Results show that, the time-varying SCBs are the main factors leading to the instability of satellite clocks, and considering SCBs in the estimation can significantly accelerate the filter convergence and improve the stability of clocks. Then, the products generated by introducing SCBs in the clock estimation based on undifferenced observations are applied to PPP experiments. Compared with the original undifferenced model, clocks estimated using the new method can significantly accelerate the convergence speed of PPP and improve the positioning accuracy, which illustrates that our estimated clocks are effective and superior.
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Sun, Leyuan, Wende Huang, Shuaihe Gao, Wei Li, Xiye Guo, and Jun Yang. "Joint Timekeeping of Navigation Satellite Constellation with Inter-Satellite Links." Sensors 20, no. 3 (January 25, 2020): 670. http://dx.doi.org/10.3390/s20030670.
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As a system of ranging and positioning based on time transfer, the timekeeping ability of a navigation satellite constellation is a key factor for accurate positioning and timing services. As the timekeeping performances depend on the frequency stability and predictability of satellite clocks, we propose a method to establish a more stable and predictable space time reference, i.e., inter-satellite link time (ISLT), uniting the satellite clocks through inter-satellite links (ISLs). The joint timekeeping framework is introduced first. Based on the weighted average timescale algorithm, the optimal weights that minimize the increment of the ISLT timescale are determined and allocated to the clock ensemble to improve the frequency stability and predictability in both the long and short term. The time deviations with respect to the system time of nine BeiDou-3 satellites through multi-satellite precise orbit determination (MPOD) are used for joint timekeeping evaluation. According to the Allan deviation, the frequency of the ISLT is more stable than the nine satellite clocks in the short term (averaging time smaller than 7000 s), and its daily stability can reach 6 × 10−15. Meanwhile, the short-term (two hours) and long-term (10 h) prediction accuracy of the ISLT is 0.18 and 1.05 ns, respectively, also better than each satellite clock. Furthermore, the joint timekeeping is verified to be robust against single-satellite malfunction.
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Chunhao, Han, Cai Zhiwu, Lin Yuting, Liu Li, Xiao Shenghong, Zhu Lingfeng, and Wang Xianglei. "Time Synchronization and Performance of BeiDou Satellite Clocks in Orbit." International Journal of Navigation and Observation 2013 (September 5, 2013): 1–5. http://dx.doi.org/10.1155/2013/371450.
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The time model of Beidou satellite clocks is analyzed. The general relations of satellite clocks with the system time are studied. The error sources of two-way radio time transfer between satellites and uplink stations are analyzed. The uncertainty of type A is about 0.3 ns in Beidou system. All the satellite clocks in orbit of Beidou satellite navigation system are evaluated by the clock offsets observed by the two-way radio time transfer. The frequency stabilities at a sample time of 10000 s and 1 day for all the satellite clocks are better than . It means that the performance of Beidou satellite clocks in orbit is consistent with the ground test, and the results in orbit are a little better than those in ground vacuum.
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Xuan, Cheng, Li ZhiGang, Yang XuHai, Wu WenJun, Lei Hui, and Feng ChuGang. "Chinese Area Positioning System With Wide Area Augmentation." Journal of Navigation 65, no. 2 (March 12, 2012): 339–49. http://dx.doi.org/10.1017/s0373463311000750.
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The Chinese Area Positioning System (CAPS) is a regional satellite navigation system; its space segment consists of some Geostationary Earth Orbit (GEO) satellites and 2∼3 Inclined Geo-Synchronous Orbit (IGSO) satellites. Only a few satellites are needed to provide good area coverage and hence it is an ideal space segment for a regional navigation system. A time transfer mode is used to transmit navigation signals, so no high-precision atomic clocks are required onboard the satellites; all of the transferred navigation signals are generated by the same atomic clock at the master control station on the ground. By using virtual clock technology, the time of emission of signals from the ground control station is transformed to the time of transfer of signals at the phase centre of the satellite antenna; thus the impact of ephemeris errors of satellite on positioning accuracy is greatly decreased, enabling the CAPS to have the capability of wide area augmentation. A novel technology of orbit determination, called Paired Observation Combination for Both Stations (POCBS), proposed by the National Time Service Centre, is used in CAPS. The generation and measurement of ranging signals for the orbit survey are carried out in the ground station and the instrument errors are corrected in real-time. The determination of the clock offset is completely independent of the determination of satellite orbit, so the error of the clock offset has no impact on orbit determination. Therefore, a very high precision of satellite orbits, better than 4·2 cm (1 drms) can be obtained by the stations under regional distribution.
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Ai, Qingsong, Kamil Maciuk, Paulina Lewinska, and Lukasz Borowski. "Characteristics of Onefold Clocks of GPS, Galileo, BeiDou and GLONASS Systems." Sensors 21, no. 7 (March 30, 2021): 2396. http://dx.doi.org/10.3390/s21072396.
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This research is focused on searching for frequency and noise characteristics for available GNSS (Global Navigation Satellite Systems). The authors illustrated frequency stability and noise characteristics for a selected set of data from four different GNSS systems. For this purpose, 30-s-interval clock corrections were used for the GPS weeks 1982–2034 (the entirety of 2018). Firstly, phase data (raw clock corrections) were preprocessed for shifts and removal of outliers; GLONASS and GPS satellites characterize a smaller number of outliers than BeiDou and Galileo clock products. Secondly, frequency and Hadamard deviation were calculated. This study concludes that the stability of GPS and Galileo is better than that of BDS (BeiDou Navigation Satellite System) and GLONASS. Regarding noise, the GPS, Galileo, and BDS clocks are affected by the random walk modulation noise (RWFM), flashing frequency modulation noise (FFM), and white frequency modulation noise (WFM), whereas the GLONASS clocks are mainly affected only by WFM.
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Chen, Guangyao, Nan Xing, Chengpan Tang, and Zhiqiao Chang. "Clock Ensemble Algorithm Test in the Establishment of Space-Based Time Reference." Remote Sensing 15, no. 5 (February 23, 2023): 1227. http://dx.doi.org/10.3390/rs15051227.
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A new concept of a space-based synchronized reference network is proposed with the development of an optical frequency reference and laser inter-satellite link. To build such time reference, three clock ensemble algorithms, namely the natural Kalman timescale (NKT) algorithm, the reduced Kalman timescale (RKT) algorithm, and the two-stage Kalman timescale (TKT) algorithm are considered. This study analyzes and compares the performance of these algorithms using BDS, GPS, and Galileo satellite clock data from the GFZ GNSS clock corrections, which will be used in constructing future space-based time references. The study shows that the NKT algorithm improves frequency stability by 0.1–0.2 orders of magnitude in the short and medium term. When the satellite clock is mostly a hydrogen clock, the RKT and NKT are close, and the short and medium-term frequency stability slightly increases. In contrast, the TKT algorithm produces a timescale that improves frequency stability by 1–3 orders of magnitude. A quadratic polynomial model predicts the three timescales, with the results indicating that the short-term prediction accuracy of the satellite clock is within 1ns, and the TKT algorithm’s prediction accuracy is 1–2 orders of magnitude higher than that of the NKT and RKT algorithms. With the deployment of next-generation Low Earth Orbit (LEO) satellites equipped with higher-precision clocks, the space-based time reference system will achieve improved accuracy and greater potential for practical applications.
