GNSS Receiver-Related Pseudorange Bias Determination Method and Its Effect on Positioning

GENG Tao; LI Zhongxing; XIE Xin; MA Zhuang; ZHAO Qile

doi:10.13203/j.whugis20210276

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GNSS Receiver-Related Pseudorange Bias Determination Method and Its Effect on Positioning

Updated：2023-06-29

- GNSS Receiver-Related Pseudorange Bias Determination Method and Its Effect on Positioning
- Geomatics and Information Science of Wuhan University
- Affiliations：
  
  1.GNSS Research Center, Wuhan University, Wuhan 430079, China
- Author bio：
- Funds：
  
  the Natural Science Foundation of Hubei Province(2019CFA051)
- DOI：10.13203/j.whugis20210276
  CLC： P228
- Published：05 July 2023，
  
  Received：06 September 2021，
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Cite this article
耿涛,李钟兴,谢新，等.GNSS接收机伪距偏差确定方法及其对定位的影响[J].武汉大学学报（信息科学版）,2023,48(7):1134-1145.

GENG Tao,LI Zhongxing,XIE Xin,et al.GNSS Receiver-Related Pseudorange Bias Determination Method and Its Effect on Positioning[J].Geomatics and Information Science of Wuhan University,2023,48(7):1134-1145.
耿涛,李钟兴,谢新，等.GNSS接收机伪距偏差确定方法及其对定位的影响[J].武汉大学学报（信息科学版）,2023,48(7):1134-1145. DOI：10.13203/j.whugis20210276

GENG Tao,LI Zhongxing,XIE Xin,et al.GNSS Receiver-Related Pseudorange Bias Determination Method and Its Effect on Positioning[J].Geomatics and Information Science of Wuhan University,2023,48(7):1134-1145. DOI：10.13203/j.whugis20210276

