The Terrestrial Reference Frame (TRF) is essential for solid Earth research, including geodesy and geodynamics, providing a unified spatiotemporal datum. With the continuous expansion of global GNSS infrastructure and data, significant progress has been made in refining TRF and models of crustal plate motion and tectonic deformation. This study provides a global velocity field and a plate motion model through three decades of Global Navigation Satellite System (GNSS) data and nonlinear TRF refinement. Key contributions include: (1) the Integrated and Improved Time Series Analysis (IITSA) model, achieving horizontal fitting precision of 3 mm and vertical precision of 6 mm for three-decade GNSS time series; (2) the Global GNSS Velocity Model 2020 (GGVM2020), with RMS values of 0.12, 0.11, and 0.26 mm/yr in the north, east, and up directions, providing new insights into the crustal movements of Antarctica and North America; (3) the Global Interpolation Velocity Model 2020 (GIVM2020), offering a global horizontal velocity grid (3 degrees x3 degrees) with interpolation accuracy better than 3 mm/yr, enabling velocity estimation for any site globally; and (4) the Global Plate Motion Model 2020 (GPMM2020), which improves the accuracy of Euler motion parameters for the 14 major tectonic plates, achieving precision better than 3 mm/yr. In conclusion, the study's results, including the global GNSS velocity field and plate motion model, enhance the reliability and application of terrestrial reference frame products.

In this research, we improve the partial ambiguity resolution strategy of LAMBDA for Android-based GNSS data. The results show that it is possible to fix the ambiguity in an open sky environment, and an accuracy of 1 and 2 centimeter on horizontal and vertical is achieved. However, when the data suffer from large cycle slip, it will be hard to fix the ambiguity and lead to a float solution with sub-meter to meter accuracy.

Nowadays, the BDS-3 satellites transmit new signals B1c and B2a that are compatible with GPS and Galileo, which is meaningful to fully take advantage of the BDS positioning capability. However, further research and analysis are needed to investigate the precise point positioning ambiguity resolution (PPP-AR) performance of the new BDS-3 signal combination. In this manuscript, the characteristics and quality of differential code bias (DCB), inter frequency clock bias (IFCB) and uncalibrated phase delay (UPD) of BDS-3 new signals are analyzed based on 30 days observation data from 70 multi GNSS experiment (MGEX) stations. The results show that the mean value of IFCB between B1I/B3I and B1C/B2a is 1.18 cm, which indicates that the IFCB can be ignored when performing the clock errors reference conversion of BDS-3 satellites. Besides, the DCB of the new BDS-3 signals varies within 0.2 ns over 30 days, and with a difference of 0.08 ns compared to the DCB product provided by chinese academy of science (CAS). The percentage of the estimated residuals less than 0.25 cycles for new signals WL UPD and less than 0.15 cycles for new signals NL UPD are 99.76% and 97.19%, respectively. The above results demonstrate the reliability of the DCB and UPD products, which can be used to estimate the carrier phase observable specific signal bias (OSB) product for the new signals. The average positioning errors of the BDS-3 new signals static PPP-AR in the N, E and U directions is 0.50 cm, 0.43 cm and 1.62 cm respectively, with an improvement of 18.3%, 28.3% and 11.5% compared to the ambiguity float static PPP. The average positioning errors of the kinematic PPP-AR are 2.09 cm, 2.67 cm and 4.79 cm in three directions, respectively, with an improvement of 17.1%, 23.9% and 15.7% compared to the ambiguity float PPP. The convergence time of the static and kinematic PPP-AR are 26.36 min and 29.12 min, respectively. & COPY; 2023 Published by Elsevier B.V. on behalf of COSPAR.