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Cheng, Peng, Wenbin Shen, Xiao Sun, Chenghui Cai, Kuangchao Wu, and Ziyu Shen. "Measuring Height Difference Using Two-Way Satellite Time and Frequency Transfer." Remote Sensing 14, no. 3 (January 18, 2022): 451. http://dx.doi.org/10.3390/rs14030451.
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According to general relativity theory (GRT), the clock at a position with lower geopotential ticks slower than an identical one at a position with higher geopotential. Here, we provide a geopotential comparison using a non-transportable hydrogen clock and a transportable hydrogen clock for altitude transmission based on the two-way satellite time and frequency transfer (TWSTFT) technique. First, we set one hydrogen clock on the fifth floor and another hydrogen clock on the ground floor, with their height difference of 22.8 m measured by tape, and compared the time difference between these two clocks by TWSTFT for 13 days. Then, we set both clocks on the ground floor and compared the time difference between the two clocks for seven days for zero-baseline calibration (synchronization). Based on the measured time difference between the two clocks at different floors, we obtained the height difference 28.0 ± 5.4 m, which coincides well with the tape-measured result. This experiment provides a method of height propagation using precise clocks based on the TWSTFT technique.
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Wang, Dongxia, Rui Guo, Li Liu, Hong Yuan, Xiaojie Li, Junyang Pan, and Chengpan Tang. "A Method of Whole-Network Adjustment for Clock Offset Based on Satellite-Ground and Inter-Satellite Link Observations." Remote Sensing 14, no. 20 (October 11, 2022): 5073. http://dx.doi.org/10.3390/rs14205073.
Full textAbstract:
The inter-satellite link is an important technology to improve the accuracy of clock offset measurement and prediction for BeiDou Navigation Satellite System (BDS). At present, BDS measures clock offsets of invisible satellite mainly through the “one-hop” reduction mode based on the satellite-ground clock offset of the node visible satellite and the inter-satellite clock offset between the two satellites. However, there exists a systematic deviation caused by the node satellite reduction, and there is still a large room for improvement in clock offset measurement and prediction. Therefore, this paper firstly proposes a method of whole-network adjustment for clock offset based on the satellite-ground and inter-satellite two-way data. The least square method is used to realize the whole-network adjustment of clock offset based on the observations of two sources, and to obtain optimal estimates of different clock offset reduction. Secondly, the evaluation method combining internal and external symbols are proposed by the fitting residual, prediction error and clock offset closure error. Finally, experimental verification is completed based on BDS measured data. In comparison with the “one-hop” reduction method, the fitting residual and prediction error of the whole-network adjustment method reduces about 45.06% and 52.15%, respectively. In addition, inter-satellite station closure error and three-satellite closure error are reduced from 0.69 ns and 0.23 ns to about 0 ns. It can be seen that the accuracy of BDS time synchronization is significantly improved.
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Jiang, Gu, Li, Ge, and Schuh. "A Decentralized Processing Schema for Efficient and Robust Real-time Multi-GNSS Satellite Clock Estimation." Remote Sensing 11, no. 21 (November 5, 2019): 2595. http://dx.doi.org/10.3390/rs11212595.
Full textAbstract:
Real-time multi-GNSS precise point positioning (PPP) requires the support of high-rate satellite clock corrections. Due to the large number of ambiguity parameters, it is difficult to update clocks at high frequency in real-time for a large reference network. With the increasing number of satellites of multi-GNSS constellations and the number of stations, real-time high-rate clock estimation becomes a big challenge. In this contribution, we propose a decentralized clock estimation (DECE) strategy, in which both undifferenced (UD) and epoch-differenced (ED) mode are implemented but run separately in different computers, and their output clocks are combined in another process to generate a unique product. While redundant UD and/or ED processing lines can be run in offsite computers to improve the robustness, processing lines for different networks can also be included to improve the clock quality. The new strategy is realized based on the Position and Navigation Data Analyst (PANDA) software package and is experimentally validated with about 110 real-time stations for clock estimation by comparison of the estimated clocks and the PPP performance applying estimated clocks. The results of the real-time PPP experiment using 12 global stations show that with the greatly improved computational efficiency, 3.14 cm in horizontal and 5.51 cm in vertical can be achieved using the estimated DECE clock.
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Wen, Tailai, Gang Ou, Xiaomei Tang, Pengyu Zhang, and Pengcheng Wang. "A Novel Long Short-Term Memory Predicted Algorithm for BDS Short-Term Satellite Clock Offsets." International Journal of Aerospace Engineering 2021 (August 27, 2021): 1–16. http://dx.doi.org/10.1155/2021/4066275.
Full textAbstract:
The satellite clocks carried on the BeiDou navigation System (BDS) are a self-manufactured hydrogen clock and improved rubidium clock, and their on-orbit performance and stabilities are not as efficient as GPS and Galileo satellite clocks caused of the orbital diversity of the BDS and the complexity of the space operating environment. Therefore, the existing BDS clock product cannot guarantee the high accuracy demand for precise point positioning in real-time scenes while the communication link is interrupted. To deal with this problem, we proposed a deep learning-based approach for BDS short-term satellite clock offset modeling which utilizes the superiority of Long Short-Term Memory (LSTM) derived from Recurrent Neural Networks (RNN) in time series modeling, and we call it QPLSTM. The ultrarapid predicted clock products provided by IGS (IGU-P) and four widely used prediction methods (the linear polynomial, quadratic polynomial, gray system (GM (1,1)), and Autoregressive Integrated Moving Average (ARIMA) model) are selected to compare with the QPLSTM. The results show that the prediction residual is lower than clock products of IGU-P during 6-hour forecasting and the QPLSM shows a greater performance than the mentioned four models. The average prediction accuracy has improved by approximately 79.6, 69.2, 80.4, and 77.1% and 68.3, 52.7, 66.5, and 69.8% during a 30 min and 1-hour forecasting. Thus, the QPLSTM can be considered as a new approach to acquire high-precision satellite clock offset prediction.
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Andrei, Constantin-Octavian, Sonja Lahtinen, Markku Poutanen, Hannu Koivula, and Jan Johansson. "Galileo L10 Satellites: Orbit, Clock and Signal-in-Space Performance Analysis." Sensors 21, no. 5 (March 1, 2021): 1695. http://dx.doi.org/10.3390/s21051695.
