Universal Time (UT1) is a core component of the Earth orientation parameters (EOP). High-precision UT1 predictions are essential for satellite navigation, deep-space exploration, and the maintenance of national standard time. Although effective angular momentum (EAM) information can improve UT1 predictions, the impacts of different angular momentum combinations on prediction performance have not yet been systematically investigated. To improve the prediction accuracy of the National Time Service Center (NTSC) UT1 products, we constructed four prediction schemes: Case 1 uses only atmospheric angular momentum (AAM) data; Case 2 uses AAM + oceanic angular momentum (OAM) data; Case 3 uses AAM + OAM + hydrological angular momentum (HAM) data; and Case 4 uses the full EAM datasets combining AAM, OAM, HAM, and sea-level angular momentum (SLAM) data. The input UT1 series is from the NTSC EOP products, and the 10-day angular momentum forecasts are provided by the German Research Centre for Geosciences (GFZ). The rolling forecast evaluation was conducted from June 2024 to September 2025. The results show that Case 2 performs best for short-term UT1 predictions over 1–12 days, improving the mean prediction accuracy by 10.7%, 10.0%, and 52.0% relative to the predictions using Case 4, IERS finals.daily, and the original NTSC predictions, respectively. For medium- and long-term UT1 predictions over 13–90 days, Case 1 performs best, with corresponding mean improvements of 9.8%, 50.7%, and 61.3%, respectively. These results indicate that incorporating more angular momentum components does not necessarily lead to better UT1 predictions, i.e., Case 2 is preferable for short-term UT1 predictions, whereas Case 1 is more suitable for medium- and long-term UT1 predictions. These findings provide empirical evidence and practical guidance for optimizing UT1 prediction models.

The Galileo navigation system offers a free High Accuracy Service (HAS) to global users via the E6 signal and the Internet, enabling the broad application of real-time precise point positioning (PPP) time transfer. However, tropospheric delay is not only a major error source in real-time PPP time transfer but also correlates with clock offset parameters, thereby limiting the achievable accuracy. We employed our proprietary ray-tracing software (NRT-2D) to compute high-precision tropospheric delays and proposed a real-time PPP time-transfer model with Zenith Tropospheric Delay (ZTD) constraints based on Galileo HAS. The experimental results showed that the root mean square error of NRT-2D ZTD and VIE-2D (a ray tracing software developed by the Vienna University of Technology) ZTD are 10.05 mm and 12.11 mm, respectively, which verifies that NRT-2D has higher accuracy in ZTD calculation. The tropospheric slant delay exhibits anisotropy that increases with decreasing elevation angle and is significantly stronger in summer and autumn than in spring and winter. Compared to conventional PPP time transfer models, the proposed model achieves accuracy improvements of up to 28.20% and 21.08% in GPS and Galileo-based PPP time transfer, respectively. Short-term frequency stability (1920 s) improvement rates reached as high as 40.27% and 52.99%. Additionally, during the PPP re-convergence stage caused by the interruption of observation data, the model can effectively suppress the volatility of time transfer results. The research demonstrated that the ZTD constrained real-time PPP time transfer based on Galileo HAS can significantly improve the accuracy and stability of the time transfer results, thereby offering robust support for high-precision time transfer applications.

Utilizing real-time precise point positioning (PPP) technology is an effective approach for obtaining high-precision zenith tropospheric delay (ZTD). Without relying on the terrestrial internet, Galileo high accuracy service (HAS) can provide precise orbit and precise clock products for the world. A thorough assessment of the ZTD accuracy of real-time PPP calculations based on Galileo HAS products in global regions is necessary to promote its application in the field of global navigation satellite system (GNSS) meteorology. The observation data of HAS from 1 to 7 September 2023 were selected for the experiment. Firstly, the accuracy of satellite orbit and clock products of the HAS GPS and HAS Galileo system are evaluated. Then, real-time PPP positioning accuracy within and outside the HAS service area is analyzed. Finally, 104 IGS stations in the world are selected to analyze the ZTD accuracy of real-time PPP calculations based on Galileo HAS products. The experimental results show that during the test period, the RMSE values of the satellite orbit products of the HAS GPS in the radial, along, and cross directions were 4.57 cm, 10.62 cm, and 7.56 cm, respectively. The HAS Galileo RMSE values were 2.81 cm, 8.02 cm, and 7.47 cm, respectively. The RMSE values of the clock products were 0.38 ns and 0.15 ns, respectively. At the selected stations, the real-time PPP positioning accuracies outside the HAS service area and within the service area were similar, and the correlation coefficient between HAS ZTD and IGS ZTD was above 0.90. In the global region, the average bias and RMSE values of the real-time PPP ZTD of the HAS GPS were −0.31 mm and 16.78 mm. Those of the HAS Galileo were 2.30 mm and 15.89 mm, and those of the HAS GPS/Galileo were −0.25 mm and 16.11 mm, respectively. Moreover, each system showed that the accuracy of the HAS ZTD inside the service area was better than that outside the service area. Compared with the single system, the real-time PPP ZTD continuity and stability of the dual system were better.