Intra-system biases (ISBs) between BDS-2 and BDS-3 are of critical importance when combining observations from the BDS-2 and BDS-3 systems, which is meaningful to fully take advantage of the BDS positioning capability. Meanwhile, ISBs should also be considered in the estimation of BDS uncalibrated phase delays (UPDs). In this research, we present a BDS-2/BDS-3 joint-processing scheme, as well as a method for estimating BDS UPDs. The characteristics of ISBs and the quality of BDS UPDs are analyzed based on 30-day data from 130 multi-GNSS experimental (MGEX) stations. Our results indicate that the ISBs are related to the type and version of the receiver. The ISBs can be regarded as constant across the course of a given day, and the mean standard deviation (STD) values of ISBs over one month for different types of receivers are generally within 0.2 m. Moreover, to assess the quality of UPD products, the residuals of the estimated UPDs and the utilization rates of the observation data are computed. The results show that the quality of BDS UPDs can be improved by correcting the satellite-induced pseudo-range variations, and by estimating the wide-lane (WL) UPD difference between BDS-2 and BDS-3. The average RMS values of the estimated residuals of WL UPD and narrow-lane (NL) UPD are 0.07 and 0.09 cycles, respectively; moreover, the utilization rate of the observation data of WL UPD and NL UPD can reach above 90 %. The performance of BDS precise point positioning (PPP) and PPP ambiguity resolution (PPP-AR) is analyzed in terms of positioning accuracy and convergence performance in both the static and kinematic modes. Compared with PPP ambiguity-float solutions, the positioning accuracy of PPP-AR is significantly improved, especially in the east direction. The impact of ISBs on PPP and PPP-AR is also analyzed, and the results indicate that ISBs can improve the convergence speed of float PPP, but can be disregarded in PPP-AR. (c) 2022 COSPAR. Published by Elsevier B.V. All rights reserved.

The current stochastic model in GNSS processing is constructed based on the prior experience, for example the ratio of the weight of the pseudorange and phase observations is generally determined as 1:10000. These methods ignore the precision differences of the different GNSS receivers and observation space. In this paper, the standard deviation of differenced ionosphere-free pseudorange and phase observations is computed with dual-frequency observations and then the weight ratio of the pseudorange and phase observations is obtained using the computed standard deviation. This method is introduced in satellite clock estimating and the data is processed. The results show that the presented method is feasible, with which the accuracy of the estimated satellite clock results is improved. The estimated satellite clock results are further adopted in PPP and the positioning results of the 10 users validate that the estimated satellite clock, which uses the presented method, can accelerate the convergence of PPP compared with the traditional method.

The current international and regional reference frame research is mainly realized by single GPS (Global Position System) technology. With the full deployment of BDS (Beidou Navigation System), it is urgent to study and establish the corresponding terrestrial reference frame. Since 2019, the global and regional BDS service performance has been evaluated and tested, and the long-term BDS observations of MGEX (Multi GNSS Experiment) sites distributed worldwide provide the possibility for the preliminary construction of the BDS terrestrial reference frame. We aim to preliminarily realize and evaluate the CTRF2020 (COMPASS/BDS Terrestrial Reference Frame at the epoch of 2020.0) that can be expressed with the coordinates and velocities of a series of reference sites at the epoch of 2020.0. Firstly, the actual BDS global service performance evaluation reflects BDS satellite's high visibility and change trend in recent three years, which provides primary input data for the frame. Then, the BDS observations of about 100 global sites in the recent three years are calculated by PPP (Precise Point Positioning) and NET solution, to obtain the global high-precision BDS coordinate time series. Then, the BDS time series of the two solutions are fitted and compared with the IGS14 velocity field. The results show that the series accuracy of PPP-BDS and NET-BDS solutions is equivalent, and there is an mm-level systematic deviation with IGS14 solutions. The horizontal series fitting accuracy of PPP-BDS and NET-BDS solutions is better than that of the vertical direction, the accuracy of NET-BDS solution is slightly better than PPP-BDS, and the difference of fitting accuracy is 0.12, 0.13, and 0.50 mm in the NEU direction. The velocity field accuracy of PPP-BDS and NET-BDS solution is the same, and the overall three-dimensional velocity difference is less than 0.2 mm/a. The velocity fields of PPP-BDS and NET-BDS solution have little difference from IGS14, and the overall difference is less than 0.5 mm/a. Finally, we give the limitations and improvement points of CTRF2020. The preliminary realization and evaluation of CTRF2020 may be expected to provide a reference for the future realization of a comprehensive terrestrial reference framework dominated by BDS technology and supplemented by multi-source space geodetic technology.