Full textAbstract:
The tenth launch (L10) of the European Global Navigation Satellite System Galileo filled in all orbital slots in the constellation. The launch carried four Galileo satellites and took place in July 2018. The satellites were declared operational in February 2019. In this study, we report on the performance of the Galileo L10 satellites in terms of orbital inclination and repeat period parameters, broadcast satellite clocks and signal in space (SiS) performance indicators. We used all available broadcast navigation data from the IGS consolidated navigation files. These satellites have not been reported in the previous studies. First, the orbital inclination (56.7±0.15°) and repeat period (50680.7±0.22 s) for all four satellites are within the nominal values. The data analysis reveals also 13.5-, 27-, 177- and 354-days periodic signals. Second, the broadcast satellite clocks show different correction magnitude due to different trends in the bias component. One clock switch and several other minor correction jumps have occurred since the satellites were declared operational. Short-term discontinuities are within ±1 ps/s, whereas clock accuracy values are constantly below 0.20 m (root-mean-square—rms). Finally, the SiS performance has been very high in terms of availability and accuracy. Monthly SiS availability has been constantly above the target value of 87% and much higher in 2020 as compared to 2019. Monthly SiS accuracy has been below 0.20 m (95th percentile) and below 0.40 m (99th percentile). The performance figures depend on the content and quality of the consolidated navigation files as well as the precise reference products. Nevertheless, these levels of accuracy are well below the 7 m threshold (95th percentile) specified in the Galileo service definition document.
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Kim, Gimin, Hyungjik Oh, Chandeok Park, and Seungmo Seo. "Real-Time Orbit Determination of Korean Navigation Satellite System based on Multi-GNSS Precise Point Positioning." E3S Web of Conferences 94 (2019): 03008. http://dx.doi.org/10.1051/e3sconf/20199403008.
Full textAbstract:
This study proposes real-time orbit/clock determination of Korean Navigation Satellite System (KNSS), which employs the kinematic precise point positioning (PPP) solutions of multiple Global Navigation Satellite System (multi-GNSS) to compensate for receiver clock offset. Global visibility of KNSS satellites in terms of geometric coverage is first analyzed for the purpose of selecting optimal locations of KNSS monitoring stations among International GNSS Service (IGS) and Multi-GNSS Experiment (MGEX) network. While the receiver clock offset is obtained from multi-GNSS PPP clock solutions of real observation data, KNSS measurements are simulated from the dynamically propagated KNSS reference orbit and the receiver clock offset. The offset and drift of satellite clock are also generated based on two-state clock model considering atomic clock noise. Real-time orbit determination results are compared with an artificially generated true or bit, wihch show 0.4m and 0.5m of 3-dimensional root-mean-square (RMS) position errors for geostationary (GEO) and ellitically-inclined-geosynchronous-orbit (EIGSO) satellites, respectively. The overall results show that the real-time precise orbit determination of KNSS should be achievable in meter level by installing KNSS-compatible multi-GNSS receivers on the IGS and/or MGEX network. The overall process can be also used to verify integrity of KNSS monitoring stations.
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Liang, Yifeng, Jiangning Xu, Miao Wu, and Fangneng Li. "Analysis of the Long-Term Characteristics of BDS On-Orbit Satellite Atomic Clock: Since BDS-3 Was Officially Commissioned." Remote Sensing 14, no. 18 (September 11, 2022): 4535. http://dx.doi.org/10.3390/rs14184535.
Full textAbstract:
Satellite atomic clocks are the key elements for position, navigation, and timing services of the Global navigation satellite system (GNSS); it is necessary to research the characteristics of BDS-3 on-orbit satellite atomic clocks for their further optimization. In this study, clock offset data with a duration of 620 days since BDS-3 was officially commissioned were applied to long-term characteristic analysis. To begin with, the precision clock offset data of Deutsches geoforschungs zentrum (GFZ) processed by a MAD-based method were used as reliable test data. Herein, the working principle and main characteristics of satellite atomic clocks are analyzed and discussed, and thus, a comprehensive long-term characteristic analysis scheme is designed. On this basis, the performance indicators—mainly including physical parameters, periodic characteristics, frequency drift rate, frequency accuracy, frequency stability—were calculated and analyzed respectively, revealing the long-term characteristics of the BDS in orbit satellite atomic clocks during the test period. The results of experimental data testify that the performance of BDS-3 satellite atomic clocks is significantly superior to that of BDS-2, especially in terms of drift rate and frequency stability, and the performance of passive hydrogen maser (PHM) is generally superior to that of rubidium atomic frequency standards (RAFS). Within about half a year since BDS-3 was officially commissioned, the frequency stability of BDS-3 satellite atomic clock gradually improved and then reached the order of 10−15, reflecting the effectiveness of system maintenance and inter-satellite link. Furthermore, some novel conclusions are drawn, such as the long-term period term of the fitting residual and drift rate, which may be caused by the earth’s revolution.
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Maciuk and Lewińska. "High-Rate Monitoring of Satellite Clocks Using Two Methods of Averaging Time." Remote Sensing 11, no. 23 (November 22, 2019): 2754. http://dx.doi.org/10.3390/rs11232754.
Full textAbstract:
Knowledge of the global navigation satellite system (GNSS) satellite clock error is crucial in real-time precise point positioning (PPP), seismology, and many other high-rate GNSS applications. In this work, the authors show the characterisation of the atomic GNSS clock’s stability and its dependency on the adopted orbit type using Allan deviation with two methods of averaging time. Four International GNSS Service (IGS) orbit types were used: broadcast, ultra-rapid, rapid and final orbit. The calculations were made using high-rate 1 Hz observations from the IGS stations equipped with external clocks (oscillators). The most stable receiver oscillator was chosen as a reference clock. The results show the advantage of the newest GPS satellite block with respect to the other satellites. Significant differences in the results based on the orbit type used have not been recorded. Many averaging time methods used in Allan deviation (ADEV) show the clock’s fluctuations, usually smoothed in 2n s averaging times.
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Zhai, Yawei, Jaymin Patel, Xingqun Zhan, Mathieu Joerger, and Boris Pervan. "An Advanced Receiver Autonomous Integrity Monitoring (ARAIM) Ground Monitor Design to Estimate Satellite Orbits and Clocks." Journal of Navigation 73, no. 5 (April 28, 2020): 1087–105. http://dx.doi.org/10.1017/s0373463320000181.
Full textAbstract:
This paper describes a method to determine global navigation satellite systems (GNSS) satellite orbits and clocks for advanced receiver autonomous integrity monitoring (ARAIM). The orbit and clock estimates will be used as a reference truth to monitor signal-in-space integrity parameters of the ARAIM integrity support message (ISM). Unlike publicly available orbit and clock products, which aim to maximise estimation accuracy, a straightforward and transparent approach is employed to facilitate integrity evaluation. The proposed monitor is comprised of a worldwide network of sparsely distributed reference stations and will employ parametric satellite orbit models. Two separate analyses, covariance analysis and model fidelity evaluation, are carried out to assess the impact of measurement errors and orbit model uncertainty on the estimated orbits and clocks, respectively. The results indicate that a standard deviation of 30 cm can be achieved for the estimated orbit/clock error, which is adequate for ISM validation.
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He, Lina, Hairui Zhou, Zhiqiang Liu, Yuanlan Wen, and Xiufeng He. "Improving Clock Prediction Algorithm for BDS-2/3 Satellites Based on LS-SVM Method." Remote Sensing 11, no. 21 (October 30, 2019): 2554. http://dx.doi.org/10.3390/rs11212554.
Full textAbstract:
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.