Galileo high accuracy service (HAS) via Galileo navigation signals has provided state space representation for GPS and Galileo since January 2023. Tropospheric delay remains a dominant error source in HAS-based real-time precise point positioning (PPP) for global positioning and timing applications. To mitigate this effect, we propose a refined NWP-constrained real-time PPP model (NWP-CR-PPP), which incorporates high-precision zenith tropospheric delay (ZTD) estimates derived from numerical weather prediction (NWP) systems into the standard PPP framework (S-PPP), thereby enhancing HAS real-time PPP timing services globally. The primary research components comprise: (1) optimal weight determination for NWP ZTD through error characteristic analysis, (2) systematic investigation of the NWP-CR-PPP model's positioning and timing performance under static and kinematic scenarios. Experimental results demonstrated that the NWP ZTD achieves mean absolute error and root mean square error values of 9.87 mm and 12.07 mm, respectively, when validated against IGS ZTD, confirming its reliability as a high-precision constraint. In the static scenario, the NWP-CR-PPP model demonstrates significant improvements in both positioning accuracy and timing precision compared to the S-PPP model, regardless of single-system or dual-system configurations. Quantitatively, the positioning accuracy mean Gain is 2.82 cm for single-GPS, 2.31 cm for single-Galileo, and 2.13 cm for the combined GPS/Galileo system, while the corresponding timing precision mean Gain are 0.07 ns, 0.06 ns, and 0.06 ns, respectively. The long-term timing stabilities (61 440 s) at MBAR and OUS2 stations fluctuate within ranges of 1.99-2.29 x 10-13 and 1.29-1.53 x 10-13, respectively. In the kinematic scenario, the NWP-CR-PPP model also demonstrates a significant improvement, and the improvement margin is greater than that in the static scenario. Quantitatively, the mean Gain values of positioning accuracy for each system are 3.00 cm, 2.79 cm, and 2.39 cm, while the mean Gain values of timing accuracy are 0.16 ns, 0.13 ns, and 0.08 ns. The long-term (61 440 s) stabilities of the timing results for each system at the two stations are within the ranges of 1.94-2.39 x 10-12 and 1.28-1.34 x 10-12, respectively. Overall, by assimilating high-precision ZTD constraints from NWP, the NWP-CR-PPP model significantly enhances positioning accuracy and timing performance in both static and kinematic scenarios.

基于干涉时差测量的卫星无源测定轨是一种有巨大发展潜力的测定轨方法,各测站使用网络传输观测数据至相关中心,再通过干涉测量手段测量卫星信号至各测站的时间差值,最后使用时差数据进行卫星定轨.为了验证基于干涉时差测量的卫星无源测定轨的定轨精度,在北京、喀什、深圳、哈尔滨搭建实验网,对GEO(geosynchronous Erath orbit)卫星亚太 6C 进行干涉时差测量测定轨,观测时长为 9天.对时差数据、定轨残差和重叠弧段轨道差的分析表明,干涉时差测量测定轨的时差测量的精度约为 0.7 ns,定轨残差的RMS(root mean square)优于 0.7 m,定轨精度(重叠弧段轨道误差)为 17.78 m.对轨道误差源进行了分析,并根据误差源提出了后续进一步提高轨道精度的几种方法.