The third generation of China’s BeiDou Navigation Satellite System (BDS-3) began to provide global service at the end of 2018, and the completion of BDS was announced in July 2020, which includes GEO (Geostationary Earth Orbit), IGSO (Inclined Geosynchronous orbit), and MEO (Medium Earth Orbit) satellites. The resulting BDS orbits vary due to the inconsistent alignment strategies used by different analysis centers. Therefore, it is necessary to study the method of determining the BDS-3 orbit products combined from different analysis centers. In this research, the accuracy of the combined orbits for BDS-3 and other GNSS systems is evaluated and analyzed. To verify the reliability of the orbit combination method proposed in this paper, the GPS orbit is first selected for verification. Compared to the analysis centers, the mean Signal in Space User Ranging Error (SISURE) for GPS combined orbits is significantly reduced, and the mean SISURE of combined orbits for Block IIF, Block IIR, and Block III is 4.15 mm, 5.43 mm, and 5.63 mm, respectively. This demonstrates the effectiveness of the orbit combination method in this research. Besides, the accuracy of the combined orbits is improved by the ERP correction, and the mean RMS of the without Earth rotation Parameters (ERP) correction orbits and with ERP correction orbits is 4.78 mm and 4.53 mm, respectively. This demonstrates that orbit consistency corrections should be considered when performing orbit combinations. Compared to the GFZ orbits, the accuracy of the combined orbits has improved for GPS, GLONASS, GALILEO, and BDS is 8.2%, 9.9%, 9.9%, and 5.5%, respectively. It shows that the orbit combination method improves the orbital accuracy compared to the individual analysis center orbits. The mean RMS of the combined orbits for GPS, GLONASS, GALILEO, BDS MEO, and BDS IGSO is 1.7 cm, 2.61 cm, 2.52 cm, 2.59 cm, and 4.90 cm, respectively. The results demonstrate that the accuracy of the combined orbit for the BDS-3 MEO satellite is already similar to other systems; an orbit combination also available for the BDS-3 satellite.

Extensive observation collection, unified and rigorous data processing, and accurate construction of the station motion model are the three essential elements for the accuracy and reliability of the Global Navigation Satellite System (GNSS) velocity field. GNSS data reprocessing not only can weaken the influence of untrue nonlinear site signals caused by imperfect models but also can eliminate the displacement offset caused by frame transformation, solution strategy, and model change. Based on the new repro3 criteria of the International GNSS Service (IGS), we process rigorously GNSS observations of continental China from the period 2000 to 2020 to refine GNSS station secular velocities and analyze the present-day crustal deformation in continental China. The main contributions of this work included the followings. Firstly, the repro3 algorithm and model are used to uniformly and rigorously process the two-decade GNSS historical observations to obtain more reliable GNSS coordinate time series with mm-level precision. Combined with the historical records of major earthquakes in continental China, we build a GNSS time series model considering nonlinear factors (velocity, offset, period, co-seismic/post-seismic deformation) to extract GNSS horizontal velocity field whose root mean square (RMS) mean is 0.1 mm/a. Secondly, the GNSS horizontal grid velocity field in continental China is interpolated using the gpsgridder method (the minimum radius is set to 16, and the Poisson’s ratio is set to 0.5). Estimation and analysis of the crustal strain rate solution lead to the conclusion that the strain degree in West China (the high strain region is mainly located in the Qinghai Tibet Plateau and Tianshan Mountains) is much more intense than that in the east (the main strain rate is less than 5 nstrain/year). In addition, most strong earthquakes in the Chinese mainland occurred on active blocks and their boundary faults with large changes in the GNSS velocity field and strain field. Then, an improved K-means++ clustering analysis method is proposed to divide active blocks using GNSS horizontal velocity field. Furthermore, different relative motion models of different blocks are constructed using the block division results. Among them, the Eurasian block has the lowest accuracy (the RMS of residual velocity in the east and north directions are 5.60 and 9.65 mm/a, respectively), and the China block 7 has the highest accuracy (the RMS mean of relative velocity in the east and north directions are 2.60 and 2.65 mm/a, respectively). More observations (2260+ sites), longer time (20 years), and updated criteria (Repro3) are to finely obtain the GNSS velocity field in continental China, and depict crustal deformation and active block with the gpsgridder and improved K-means++ methods.

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.