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He, Lina, Hairui Zhou, Yuanlan Wen, and Xiufeng He. "Improving Short Term Clock Prediction for BDS-2 Real-Time Precise Point Positioning." Sensors 19, no. 12 (June 19, 2019): 2762. http://dx.doi.org/10.3390/s19122762.
Full textAbstract:
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.
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Li, Menghao, Weiquan Huang, Hui Li, Renlong Wang, and Peng Cui. "Satellite Clock Batch Estimation Accuracy Analysis and Its Impacts on PPP." Remote Sensing 14, no. 16 (August 13, 2022): 3932. http://dx.doi.org/10.3390/rs14163932.
Full textAbstract:
The ultra-rapid satellite clock product based on the satellite clock batch estimation is commonly used for high-precision and reliable precise point positioning (PPP) services. In order to clarify the effect of different ranging errors on the satellite clock batch estimation accuracy, the source of the satellite clock bias induced by the batch observation model is classified into the initial clock bias (ICB) and time-dependent bias (TDB). In addition to the effect of the ICB and TDB, the analytic relationship between the observation redundancy and the satellite clock batch estimation accuracy are derived and verified. The suitable number of stations is suggested to be 40 for the satellite clock batch estimation to achieve the counterbalance between the efficiency and saturable accuracy. For the PPP based on the batch-estimated satellite clock, the impacts of the ICB and TDB on PPP are clarified. The satellite clock batch estimation and PPP experiments are carried out to investigate the impacts of the ICB and TDB on the satellite clock batch estimation accuracy and the PPP performance. The ICB causes a significant bias for the batch-estimated satellite clock. The TDB is impacted by the assimilation ability of the batch-estimated satellite clock to the satellite orbit error. The convergence time and the positioning accuracy after the convergence of PPP are primarily affected by the ICB and TDB, respectively.
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Chen, Yongchang, Chuanzhen Sheng, Qingwu Yi, Ran Li, Guangqing Ma, and Jingkui Zhang. "Analysis and improvement of the Bancroft algorithm for GNSS satellite orbit determination." Measurement Science and Technology 33, no. 4 (January 7, 2022): 045002. http://dx.doi.org/10.1088/1361-6501/ac4434.
Full textAbstract:
Abstract Satellite orbit information is crucial for ensuring that global navigation satellite systems (GNSSs) provide appropriate positioning, navigation and timing services. Typically, users can obtain access to orbit information of a specific accuracy level from navigation messages or precise ephemeris products. Without this information, a system will not be able to provide normal service. In response to this problem, initial orbit information of a certain level of precision must be obtained to support subsequent applications, such as broadcasting or precise ephemeris calculations, thereby ensuring the successful subsequent operation of the navigation system. One of two ways to calculate the initial orbit of a GNSS satellite is to utilize ground tracking stations to observe satellite vector information in the geocentric inertial system; the second way is to utilize GNSS range observations and known orbit information from other satellites. For the second approach, some researchers use the Bancroft algorithm combined with receiver clock offset to determine the initial orbit of GNSS satellites. Because this method requires an additional known receiver clock offset, we study the dependence of the Bancroft algorithm on clock offset in GNSS orbit determination. By assessing the impact of errors of different magnitude on the accuracy of the orbit results, we obtain experimental conclusions. After comprehensively analyzing various errors, we determine the accuracy level that the Bancroft algorithm can achieve for orbit determination without considering receiver clock correction. Dual-frequency and single-frequency pseudorange data from International GNSS Service stations are used in orbit determination experiments. When a small receiver clock offset is considered and no correction is made, the deviations in the calculated satellite positions in three dimensions are approximately 979.3 and 1118.1 m (dual and single frequency); with a satellite clock offset, these values are approximately 928.8 and 1062.7 m (dual and single frequency).
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Pelc-Mieczkowska, Renata, and Dariusz Tomaszewski. "Space State Representation Product Evaluation in Satellite Position and Receiver Position Domain." Sensors 20, no. 13 (July 6, 2020): 3791. http://dx.doi.org/10.3390/s20133791.
Full textAbstract:
In Global Navigation Satellite Systems (GNSS) positioning, important terms in error budget are satellite orbits and satellite clocks correction errors. International services are developing and providing models and correction to minimize the influence of these errors both in post-processing and real-time applications. The International GNSS Service (IGS) Real-Time Service (RTS) provides real-time orbits and clock corrections for the broadcast ephemeris. Real-time products provided by IGS are generated by different analysis centres using different algorithms. In this paper, four RTS products—IGC01, CLK01, CLK50, and CLK90—were evaluated and analysed. To evaluate State Space Representation (SSR) products’ GPS satellites, the analyses were made in three variants. In the first approach, geocentric real-time Satellite Vehicle (SV) coordinates and clock corrections were calculated. The obtained results were compared with the final IGS, ESA, GFZ, and GRG ephemerides. The second approach was to use the corrected satellite positions and clock corrections to determine the Precise Point Position (PPP) of the receiver. In the third analysis, the impact of SSR corrections on receiver Single Point Position (SPP) was evaluated. The first part of the research showed that accuracy of the satellite position is better than 10 cm (average 3 to 5 cm), while in the case of clock corrections, mean residuals range from 2 cm to 17 cm. It should be noted that the errors of the satellites positions obtained from one stream differ depending on the reference data used. This shows the need for an evaluation of correction streams in the domain of the receiver position. In the case of PPP in a kinematic mode, the tests allowed to determine the impact that the use of different streams has on the final positioning results. These studies showed differences between specific streams, which could not be seen in the first study. The best results (3D RMS at 0.13 m level) were obtained for the CLK90 stream, while for IGC01, the results were three times worse. The SPP tests clearly indicate that regardless of the selected SSR stream, one can see a significant improvement in positioning accuracy as compared to positioning results using only broadcast ephemeris.
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Sušnik, Andreja, Andrea Grahsl, Daniel Arnold, Arturo Villiger, Rolf Dach, Gerhard Beutler, and Adrian Jäggi. "Validation of the EGSIEM-REPRO GNSS Orbits and Satellite Clock Corrections." Remote Sensing 12, no. 14 (July 19, 2020): 2322. http://dx.doi.org/10.3390/rs12142322.
Full textAbstract:
In the framework of the European Gravity Service for Improved Emergency Management (EGSIEM) project, consistent sets of state-of-the-art reprocessed Global Navigation Satellite System (GNSS) orbits and satellite clock corrections have been generated. The reprocessing campaign includes data starting in 1994 and follows the Center for Orbit Determination in Europe (CODE) processing strategy, in particular exploiting the extended version of the empirical CODE Orbit Model (ECOM). Satellite orbits are provided for Global Positioning System (GPS) satellites since 1994 and for Globalnaya Navigatsionnaya Sputnikovaya Sistema (GLONASS) since 2002. In addition, a consistent set of GPS satellite clock corrections with 30 s sampling has been generated from 2000 and with 5 s sampling from 2003 onwards. For the first time in a reprocessing scheme, GLONASS satellite clock corrections with 30 s sampling from 2008 and 5 s from 2010 onwards were also generated. The benefit with respect to earlier reprocessing series is demonstrated in terms of polar motion coordinates. GNSS satellite clock corrections are validated in terms of completeness, Allan deviation, and precise point positioning (PPP) using terrestrial stations. In addition, the products herein were validated with Gravity Recovery and Climate Experiment (GRACE) precise orbit determination (POD) and Satellite Laser Ranging (SLR). The dataset is publicly available.