With precise orbits of GEO satellites, the precise time transfer between stations can be realized by VLBI observations of GEO satellite. This can be a new time transfer method independent of GNSS co-view, and can obtain same or even higher time transfer accuracy.In this paper, a VLBI time transfer method based on GEO satellite observation is proposed. The time transfer measurement model is established, and the major systematic errors and correction methods are studied. The precise orbits of GEO satelltes which are critical for VLBI measurement model, are determined by GNSS and by the method of Orbit Determination Transfer Tracking (ODTT). The VLBI time transfer experiment was carried out by observing Beidou GEO satellite using Jilin and Sanya stations of the National Time Service Center (NTSC) VLBI network. The GNSS PPP time transfer results are used as a standard for evaluation. The results show that the consistency between VLBI time transfer and GNSS PPP time transfer is consistent within 2 nanoseconds.Here, we present the preliminary experimental results. Further improvements include: Selection of setellites with larger bandwidth to improve the time transfer accuracy; the correction of satellite antenna phase center to satellite center of mass; the geometric tide correction of stations and other error sources should be investigated in the future.

It is important for a geostationary Earth orbit (GEO) satellite to rapidly recover its orbit after a maneuver with short-arc precise orbit determination (POD). Based on orbit determination by transfer tracking (ODTT), the POD accuracy of a GEO satellite is less than 10 m over a short arc. ODTT can achieve high accuracy in the radial direction but is weak in the transverse direction. Considering that very long baseline interferometry (VLBI) can reduce the value of position dilution of precision (PDOP), especially in the transverse direction, a joint POD method using both VLBI and ODTT is proposed herein to improve POD accuracy and rapidly recover the orbit. An ODTT system and the first VLBI 2010 Global Observation System (VGOS) in China was used to track the ZX 12# GEO satellite. The results showed that the ODTT POD accuracy was 3.016 and 2.707 m for 2 and 4 h arcs, respectively. When using both VLBI and ODTT, the POD accuracy was 2.658 m for the 2 h arc, an improvement of 11.87% compared to the POD using ODTT alone. Therefore, VLBI and ODTT can be used together to increase the short-arc POD accuracy while also reducing the arc length necessary to recover the orbit.

VLBI (Very Long Baseline Interferometry)技术观测卫星需要对干涉测量数据进行相关和后处理,通过相关、时延校准、条纹搜索,最终得到卫星的基线几何时延.基于天文开源软件建立起一套卫星干涉测量数据处理系统.该系统可工作在实时和事后两种状态,实现相关、中性大气、电离层、钟模型以及仪器硬件的时延校准、条纹搜索、生成基线时延和时延率序列.使用该系统处理北斗GEO (Geosynchronous Earth Orbit)卫星的干涉测量试验数据,得到了精度在1-2 ns量级的卫星基线时延序列.

Based on the principle of TWSTFT, the technology of satellite Orbit Determination by Two-way Tracking (ODTT) is proposed in this contribution. In contrast to the TWSTFT, the signal is transmitted from and received by the same station in ODTT. The time delay of the signal from the station to the Geostationary (GEO) satellite, and then back to the station can be precisely measured, which realizes the range determination between the station and the satellite. Based on the determined ranges of several stations and dynamic models for orbit determination, precise satellite orbits can be obtained. In this study, in addition to the ODTT measurement model, the methods of correcting the station hardware delays, the tropospheric and the ionospheric delays are explained in details. In collaboration with several other institutions, National Time Service Center (NTSC), Chinese Academy of Sciences(CAS) setup a Two-way Tracking network of 5 stations in China, and performed a large amount of experiments for GEO satellite orbit determination. The results show that the precision of the range measurements is about 2 cm, and the GEO satellite orbit precision is a few meters with long arc observation. According to the experimental results, the main characters of ODTT are shown as follows: 1) the ranges measured by the ODTT do not include the time difference between the ground and the satellite clocks, which is beneficial for realizing the precise orbit determination; 2) the measurement precision is very high, i.e., about 2 cm; 3) the ODTT utilizes the microwave frequency and the technology of spread spectrum, which supports the orbit determination for satellites of high orbits and the measurements in diverse atmosphere conditions. The ODTT is a new space technology under development. It will support the research of spatial sciences and geosciences in the future.

