Page 98 - 《武汉大学学报（信息科学版）》2025年第9期

1826 武 汉 大 学 学 报 （信 息 科 学 版） 2025 年 9 月

takes the real-time orbit and clock products of Chinese Academy of Sciences (CAS) in 2022 as a case study
and evaluates the performance of products from the perspectives of long-term products accuracy and dynamic
precise point positioning (PPP) accuracy. It also assesses the distribution characteristics of signal-in-space
user range error of real-time orbit and clock products by analyzing instantaneous signal-in-space user range
error (IURE) calculated by 100 uniformly distributed stations worldwide. The integrity support information
for CAS real-time orbit and clock products is computed. Results: By comparing CAS real-time orbits and
clocks with post-processed precision products provided by Deutsches GeoForschungsZentrum （GFZ）, it is
observed that the orbit accuracy of GPS and Galileo is better than 5 cm, with a standard deviation of clock
errors better than 0.08 ns. However, the orbit accuracy of BDS and GLONASS is better than 15 cm, with
a standard deviation of clock errors better than 0.3 ns. The kinematic PPP using CAS real-time products is
conducted with observations collected from 28 globally distributed stations. The positioning accuracy of
PPP with the combined four GNSS systems is better than 4 cm, and the corresponding convergence time is
better than 11 min. The IURE root mean square (RMS) for GPS and Galileo is better than 4 cm, and the
distribution of IURE can be accepted as a Gaussian distribution. GLONASS exhibits an IURE RMS within
10 cm, with noticeable differences among satellites, leading to an obvious leptokurtic and fat-tailed distri⁃
bution. The BDS demonstrates an IURE RMS better than 11 cm, but the IURE distribution differs among
different types of satellites, and BDS-3 satellites from Shanghai Engineering Center for Microsatellites
（SECM） display distinct bimodal characteristics. Regarding the prior probability of constellation fault and
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satellite fault, the prior probability of GPS constellation fault is the smallest, which is 5.2×10 , while the
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prior probability of constellation fault of other systems is less than 1.0×10 except for BDS-2. The prior
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probability of GLONASS satellite fault reaches 2.7×10 , and the prior probability of Galileo satellite fault is
the smallest, which is 8.7×10 . Regarding envelope standard deviation and standard deviation of signal-
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in-space user range error, the difference of these two standard deviations of GPS and Galileo is within 4
cm, the difference of these two standard deviations of GLONASS is basically greater than 5 cm, and the
difference of envelope standard deviation between BDS-2 and BDS-3 is larger than that of standard devia⁃
tion. Conclusions: The accuracy of BDS and GLONASS real-time orbit and clock products provided by
CAS needs to be further improved to support high-precision and assured positioning.
Key words： precise point positioning； real-time orbit and clock； signal-in-space user ranging error； integrity

相较于实时动态定位（real-time kinematic po⁃ 提供实时 PPP 服务。目前实时分析中心包括欧
sitioning， RTK），精密单点定位（precise point po⁃ 洲 空 间 局（European Space Agency，ESA）、德 国
sitioning， PPP）具有单机作业、机动灵活、全球覆 地 学 研 究 中 心（Deutsches GeoForschungsZen⁃
盖 等 优 势 ，为 高 精 度 定 位 提 供 了 全 新 的 解 决 方 trum， GFZ）等 国 际 组 织 ，以 及 中 国 科 学 院（Chi⁃
法。在精密轨道和钟差产品的基础上，PPP 可以 nese Academy of Sciences， CAS）、武汉大学（Wu⁃
实现厘米级甚至毫米级精度的定位 ［1-2］ ；在 PPP 的 han University， WHU）等国内机构。学者们研究
基础上固定整周模糊度可以提高定位精度和缩 了不同机构的实时轨道、钟差产品精度以及定位
短收敛时间，即 PPP-AR（ambiguity resolution）技 精度 ［11-14］ ，目前 GPS 的实时轨道和钟差产品精度
术 ［3-5］ 。从区域参考网生成精密大气产品可进一 分别优于 5 cm 和 0.15 ns，其次是 Galileo、BDS-3、
步缩短 PPP 的收敛时间，实现实时动态 PPP，称 GLONASS 和 BDS-2，四系统实时 PPP 定位收敛
为 PPP-RTK 技 术 ［6-8］ 。 随 着 全 球 导 航 卫 星 系 统 时间通常优于 15 min，定位精度优于 5 cm ［15］ 。部
（global navigation satellite system， GNSS）的 发 分 研 究 也 对 实 时 相 位 偏 差 产 品 进 行 了 深 入 分
展，充分利用多星座、多频率资源会进一步提高 析 ［16］ 。然而，相较于事后轨道、钟差精密产品，实
定位精度、缩短收敛时间 ［9-10］ 。 时轨道、钟差产品受到各种因素的综合影响，不
为了满足实时高精度定位和应用日益增长 可避免地会存在各类故障。首先，针对实时轨道
的 需 求 ，国 际 GNSS 服 务 中 心（International 产品，卫星发生轨道机动或者不正确的轨道建模
GNSS Service， IGS）成立了实时工作组，向用户 均会导致轨道产品精度降低；其次，实时卫星轨