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Liu, Wenxuan, Hu Wang, Hongyang Ma, Yingyan Cheng, Pengyuan Li, Bo Li, and Yingying Ren. "Analysis of Regional Satellite Clock Bias Characteristics Based on BeiDou System." Remote Sensing 14, no. 23 (November 29, 2022): 6047. http://dx.doi.org/10.3390/rs14236047.
Full textAbstract:
With the continuous development of the Global Navigation Satellite System (GNSS), the calculation theory and strategy of the global Satellite Clock Bias (SCB) tends to be mature. However, in some eventualities with restricted conditions, the calculation and application of the global SCB are limited; hence, the application of regional SCB is derived. This paper focuses on the quality of regional SCB products in different regions, calculates three groups of regional SCB products, and analyzes their properties and application effects. We expand the double-differenced assessment method for SCB and extend satellite clock accuracy assessment to regional satellite clock products. Additionally, the Regional Effect Bias (REB) is introduced to analyze the influence of the relative position of satellite geometry on the SCB products due to the regional effects. The conclusions are as follows: (1) In low-latitude regions, SCB products have a high degree of completeness and a large number of satellite observations, which is conducive to expanding the positioning application range of regional SCB; (2) the low-latitude regions SCB will be affected by ionospheric activity, and the accuracy will be slightly lower than that of satellite clocks deviation in mid-latitudes; (3) in this paper, the REB in this area is in the level of 10−7. The experiment displays the result that the values of REB in low-latitude areas are larger, leading to fluctuated Precise Point Position (PPP) results. However, there are fewer stations in the mid-latitude regions, which will also affect the accuracy of PPP; (4) the accuracy of the positioning results of the regional satellite clock deviation in the Chinese region is higher than that of the global clock.
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Ai, Qingsong, Yunbin Yuan, Baocheng Zhang, Tianhe Xu, and Yongchang Chen. "Refining GPS/GLONASS Satellite Clock Offset Estimation in the Presence of Pseudo-Range Inter-Channel Biases." Remote Sensing 12, no. 11 (June 4, 2020): 1821. http://dx.doi.org/10.3390/rs12111821.
Full textAbstract:
Because of the frequency division multiple access (FDMA) technique, Russian global navigation satellite system (GLONASS) observations suffer from pseudo-range inter-channel biases (ICBs), which adversely affect satellite clock offset estimation. In this study, the GLONASS pseudo-range ICB is treated in four different ways: as ignorable parameters (ICB-NONE), polynomial functions of frequency (ICB-FPOL), frequency-specific parameters (ICB-RF), and satellite-specific parameters (ICB-RS). Data from 110 international global navigation satellite system (GNSS) service stations were chosen to obtain the ICBs and were used for satellite clock offset estimation. The ICBs from the different schemes varied from −20 ns to 80 ns. The ICB-RS model yielded the best results, improving the clock offset accuracy from 300 ps to about 100 ps; it could improve the GLONASS precise point positioning (PPP) accuracy and the converging time by approximately 50% and 30%, respectively. Along similar lines, we introduced the GPS-ICB parameters in the process of GPS satellite clock estimation and GPS/GLONASS PPP, as ICBs may exist for GPS because of different chip shape distortions among GPS satellites. This possibility was found to be the case. Further, the GPS-ICB magnitude ranged from −2 ns to 2 ns, and the estimated satellite clock offsets could improve the accuracy of the GPS and combined GPS/GLONASS PPP by 10%; it also accelerated the converging time by more than 15% thanks to the GPS-ICB calibration.
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Baranov, Alexey, Sergey Ermak, Roman Lozov, and Vladimir Semenov. "Comparison of Gravitational and Light Frequency Shifts in Rubidium Atomic Clock." Universe 7, no. 1 (December 24, 2020): 3. http://dx.doi.org/10.3390/universe7010003.
Full textAbstract:
The article presents the results of an experimental study of the external magnetic field orientation and magnitude influence on the rubidium atomic clock, simulating the influence of the geomagnetic field on the onboard rubidium atomic clock of navigation satellites. The tensor component value of the atomic clock frequency light shift on the rubidium cell was obtained, and this value was ~2 Hz. The comparability of the relative light shift (~10−9) and the regular gravitational correction (4×10−10) to the frequency of the rubidium atomic clock was shown. The experimental results to determine the orientational shift influence on the rubidium atomic clock frequency were presented. A significant effect on the relative frequency instability of a rubidium atomic clock at a level of 10−12(10−13) for rotating external magnetic field amplitudes of 1.5 A/m and 3 A/m was demonstrated. This magnitude corresponds to the geomagnetic field in the orbit of navigation satellites. The necessity of taking into account various factors (satellite orbit parameters and atomic clock characteristics) is substantiated for correct comparison of corrections to the rubidium onboard atomic clock frequency associated with the Earth’s gravitational field action and the satellite orientation in the geomagnetic field.
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Li, Haojun, Weidong Zhu, Rungen Zhao, and Jiexian Wang. "Service and Evaluation of the GPS Triple-Frequency Satellite Clock Offset." Journal of Navigation 71, no. 5 (April 22, 2018): 1263–73. http://dx.doi.org/10.1017/s0373463318000218.
Full textAbstract:
This paper considers the effect of the biases in Global Positioning System (GPS) observations on satellite clock offset estimation. GPS triple-frequency satellite clock and reference observations are discussed. When the reference observation is selected and the corresponding satellite clock offset is computed, satellite clock offsets for all observations are obtained based on the computed satellite clock offset and the biases between the reference observation and other observations. The characteristics of these biases are analysed, and a service strategy for the GPS triple-frequency satellite clock offset is presented. To evaluate the computed GPS satellite clock offset, the performance in single-point positioning is validated. The positioning results show that the average relative improvements are about 20%, 28% and 19% for north, east and vertical components, when the Differential Code Bias (DCB) (P1-P2), DCB (P1-P5) and modelled Inter-Frequency Clock Bias (IFCB) are corrected. The effect of DCB (P1-P2), DCB (P1-P5) and modelled IFCB on the altitude direction is more evident than on the horizontal directions.
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Yang, Songfeng, Qiyuan Zhang, Xi Zhang, and Donglie Liu. "Impact of GPS/BDS Satellite Attitude Quaternions on Precise Point Positioning with Ambiguity Resolution." Remote Sensing 13, no. 15 (August 2, 2021): 3035. http://dx.doi.org/10.3390/rs13153035.