针对甚长基线干涉测量(VLBI)技术中,测站坐标精度与高精度的VLBI宽带观测不相匹配的问题,该文提出一种利用VLBI本身观测结果分析测站坐标改正量的方法.利用观测得到的时延值扣除几何时延及各种已知误差项后,残余部分还存在由基线矢量误差引起的时延、两地原子钟同步误差和系统误差引起的时延,给出残余时延与基线矢量误差等的计算模型.采用国家授时中心VLBI2010系统观测数据,计算结果表明,吉林-喀什基线的基线长度改正量约为11.467 7 cm,观测值与拟合值的对比表明这种方法的可行性.

卫星轨道精度是决定卫星导航系统性能的关键因素之一.在转发式卫星导航的试验项目的支持下,对I1-S卫星的观测数据进行分时段处理,模拟分时观测的过程,利用处理后的数据进行定轨.目的是验证在数据量少的情况下是否不影响定轨精度,如果结论成立,则可以在有多个观测任务时,对不同的卫星进行轮替观测,提高设备的利用率.利用201 5年8月14日到201 5年8月20日的观测资料进行定轨实验,分别从定轨残差以及轨道重叠误差等方面分析卫星的定轨精度,5站总的RMS在0.14～ 0.17m的范围之内,平均值是0.15m.在三维方向上的重叠差小于1m.利用分时观测的数据进行定轨,5站总的残差RMS都小于0.20m,在0.13～0.18 m的范围内,分时段数据解算的卫星轨道与全时段解算的轨道比较差异RMS小于1 m,和全时段定轨残差在同一水平上,没有降低定轨精度,证明了在米级定轨需求下分时观测的可行性.

基于卫星双向时间传递原理,国家授时中心提出了转发式卫星测定轨方法,已将GEO通信卫星的测定轨精度提高到米级水平.近年来,转发式测定轨技术不断发展完善,观测目标已由单一GEO卫星扩展到北斗IGSO卫星(I1-S).本文描述了转发式测量模型,并给出了转发式测定轨新系统对GEO卫星和北斗IGSO卫星(I1-S)的测定轨结果.经过试验验证,GEO、IGSO卫星的重叠弧段的轨道差的RMS值已分别达到2m和0.9in.长期的试验应用和分析表明,转发式测定轨技术的主要特色和优越性在于:转发测距与钟差分离,便于实现精密定轨;以精密时间测量为基础,测距精度高(2cm),并且不受气象条件制约;使用微波频段和扩频技术,易于远距离测轨;该技术所需的星上透明转发器载荷成熟且易于小型化.从未来应用来看,转发式测定轨技术适用于中高轨航天器的精密测定轨,尤其对高轨卫星测定轨有明显优势,可用于开展相关科学研究.

In CAPS, the temperature changes greatly in one day, especially for master station with continental climate by 10 °C. Moreover, there is periodic tendency in temperature and clock offset residuals. The relation between temperature and clock offset residuals should be researched to improve TWSTFT precision. However, there is no explicit model for effect of temperature on clock offset. In order to test the effect of temperature on clock comparison, experiment has been conducted using C-B and observation on 17 June, 2005. There are two TWSTFT links: Shanghai-Linton, Changchun-Linton. The RMS for clock offset residuals between Shanghai and Linton has decreased from 0.6174ns to 0.2771ns, with that being from 0.6445ns to 0.4050ns. The TWSTFT precision has increased by 55% for Shanghai-Linton link and 37% for Changchun-Linton link. Therefore, TWSTFT precision has been improved after temperature compensation. The temperature of each station should be set constant, which is significant for TWSTFT in CAPS.

Combined with two-way satellite time and frequency transfer(TWSTFT),a Sagnac effect solution about satellite motion is proposed.The TWSTFT technique is based on geostationary satellite.As a result of the perturbation forces,the geostationary satellite is not absolutely stationary,but it does the diurnal motion with small amplitude.Sagnac effect is closely related to both satellite and earth observation station positions.The satellite' motion makes Sagnac effect have diurnal variance characteristic.The Sagnac effect value is calculated by using the high accuracy orbit data of geostationary satellite.It is shown that the Sagnac effect value is variable with variety of satellite positions.The variety value is about several hundred picoseconds.It improves the Sagnac effect correction accuracy comparing with the conventional method assuming that the geostationary satellite is absolutely stationary.It has the important application value for all kinds of time transfer methods and satellite navigation community.