The current research of the international and regional coordinate reference framework is mainly realized by GPS technology. The launch of the last BDS3 satellite on June 23 of 2020 marked the completion of the global deployment of BDS. Therefore, it is urgent to study and establish the corresponding coordinate reference framework. We aim to preliminarily realize and evaluate the BDS3/COMPASS terrestrial reference framework (CTRF2020). CTRF2020 reference epoch is 2020.0, and it can be expressed with the coordinates and velocities of a series of reference sites at the epoch of 2020.0. Firstly, the evaluation of the actual service performance of BDS in the global region reflects the high visibility and change trend of BDS satellite in recent three years, which provides basic input data for CTRF2020. Then, the BDS observations of about 100 global stations in the recent three years are calculated by PPP and NET solution, to obtain the global high-precision BDS coordinate time series. Then, the BDS time series of the two solutions are fitted and compared with the IGS14 velocity field. The results show that the series accuracy of PPP-BDS and NET-BDS solutions is equivalent, and there is an mm-level systematic deviation with IGS14 solutions. The horizontal series fitting accuracy of PPP-BDS and NET-BDS solutions is better than that of the vertical direction, the accuracy of NET-BDS solution is slightly better than PPP-BDS, and the difference of fitting accuracy is 0.12, 0.13, and 0.50 mm in the NEU direction. The velocity field accuracy of PPP-BDS and NET-BDS solution is the same, and the overall three-dimensional velocity difference is less than 0.2 mm/a. The velocity fields of PPP-BDS and NET-BDS solution have little difference from IGS14, and the overall difference is less than 0.5 mm/a. Finally, we give the limitations and improvement direction of CTRF2020. The preliminary realization and evaluation of CTRF2020 may be expected to provide a reference for the future realization of a comprehensive terrestrial reference framework dominated by BDS3 technology and supplemented by multi-source space geodetic technology.

Extensive data collection, unified and rigorous data processing, and accurate construction of station motion model (especially the correction of co-seismic/post-seismic effects of large earthquakes) are three basic elements for the accuracy and reliability of Global Navigation Satellite System (GNSS) velocity. Thus, we take advantage of the sensitivity features of the spectral analysis and hypothesis test to refine the site movement trajectory model, and apply it to the reprocessed GNSS three-decade coordinate time series. Firstly, we reprocess GNSS observations and seismic records based on the updated convention and processing settings of International GNSS Service (IGS) repro3. Secondly, we use the Improved Lomb-Scargle Periodogram (ILSP) model to analyze the periodic characteristics of GNSS vertical time series. The results represent that the primary period of about 35% of sites is 365 days, and the secondary period of 20% of sites is 182 days. Thirdly, we evaluate the performance of different time series model component combination of the time series (a: veloc-ity only; b: velocity + offset; c: velocity + offset + PSD; d: velocity + offset + PSD + period) and Post-Seismic Deformation (PSD) modes (PSD1: None; PSD 2: Exp; PSD 3: Log; PSD 4: Exp + Log). Fourthly, we use the chi-square test to assess the overall correctness of the trajectory model, followed by the t-test to test the significance of each parameter further, and then use the optimized model to refit and reanalyze GNSS time series. The analysis of the velocity results illustrates that the fitting accuracy of GNSS time series is 3-6 mm in the horizontal direction and 4-9 mm in the vertical direction. Lastly, we obtain a refined global three-dimensional velocity field based on GNSS three-decade time series, with the median velocity of Root Mean Square Error (RMSE) as 0.17, 0.17, and 0.32 mm/a in N/E/ U direction. Compared with ITRF2014, the velocity difference is at 1-2 mm/a level due to differences in GNSS observations, trajectory model, and geodetic technology.(c) 2022 COSPAR. Published by Elsevier B.V. All rights reserved.

首先通过改进圆柱拟合的误差方程进行去相关变换,降低参数之间的相关性;再使用再生权最小二乘法(self-born weighted least squares,SBWLS)稳健估计方法来计算观测值的再生权,达到抗差的效果;最终迭代收敛得到圆柱参数估计值.该方法可以任意选取参数初值,也不用进行剔除粗差的处理.通过与目前常用的圆柱拟合方法相比较,以及对不同点云数据的计算结果进行评定分析,结果表明该方法能更有效地消除或减弱粗差对参数估计的影响,适用于各种情况下的圆柱拟合.

爱国主义教育是大学教育的重要组成部分,在专业课程中,挖掘融入爱国主义教育内容,是爱国主义教育多维度展开的补充.结合卫星导航定位课程,从卫星导航定位在战争中的应用、独立自主建设系统和人才培养的重要性出发,激发学生的学习兴趣,形成爱国主义教育与文化知识相互促进的作用.