Full textAbstract:
Precise point positioning with ambiguity resolution (PPP-AR) based on multiple global navigation satellite system (multi-GNSS) constellations is an important high-precision positioning tool. However, some unmodeled satellite and receiver biases (such as errors in satellite attitude) make it difficult to fix carrier-phase ambiguities. In order to fix ambiguities of eclipsing satellites, accurate integer clock and satellite attitude products (i.e., attitude quaternion) have been provided by the International GNSS Service (IGS). Nevertheless, the quality of these products and their positioning performance in multi-GNSS PPP-AR have not been investigated yet. Using the PRIDE PPP-AR II software associated with the corresponding rapid satellite orbit, integer clock and attitude quaternion products of Wuhan University (WUM), we carried out GPS/BDS PPP-AR using 30 days of data in an eclipsing season of 2020. We found that about 75% of GPS, 60% of BDS-2 and 57% of BDS-3 narrow-lane ambiguity residuals after integer clock corrections fall within ±0.1 cycles in the case of using nominal attitudes. However, when using attitude quaternions, these percentages will rise to 80% for GPS, 70% for BDS-2 and 60% for BDS-3. GPS/BDS daily kinematic PPP-AR after integer clock and nominal attitude corrections can usually achieve a positioning precision of about 10, 10 and 30 mm for the east, north and up components, respectively. In contrast, the counterparts are 8, 8 and 20 mm when using attitude quaternions. Compared with the case of using attitude quaternions only at the network end for the integer clock estimation, using attitude quaternions only at the user end shows a pronounced improvement of 15% in the east component and less than 10% in the north and up components. Therefore, we suggest PPP users apply integer clock and satellite attitude quaternion products to realize more efficient ambiguity fixing, especially in satellite eclipsing seasons.
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Heo, Youn-Jeong, Jeong-Ho Cho, and Moon-Beom Heo. "Improving Estimation Accuracy of Satellite Clock Error for GPS Satellite Clock Anomaly Detection." Journal of the Korean Society for Aeronautical & Space Sciences 39, no. 3 (March 1, 2011): 225–31. http://dx.doi.org/10.5139/jksas.2010.39.3.225.
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Guo, Nan-nan, Xu-hua Zhou, Kai Li, and Bin Wu. "Research on the impact factors of GRACE precise orbit determination by dynamic method." Journal of Applied Geodesy 12, no. 3 (July 26, 2018): 249–57. http://dx.doi.org/10.1515/jag-2018-0008.
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Abstract With the successful use of GPS-only-based POD (precise orbit determination), more and more satellites carry onboard GPS receivers to support their orbit accuracy requirements. It provides continuous GPS observations in high precision, and becomes an indispensable way to obtain the orbit of LEO satellites. Precise orbit determination of LEO satellites plays an important role for the application of LEO satellites. Numerous factors should be considered in the POD processing. In this paper, several factors that impact precise orbit determination are analyzed, namely the satellite altitude, the time-variable earth’s gravity field, the GPS satellite clock error and accelerometer observation. The GRACE satellites provide ideal platform to study the performance of factors for precise orbit determination using zero-difference GPS data. These factors are quantitatively analyzed on affecting the accuracy of dynamic orbit using GRACE observations from 2005 to 2011 by SHORDE software. The study indicates that: (1) with the altitude of the GRACE satellite is lowered from 480 km to 460 km in seven years, the 3D (three-dimension) position accuracy of GRACE satellite orbit is about 3∼4 cm based on long spans data; (2) the accelerometer data improves the 3D position accuracy of GRACE in about 1 cm; (3) the accuracy of zero-difference dynamic orbit is about 6 cm with the GPS satellite clock error products in 5 min sampling interval and can be raised to 4 cm, if the GPS satellite clock error products with 30 s sampling interval can be adopted. (4) the time-variable part of earth gravity field model improves the 3D position accuracy of GRACE in about 0.5∼1.5 cm. Based on this study, we quantitatively analyze the factors that affect precise orbit determination of LEO satellites. This study plays an important role to improve the accuracy of LEO satellites orbit determination.
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Zhao, Lin, Nan Li, Hui Li, Renlong Wang, and Menghao Li. "BDS Satellite Clock Prediction Considering Periodic Variations." Remote Sensing 13, no. 20 (October 11, 2021): 4058. http://dx.doi.org/10.3390/rs13204058.
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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.
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Li, Xingxing, Yiting Zhu, Kai Zheng, Yongqiang Yuan, Gege Liu, and Yun Xiong. "Precise Orbit and Clock Products of Galileo, BDS and QZSS from MGEX Since 2018: Comparison and PPP Validation." Remote Sensing 12, no. 9 (April 30, 2020): 1415. http://dx.doi.org/10.3390/rs12091415.
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In recent years, the development of new constellations including Galileo, BeiDou Navigation Satellite System (BDS) and Quasi-Zenith Satellite System (QZSS) have undergone dramatic changes. Since January 2018, about 30 satellites of the new constellations have been launched and most of the new satellites have been included in the precise orbit and clock products provided by the Multi Global Navigation Satellite System (Multi-GNSS) Experiment (MGEX). Meanwhile, critical issues including antenna parameters, yaw-attitude models and solar radiation pressure models have been continuously refined for these new constellations and updated into precise MGEX orbit determination and precise clock estimation solutions. In this context, MGEX products since 2018 are herein assessed by orbit and clock comparisons among individual analysis centers (ACs), satellite laser ranging (SLR) validation and precise point positioning (PPP) solutions. Orbit comparisons showed 3D agreements of 3–5 cm for Galileo, 8–9 cm for BDS-2 inclined geosynchronous orbit (IGSO), 12–18 cm for BDS-2 medium earth orbit (MEO) satellites, 24 cm for BDS-3 MEO and 11–16 cm for QZSS IGSO satellites. SLR validations demonstrated an orbit accuracy of about 3–4 cm for Galileo and BDS-2 MEO, 5–6 cm for BDS-2 IGSO, 4–6 cm for BDS-3 MEO and 5–10 cm for QZSS IGSO satellites. Clock products from different ACs generally had a consistency of 0.1–0.3 ns for Galileo, 0.2–0.5 ns for BDS IGSO/MEO and 0.2–0.4 ns for QZSS satellites. The positioning errors of kinematic PPP in Galileo-only mode were about 17–19 mm in the north, 13–16 mm in the east and 74–81 mm in the up direction, respectively. As for BDS-only PPP, positioning accuracies of about 14, 14 and 49 mm could be achieved in kinematic mode with products from Wuhan University applied.
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Zhang, Shaocheng, Shikang Du, Wei Li, and Guangxing Wang. "Evaluation of the GPS Precise Orbit and Clock Corrections from MADOCA Real-Time Products." Sensors 19, no. 11 (June 6, 2019): 2580. http://dx.doi.org/10.3390/s19112580.