It is almost reciprocity of the Two-way satellite time and frequency transfer(TWSTFT) communication links. The path delays are almost canceled out due to the symmetry. It is the advantage of TWSTFT. But as the technology development, the higher accurate is required for time comparison. The incomplete reciprocity must be studied in detail for TWSTFT. Satellite motion is a kind of the incomplete reciprocity and can result that the uplink geometry paths aren't equal to the downlink geometry paths. Satellite motion's correction depends on the satellite velocity and time difference between the signal from two stations arrive at the satellite.

The ionosphere errors are corrected in Two-way satellite time and frequency transfer(TWSTFT) using the ionosphere data provided by IGS.The ionosphere total electron content(TEC) is released by IGS at fixed time and geographic grid.The TEC of pierce point at requisite time is calculated by spatial four grids interpolation algorithms and temporal two linear interpolation algorithms.Then it is used to TWSTFT corrected after some processing.The results show that the ionosphere effect on C-band is about(0~0.5)ns range.It is must be considered for time comparison at sub-nanosecond level.The ionosphere product provided by IGS is suit TWSTFT ionosphere correction.It has the advantages of simple method,low cost and high accuracy.

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.

A new strategy of precise orbit determination (POD) for GEO (Geostationary Earth Orbit) satellite using SATRE (SAtellite Time and Ranging Equipment) is presented. Two observation modes are proposed and different channels of the same instruments are used to construct different observation modes, one mode receiving time signals from their own station and the other mode receiving time signals from each other for two stations called pairs of combined observations. Using data from such a tracking network in China, the results for both modes are compared. The precise orbit determination for the Sino-1 satellite using the data from 6 June 2005 to 13 June 2005 has been carried out in this work. The RMS (Root-Mean-Square) of observing residuals for 3-day solutions with the former mode is better than 9.1cm. The RMS of observing residuals for 3-day solutions with the latter mode is better than 4.8cm, much better than the former mode. Orbital overlapping (3-day orbit solution with 1-day orbit overlap) tests show that the RMS of the orbit difference for the former mode is 0.16m in the radial direction, 0.53m in the along-track direction, 0.97m in the cross-track direction and 1.12m in the 3-dimension position and the RMS of the orbit difference for the latter mode is 0.36m in the radial direction, 0.89m in the along-track direction, 1.18m in the cross-track direction and 1.52m in the 3-dimension position, almost the same as the former mode. All the experiments indicate that a meter-level accuracy of orbit determination for geostationary satellite is achievable.

Two-way satellite time and frequency transfer (TWSTFT) is one of the most precise and accurate long-distance time transfer techniques nowadays. A C band multi-station satellite tracking system is developed based on TWSTFT in China. This system can not only measure the distance between a satellite with transponders and earth stations, but also realize the time synchronization between all earth stations. The satellite orbit can be determined by the distances. Five earth stations have been constructed in China. The master station is placed at the National Time Service Center (NTSC) in Lintong. There are a very small antenna terminal (VSAT) of 3.7 meters, up/down converters, a modem and an atomic clock in each station. The up and down link frequencies are 6GHz and 4GHz. The spread spectrum signal generated by the modem is 20MHz chip rate. The transmitter power is less than 1 W. The results show that the accuracy of ranging, orbit determination and time synchronization between all earth stations is about 1cm, 10cm and 0.1ns respectively.

This paper presents a time synchronization method based on the COMPASS code measurements in combination with two-way transfer ranging, which results the clock offset between COMPASS GEO satellite and the ground station. The clock offset of COMPASS G3 satellite on board is computed by using the data observed on October 2010. In order to verify the accuracy of this method, the results are compared with the results, which are determined only by pseudo-range observation. By comparison and analysis, the following facts can be drawn. (1) The precision of navigation satellite clock bias is better than 10 ns, when the clock bias is calculated by the new method. There is no systematic error between our results and clock bias deduced from precise satellite orbit. (2) The new method can separate satellite orbit and clock bias, it is beneficial to researching satellite clock bias.