通过三维激光扫描技术获取不规则物体的点云数据,将数据沿三个坐标轴方向以固定的间隔切片,将各切片层内扫描点投影至切片底面,用Alpha-shape算法搜索外接多边形,计算多边形的面积.计算各切片的体积,对所有的切片计算结果进行内插和累加,即可得到物体的重心坐标和体积.通过计算不规则物体的实测点云数据,验证了该方法的可靠性.对计算中切片间隔和搜索半径的选取作了适当的分析,得出一些有益结论.

With the rapid development of Global Navigation Satellite System (GNSS) technology, the long-term accumulated GNSS observations of global reference stations have provided valuable data for geodesy and geodynamics studies since the 1990s. Acquiring the precise velocity of GNSS stations is very important for the study of global plate movement, crustal deformation, etc. However, the seismic activities nearby some GNSS observation stations may seriously change the station’s motion trajectory. Therefore, our research was motivated to propose a method allowing for station seismic deformation, and apply it to construct an updated global GNSS velocity field. The main contributions of this work included the following. Firstly, we improved the GNSS data processing procedures and seismic data selection strategies to obtain GNSS coordinate time series with mm-level precision (3–5 and 6–8 mm in the horizontal and vertical, respectively) and information of each site impacted by seismic events, which provides necessary input data for further analysis. Secondly, an Integrated Time Series Method (ITSM) concerning the effect of seismic deformation was proposed to model the station’s nonlinear motion accurately. Distinguished with existing studies, all parameters including seismic relaxation time can be simultaneously estimated by ITSM, which improves the accuracy and reliability of GNSS station velocity significantly. Thirdly, to optimize the ITSM-based model, the influences of seismic relaxation time (a. 0.1 × true, b. 10 × true, c. true), parameterization mode (a. Offset + Velocity, b. Offset + Velocity + PSD, c. Offset + Velocity + PSD + Period), and the Post-Seismic Deformation (PSD) model (a. None, b. Exp, c. Log, d. Exp + Log) on results of GNSS time series analyzing were discussed. The results showed that the fitting accuracy of GNSS displacements was better than 5 mm and 10 mm in the horizontal and vertical, respectively. Finally, the global GNSS station velocity field (referred to as GGV2020 hereafter) was refined by ITSM using global GNSS observations and seismic data during 1990–2020. This not only helps interpret plate tectonic motion, establish and maintain a Dynamic Terrestrial Reference Frame (DTRF) but also contributes to better investigating geodynamic processes. GGV2020 results showed that the accuracy of global velocity was better than 1 mm/a, and the averages of Root Mean Square Error (RMSE) were 0.19 mm/a, 0.19 mm/a, and 0.33 mm/a in the north, east, and up direction, respectively. Besides, the RMSE obeys normal distribution. Compared with ITRF2014, there was a difference of about 1–2 mm/a between them due to differences in terms of observation span, processing model, and geodetic technology. Moreover, GGV2020 is expected to enrich and update the existing velocity field products to describe the characteristics of regional crustal movement in more detail, especially in Antarctica.

Low earth orbit (LEO) satellite constellations have the potential to augment global navigation satellite system services. Among the ongoing tasks of LEO-based navigation, providing broadcast ephemerides that satisfy the accuracy requirement for positioning, navigation, and timing is one of the most critical prerequisites. Singularities can occur when fitting broadcast ephemeris parameters in the case of a small eccentricity or small or large inclination. We choose an improved nonsingular element set for the LEO broadcast ephemeris design. We establish suitable broadcast ephemeris models, considering the fit accuracy, number of parameters, orbital altitude, and inclination. The fit accuracy using different orbital altitudes, orbital inclinations, and eccentricities suggests that the optimal parameters are $$\dot{n}$$ , $$\ddot{n}$$ , Crc3, Crs3, $$C_{\lambda c3}$$ , and $$C_{\lambda s3}$$ , together with the basic broadcast ephemeris model. After adding these six parameters, a fit accuracy of better than 10 cm can be achieved with a 20 min arc length and 500–1400 km orbital altitudes. The effects of the number of parameters, orbital altitude, inclination, and eccentricity on the fit accuracy are discussed in detail. Finally, the performance is validated with real LEO satellites to confirm the effectiveness of the proposed method.