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The Japanese Quasi-Zenith Satellite System (QZSS) is a regional navigation satellite system covering the entire Asia-Oceania region. Except for the standard satellite navigation signals, QZSS satellites also broadcast L6E augmentation signals with real time GNSS precise orbit every 30 s and clock messages every 1 s, which is very important and necessary for Real-Time precise point positioning (RTPPP) applications. In this paper, the MADOCA real-time services derived from L6E augmentation signals were evaluated for both accuracy and availability compared with IGS final products. To avoid the datum difference of GPS orbit between MADOCA real-time and IGS final products, the 7-parameters Helmert transformation was firstly used in this paper, and then the orbit was evaluated on radial, along, and cross-track directions. On the clock evaluation, the mean satellites clock errors were taken as reference clock error, and then the standard deviation (STD) was calculated for each satellite. Furthermore, the signal in space range errors (SISRE) were also summarized to evaluate the ranging-measurement accuracy. Seven-day evaluation results show that satellite orbit, clock errors, and the final SISRE errors range as being 1.8–3.9 cm, 0.04–0.15 ns (1.2–4.5 cm), and 5–10 cm, respectively. For the one-year long-term evaluation, daily SISRE errors in 2018 show consistent performance with that of seven days. Furthermore, the open source software RTKLIB was used to evaluate the kinematic PPP performance based on the MADOCA real-time products, and it shows that the daily positioning accuracy of the 20 globally distributed IGS stations can reach 4.9, 4.2, 11.7, and 12.1 cm in the east, north, up, and 3D directions, respectively. Hence, it is concluded that the current MADOCA real-time ephemeris products can provide orbit and clock products with SISRE on centimeters level with high interval, which could meet the demands of the RTPPP solution and serve real-time users who can access the MADOCA real-time products via L6E signal or internet.
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Piester, D., M. Rost, M. Fujieda, T. Feldmann, and A. Bauch. "Remote atomic clock synchronization via satellites and optical fibers." Advances in Radio Science 9 (July 29, 2011): 1–7. http://dx.doi.org/10.5194/ars-9-1-2011.
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Abstract. In the global network of institutions engaged with the realization of International Atomic Time (TAI), atomic clocks and time scales are compared by means of the Global Positioning System (GPS) and by employing telecommunication satellites for two-way satellite time and frequency transfer (TWSTFT). The frequencies of the state-of-the-art primary caesium fountain clocks can be compared at the level of 10−15 (relative, 1 day averaging) and time scales can be synchronized with an uncertainty of one nanosecond. Future improvements of worldwide clock comparisons will require also an improvement of the local signal distribution systems. For example, the future ACES (atomic clock ensemble in space) mission shall demonstrate remote time scale comparisons at the uncertainty level of 100 ps. To ensure that the ACES ground instrument will be synchronized to the local time scale at the Physikalisch-Technische Bundesanstalt (PTB) without a significant uncertainty contribution, we have developed a means for calibrated clock comparisons through optical fibers. An uncertainty below 40 ps over a distance of 2 km has been demonstrated on the campus of PTB. This technology is thus in general a promising candidate for synchronization of enhanced time transfer equipment with the local realizations of Coordinated Universal Time UTC. Based on these experiments we estimate the uncertainty level for calibrated time transfer through optical fibers over longer distances. These findings are compared with the current status and developments of satellite based time transfer systems, with a focus on the calibration techniques for operational systems.
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Feng, Lei, and Guotong Li. "Research on Self-Monitoring Method for Anomalies of Satellite Atomic Clock." International Journal of Aerospace Engineering 2016 (2016): 1–16. http://dx.doi.org/10.1155/2016/1759512.
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Atomic clock is the core component of navigation satellite payload, playing a decisive role in the realization of positioning function. So the monitoring for anomalies of the satellite atomic clock is very important. In this paper, a complete autonomous monitoring method for the satellite clock is put forward, which is, respectively, based on Phase-Locked Loop (PLL) and statistical principle. Our methods focus on anomalies in satellite clock such as phase and frequency jumping, instantaneous deterioration, stability deterioration, and frequency drift-rate anomaly. Now, method based on PLL has been used successfully in China’s newest BeiDou navigation satellite.
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Fu, Wenju, Lei Wang, Ruizhi Chen, Haitao Zhou, Tao Li, and Yi Han. "Improved Single-Frequency Kinematic Orbit Determination Strategy of Small LEO Satellite with the Sun-Pointing Attitude Mode." Remote Sensing 13, no. 19 (October 8, 2021): 4020. http://dx.doi.org/10.3390/rs13194020.
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Kinematic orbit determination (KOD) of low earth orbit (LEO) satellites only using single-frequency global navigation satellite system (GNSS) data is a suitable solution for space applications demanding meter-level orbit precision. For some small LEO satellites with the sun-pointing attitude mode, the rotation of the GNSS antenna radiation pattern changes the observation noise characteristics. Since the rotation angle information of the antenna plane may not be available for most low-cost missions, the true elevation cannot be computed and a general elevation-dependent weighting model remains invalid for the onboard GNSS observations. Furthermore, the low-stability GNSS receiver clock oscillator of the LEO satellite at high speeds makes single-frequency cycle slip detection ineffective and difficult since the clock steering events occur frequently. In this study, we investigated the improved KOD strategy to improve the performance of orbit solution using single-frequency GPS and BeiDou navigation satellite system (BDS) observations collected from the Luojia-1A satellite. The weighting model based on exponential function and signal strength is proposed according to the analysis of satellite attitude impact, and a joint single-frequency detection algorithm of receiver clock jump and cycle slip is investigated as well. Based on the GPS/BDS-combined KOD results, it is demonstrated that the clock jump and cycle slip can be properly detected and observations can be effectively utilized with the proposed weighting model considering satellite attitude, which significantly improves the availability and accuracy of orbit solution. The number of available epochs is increased by 12.9% benefitting from this strategy. The orbital root mean square (RMS) precision improvements in the radial, along-track, and cross-track directions are 22.1%, 16.4%, and 6.5%, respectively. Combining BDS observations also contributes to orbit precision improvement, which reaches up to 28.8%.
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ZIĘTALA, Michał. "STABILITY OF GPS AND GLONASS ONBOARD CLOCKS ON A MONTHLY BASIS." Scientific Journal of Silesian University of Technology. Series Transport 114 (January 1, 2022): 193–209. http://dx.doi.org/10.20858/sjsutst.2022.114.16.
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This paper presents the stability of the GPS and GLONASS system clocks’ stability. It describes the construction of these two systems and calculated four different Allan variances (AVAR), based on the MGEX (the Multi-GNSS Experiment) clock products. Four used variances allowed making a better analysis of each GNSS system clock. The results are shown at different averaging times from 5 s as successive multiples to 655,360 s in a monthly period. The stability of GPS and GLONASS clocks is included in the range of 10-12~10-14 s. The results showed that GLONASS clocks are stable (10-12~10-14 s) and are affected with white frequency noise (WFM). The GPS clock stability models have more fluctuations for τ > 40,960 s and the mean stability is concluded between 10-12~10-13 s. Mean frequency accuracy for GPS clocks is related with WFM and Random Walk Frequency (RWF). The differences in clock stability are caused by several factors – block type, type of clock and the time of a satellite in orbit. These factors have an influence on stability results.
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Yang, Jianhua, Chengpan Tang, Sanshi Zhou, Yezhi Song, Jinhuo Liu, Yu Xiang, Yuchen Liu, et al. "High-Accuracy Clock Offsets Estimation Strategy of BDS-3 Using Multi-Source Observations." Remote Sensing 14, no. 18 (September 19, 2022): 4674. http://dx.doi.org/10.3390/rs14184674.
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Satellite clock offsets are the critical parameters for The Global Navigation Satellite Systems (GNSSs) to provide position and timing (PNT) service. Unlike other GNSSs, BDS-3 uses the two-way superimposition strategy to measure satellite clock offsets. However, affected by some deficiencies of the two-way superimposition strategy, the accuracy of BDS-3 clock offsets parameters is 1.29 ns (RMS), which is the main bottleneck for BDS-3 to improve its space signal accuracy. After analyzing problems in the clock offsets measurement process of BDS-3, the paper proposes a new strategy to real-time estimate high-accuracy satellite clock offsets. The clock offsets estimated by the new strategy show a good consistency with GBM clock offsets. The averaged STD of their differences in MEO is 0.14 ns, and the clock offsets estimated by the new strategy present less fluctuation in the 1-day fitting residuals. Applying the new clock offsets to prediction, BDS-3 can reduce its clock offsets errors from 1.05 ns to 0.29 ns (RMS), about 72%. The above results indicate that the new clock offsets estimated strategy can improve the accuracy of clock offsets parameters of BDS-3 effectively.
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Kuang, Kaifa, Jian Wang, and Houzeng Han. "Real-Time BDS-3 Clock Estimation with a Multi-Frequency Uncombined Model including New B1C/B2a Signals." Remote Sensing 14, no. 4 (February 16, 2022): 966. http://dx.doi.org/10.3390/rs14040966.
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The global system of BDS (BeiDou Navigation Satellite System), i.e., BDS-3, is characterized with a multi-frequency signal broadcasting capability, which was demonstrated as beneficial for GNSS (Global Navigation Satellite System) data processing. However, research on real-time BDS-3 clock estimation with multi-frequency signals is quite limited, especially for the new B1C and B2a signals. In this study, we developed models for BDS-3 multi-frequency real-time data processing, including the uncombined model for clock estimation and the GFIF (Geometry-Free Ionosphere-Free) combined model for IFCB (Inter-Frequency Clock Bias) determination. Based on the models, simulated real-time numerical experiments with about 80 global IGS (International GNSS Service) network stations are conducted for validation and analysis. The results indicate that: (1) the uncombined model with multi-frequency signals can achieve comparable accuracy with the traditional dual-frequency IF model in terms of clock estimation, and the double-differenced clock STDs (Standard Deviations) are generally less than 0.05 ns with post-processed clocks as a reference; (2) unlike the B1C and B1I/B3I signals, the satellite IFCBs generated from multi-frequency clock estimation show apparent temporal variations for B2a and B1I/B3I signals, further investigation with GFIF models confirm the variations mainly result from the errors of receiver antenna corrections. Therefore, we addressed the feasibility of the uncombined model and the importance of accurate antenna information in the multi-frequency data processing.
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Hu, Chao, and Zhongyuan Wang. "Improved Strategies for BeiDou Ultrarapid Satellites’ Clock Bias Prediction Using BDS-2 and BDS-3 Integrated Processing." Mathematical Problems in Engineering 2020 (April 16, 2020): 1–16. http://dx.doi.org/10.1155/2020/1804621.
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GNSS ultrarapid clock biases are key inputs of rapid high-accuracy applications, especially for its prediction parts. With the fast development of the BeiDou system (BDS), the system performances are mainly represented by orbit and clock products. However, it is suggested that the BDS-predicted clock biases cannot meet the requirement of real-time or near real-time services. In this research, the BDS satellite-predicted ultrarapid clock bias products are optimized with three methods, namely, one-step strategy, intersatellite correlation, and variogram model, using the combined estimation of BDS-2 and BDS-3 satellites. Firstly, considering the traditional two-step strategy for modelling clock bias prediction, we take all terms (including trend and periodic terms) into one-step solution of model estimation based on the sparse modelling in machine learning. Secondly, because of the much more stable on-board atomic clock of BDS-3 satellites, the intersatellite correlations between BDS-2 and BDS-3 are utilized to enhance the solution of model coefficients. Thirdly, to further improve the model, the temporal correlations in model residuals are used to reconstruct the stochastic function obtained by variogram. In addition, to verify the proposed improved strategies, 12 schemes of BDS clock bias prediction experiments are designed and analyzed with different conditions. According to the results of predicted clock biases, it is indicted that (1) the stability of BDS-3 on-board clocks is more optimal compared with BDS-2, which can be used to strengthen the solution of the clock bias prediction model; (2) the one-step estimation of the clock bias model by sparse modelling can slightly increase the accuracy of prediction results; (3) both BDS-2- and BDS-3-predicted clock biases benefited each other by inserting the intersatellite correlations into the weight matrix, in which the accuracy of 18-hour period with one-step strategy can be improved by 28.6% and 27.2% for BDS-2 and BDS-3, respectively; and (4) after the introduction of the variogram model in updating the weight matrix, the clock bias prediction model is further corrected by 8.0% and 11.1% for BDS-2 and BDS-3. In summary, improved strategies for BDS ultrarapid satellites’ clock bias prediction using BDS-2 and BDS-3 integrated processing are meaningful for the current BDS ultrarapid satellites’ clock bias prediction products.
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Liu, Yan, Cheng Yang, and Mengni Zhang. "Comprehensive Analyses of PPP-B2b Performance in China and Surrounding Areas." Remote Sensing 14, no. 3 (January 28, 2022): 643. http://dx.doi.org/10.3390/rs14030643.
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BeiDou Global Navigation Satellite System (BDS-3) provides a regional Precise Point Positioning (PPP) service, called PPP-B2b, for users in China and surrounding areas through B2b signal transmitted from its three geostationary earth orbit (GEO) satellites. The information broadcasted by the B2b signal include satellite orbit corrections, satellite clock offset corrections, and differential code bias (DCB) corrections of BDS-3 satellites. In this study, the accuracies of PPP-B2b corrections along with real-time PPP performance are comprehensively evaluated referenced to precise orbit and clock products from GFZ and the precise DCB products from CAS. The result indicates that the accuracy of the BDS-3 broadcast orbit is similar to that of the PPP-B2b real-time orbit. The PPP-B2b clock offset correction improved the satellite clock offset precision of the BDS-3 broadcast ephemeris. The Signal-in-Space Range Error (SISRE) of broadcast ephemeris and PPP-B2b are calculated, which are 0.536 and 1.24 m, respectively. The large SISRE value of PPP-B2b is caused by the satellite-specified systematic bias to IGS final products. The positioning performance evaluation of real-time PPP with B2b service is carried out and compared with the real-time product provided by Wuhan University (WHU) based on the eight IGS MGEX stations in China and surrounding countries. The positioning accuracy of static positioning mode with PPP-B2b service achieved centimeter-level accuracy in the selected station, and that of kinematic positioning mode achieved decimeter-level accuracy. The availability rate of PPP-B2b corrections in the surrounding area of China, however, degrades from 88.76% to 60.91% in the selected stations. The accuracy of the PPP solution using PPP-B2b correction is better than that of using WHU real-time product within China. The positioning performance of stations located at the boundary of the PPP-B2b service area, however, is affected by the number of PPP-B2b available satellites. The positioning accuracy in kinematic positioning mode is worse than that of using WHU real-time precise product.