本文提出一种将原城市坐标系转换为CGCS2000椭球时投影参数的最佳选取方法,该方法采用坐标转换、高斯投影等模型,通过修正投影面高程和子午线收敛角来保证新老城市坐标投影变形尺度比一致,实现了老城市坐标系到基于CGCS2000的新城市坐标系的转换,使得新老城市坐标差异极小,老城市坐标无须转换就可以直接在新坐标系下使用,极大地减小了测绘成果转换的工作量.

精密单点定位不受局域观测和设施影响,有利于形变监测.为降低电离层延迟对单频精密单点定位结果的影响,提出了单双频混合观测的方法.但单频精密单点定位仍受相位非小数偏差影响,为此提出采用双差模糊度应用于单频精密单点定位.观测数据解算结果表明,电离层延迟精度优于1 cm,满足单频精密单点高精度定位的要求,对应的单频精密单点定位可实现厘米级结果.双差模糊度应用于单频精密单点定位时,参数收敛时间平均缩短约7 min,在北、东、高程3个方向的定位结果平均分别提升0.23、0.14、0.21 cm.

The quality and availability of Uncalibrated Phase Delay (UPD) solutions are crucial to the Precise Point Positioning (PPP) service, and the long-term temporal variability and its contributing factors should be better understood. In this paper, we comprehensively investigate the long-term time-varying characteristics of each UPD product respectively generated by a global and regional network and their interoperable application in PPP-AR (ambiguity resolution), the sampling of the WL and NL UPDs are daily and 30 s, respectively. Firstly, in terms of our 30 day Wide-Lane (WL) UPD products of 31 satellites, the Standard Deviation (STD) of each satellite WL UPDs ranges from 0.04 to 0.06 cycles, indicating that the long-term prediction accuracy of satellite WL UPD is sufficient for fixing Wide-Lane ambiguities. Secondly, when a satellite in eclipsing the discontinulity may corrupt the determination of Narrow-Lane (NL) UPD in form of offset, as a result of lacking or poor satellite attitude dynamic modeling. When the influence of discontinuity is removed, the STD of our estimated satellite NL UPDs is less than 0.05 cycles. Thirdly, the STD of our estimated receiver WL UPDs is mainly below 0.2 cycles, which implies that its stability is one order poorer that of the satellite. In addition, if they are used for stations in and around the network covered region, the stability of the UPD products from the CMONOC (Crustal Movement Observation Network of China) is better than that from a global network, benefit from the fact that all the CMONOC stations are equipped with the same receiver type. Finally, the PPP-AR results show that a rate of 82.9% for stations with a WL-ambiguity-fixed rate of over 90% while 69.5% for stations with an NL-ambiguity-fixed rate of over 80% can be achieved when using UPD from the global network, which is worse than that of using UPD from the CMONOC (85.7% for stations with a WL-ambiguity-fixed rate of over 90% while 75% for stations with an NL-ambiguity-fixed rate of over 80%). The results of the experiment on the UPD interoperable application in PPP show that the global network UPD products can provide a fast AR at any single station, and the convergence time is well below 25 min. Particularly, when the location of a station is in and around the regional network, our results show that the PPP results obtained using regional UPDs enable the consistent use of global UPDs. When the location of a station is far away from the regional network, using the regional UPDs can not achieve PPP-AR. Finally, the WL UPDs of the previous day is used for forecasting to estimate the NL UPDs, the stability analysis results of NL UPDs solution and positioning results are demonstrate the validity of forecasted UPD products. (C) 2020 COSPAR. Published by Elsevier Ltd. All rights reserved.

Low Earth orbit (LEO) satellites are a promising type of navigation augmentation satellite for current global navigation satellite systems. Aiming at the navigation function, an effective broadcast ephemeris model needs to be designed for LEO satellites. An enhanced integration-type broadcast ephemeris model is proposed in this study. First, the short-term periodical variation characteristics of LEOs’ accelerations in the Earth-centered Earth-fixed coordinate system are analyzed. The Chebyshev polynomials and harmonic functions are then applied to represent the variation perturbation of accelerations. Tests using simulated and real data from LEO satellites at altitudes from 600 to 1400 km are conducted to evaluate the fit accuracy of the proposed models in terms of arc length, integration method, integration step length, orbital altitude, inclination, eccentricity, etc. The fit accuracy is dramatically improved compared to that of the current GLONASS integration-type broadcast model, where fit errors less than 10 cm are achieved with an arc length of 20 min.