GNSS接收机伪距偏差确定方法及其对定位的影响 GNSS Receiver-Related Pseudorange Bias Determination Method and Its Effect on Positioning 1 first-author 耿涛，博士，教授，主要从事卫星导航精密数据处理研究工作。gt_gengtao@whu.edu.cn 耿涛，博士，教授，主要从事卫星导航精密数据处理研究工作。gt_gengtao@whu.edu.cn gt_gengtao@whu.edu.cn 1 1 corresp 谢新，博士。xiexin@whu.edu.cn 谢新，博士。xiexin@whu.edu.cn xiexin@whu.edu.cn 1 1 武汉大学卫星导航定位技术研究中心，湖北武汉，430079 武汉大学卫星导航定位技术研究中心，湖北武汉，430079 GNSS Research Center, Wuhan University, Wuhan 430079, China GNSS Research Center, Wuhan University, Wuhan 430079, China 全球导航卫星系统（global navigation satellite system，GNSS）接收机伪距偏差是指卫星导航信号非理想特征导致的不同接收机的伪距测量常数偏差。研究表明，接收机伪距偏差无法被钟差参数吸收，将影响GNSS精密应用。选取了多GNSS实验全球跟踪网的9条零/短基线，将基线按照接收机类型分为3组，即相同厂商相同型号、不同厂商以及相同厂商不同型号，通过双差法确定了每组基线GPS/北斗卫星导航系统(BeiDou satellite navigation system，BDS)/伽利略卫星导航系统（Galileo satellite navigation system，Galileo）的接收机伪距偏差，并分析了接收机伪距偏差的稳定性及其对整周模糊度解算和伪距相对定位的影响。结果表明，不同厂商接收机构成的基线，伪距偏差可达160 cm，即使同一厂商不同型号的接收机间也存在不可忽略的伪距偏差；对于GPS、BDS和Galileo，Galileo伪距偏差最小，BDS伪距偏差最大。此外，接收机伪距偏差具有良好的稳定性，60 d标准差不超过12 cm。接收机伪距偏差改正后，GPS、BDS、Galileo双差宽巷Melbourne-Wübbena组合非整周部分均方根分别降低了17%、22%、14%，GPS、BDS、Galileo伪距相对定位三维误差分别从84.4、77.3、60.0 cm降低到80.1、72.1、57.0 cm。 Objectives 2 Global navigation satellite system（GNSS） satellite chip shape distortions lead to individual biases in the pseudorange measurements. These biases are the results of the correlator's tracking response and thus depend on the correlator and front-end design of the receiver. As a result, different receivers are likely to exhibit inconsistent biases, called receiver-related pseudorange biases. The researches show that the receiver-related pseudorange biases cannot be absorbed by clock offset, which will affect GNSS precision applications. Methods 2 We estimate the receiver-related pseudorange biases of global positioning system （GPS）/ BeiDou satellite navigation system （BDS）/Galileo satellite navigation system（Galileo）from 9 short/zero-baselines stations from the multi-GNSS experiment network using double difference method. The baselines are divided into three groups according to the combinations of two receivers of one baseline. Results 2 The results indicate that the receiver-related pseudorange biases of receivers with different manufacturers even the same manufacturers with different models cannot be neglected. For baselines with receivers from different manufacturers,the inconsistences of pseudorange biases can reach up to 160 cm. Conclusions 2 Among GPS, Galileo and BDS, Galileo shows the smallest pseudorange biases, while BDS in general is the largest. Furthermore, the stability of pseudorange biases is analyzed, the results suggest that estimated receiver-related pseudorange biases are quite stable with the standard deviation less than 12 cm for the three systems. We investigate the effect of receiver-related pseudorange biases on integer ambiguity resolution and pseudorange relative positioning, with the pseudorange biases correction, the root mean squares of fractional parts of double difference Melbourne⁃Wübbena combination are decreased by 17%, 22%, and 14% for GPS, BDS, Galileo, respectively. An improvement of pseudorange relative positioning accuracy is also confirmed, the 3D positioning errors of GPS, BDS, Galileo are reduced from 84.4, 77.3 and 60.0 to 80.1, 72.1 and 57.0 cm, respectively. 接收机伪距偏差零/短基线模糊度解算 MW组合伪距相对定位 receiver-related pseudorange bias short/zero-baselines integer ambiguity resolution MW combination pseudorange relative positioning 随着全球导航卫星系统（global navigation satellite system，GNSS）的不断发展，为满足日益严苛的定位、导航和授时需求［ 1 1 ］，GNSS高精度数据处理应充分考虑包括硬件偏差在内的所有误差源。卫星和接收机硬件的物理限制导致GNSS偏差有多种表现形式，例如系统间偏差［ 2 2 ］、载波相位非整周偏差［ 3 3 ］以及伪距偏差［ 4 4 ］。针对伪距偏差，20世纪90年代，有学者在利用GPS开展电离层研究过程中发现了卫星端伪距偏差［ 5 5 - 6 6 5-6 ］，这种偏差源于测距信号码失真，在不同卫星和信号频点间存在差异［ 7 7 ］。该偏差可通过广播星历中播发的时间群延迟参数（time group delay，TGD）［ 8 8 - 9 9 8-9 ］，或国际GNSS服务（international GNSS service，IGS）分析中心发布的差分码偏差（differential code bias，DCB）产品进行改正［ 10 10 ］。此外，北斗二号卫星导航系统（BeiDou-2 satellite navigation system，BDS-2）还发现了由星上多路径引起的随卫星高度角变化的偏差，其幅度可达1 m，针对这一问题，文献［ 11 11 - 12 12 11-12 ］提出了改正模型，模型改正后，模糊度固定成功率、精密单点定位精度［ 12 12 ］以及精密定轨精度［ 13 13 ］显著提高。在GNSS精密数据处理时，通常认为伪距偏差较为稳定，且卫星端伪距偏差对所有接收机相同，接收机伪距偏差对使用码分多址（code division multiple access，CDMA）信号体制的同一系统所有卫星都相同［ 14 14 ］。然而，文献［ 15 15 - 17 17 15-17 ］等研究表明，不同硬件配置（例如相关器间隔、前端带宽等）的接收机对卫星信号失真的跟踪响应存在差异，进而导致不同类型接收机、不同卫星的伪距观测值产生系统性偏差（即伪距偏差）。这种现象最早发现于1993年，由于GPS空间飞行器编号（space vehicle number，SVN）19号卫星发生故障导致下行信号异常，引起使用不同类型接收机的差分定位误差显著增大［ 18 18 ］。后续研究表明，即使健康卫星同样也存在接收机伪距偏差［ 19 19 - 22 22 19-22 ］，这类偏差和码元构造［ 20 20 ］、相关器间隔［ 23 23 - 24 24 23-24 ］以及整个信号链的传递函数［ 25 25 ］相关。为削弱其对定位应用的影响，在GPS接口控制文件中明确定义了相关器间距和前端带宽的适用值［ 8 8 ］，然而北斗卫星导航系统（BeiDou satellite navigation system，BDS）和伽利略卫星导航系统（Galileo satellite navigation system，Galileo）目前还暂未提供相关的适用值。接收机伪距偏差的确定方法包括并置接收机双差法、伪距残差法、基于DCB残差的偏差计算方法等。文献［ 7 7 ， 10 10 ］利用并置接收机双差法计算了GPS、Galileo以及BDS-2卫星的接收机伪距偏差，分析了其对DCB和钟差估计的影响。文献［ 26 26 ］利用伪距残差法标定了BDS-2卫星的接收机伪距偏差，伪距偏差改正后标准单点定位和卫星钟差估计精度有所提高。随着GNSS快速发展，尤其是2020年全面建成的北斗三号卫星导航系统（BeiDou-3 satellite navigation system，BDS-3），有必要研究其不同频点、不同接收机类型间的伪距偏差特性。由于不同卫星、不同接收机类型的伪距偏差不一致，接收机伪距偏差无法被钟差参数吸收，将影响一些典型的GNSS精密应用。因此，本文首先介绍了接收机伪距偏差确定方法，并通过不同类型接收机组合的基线计算了多GNSS系统、多频点的接收机伪距偏差，然后研究了接收机伪距偏差特性及其对模糊度固定、相对定位等精密应用的影响。 1　接收机伪距偏差确定方法 1 考虑接收机伪距偏差的GNSS伪距观测方程为［ 10 10 ］： <math display="block" id="M1"><msubsup><mrow><mi>P</mi></mrow><mrow><mi>r</mi><mo>,</mo><mi>i</mi></mrow><mrow><mi>s</mi></mrow></msubsup><mo>=</mo><msubsup><mrow><mi>ρ</mi></mrow><mrow><mi>r</mi><mo>,</mo><mi>i</mi></mrow><mrow><mi>s</mi></mrow></msubsup><mo>+</mo><mi>c</mi><mo>⋅</mo><mo stretchy="false">(</mo><msub><mrow><mi>t</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>-</mo><msup><mrow><mi>t</mi></mrow><mrow><mi>s</mi></mrow></msup><mo stretchy="false">)</mo><mo>+</mo><msub><mrow><msubsup><mrow><mi>b</mi></mrow><mrow><mi>r</mi><mo>,</mo></mrow><mrow><mi>s</mi></mrow></msubsup></mrow><mrow><mi>i</mi></mrow></msub><mo>+</mo><msub><mrow><msubsup><mrow><mi>I</mi></mrow><mrow><mi>r</mi></mrow><mrow><mi>s</mi></mrow></msubsup></mrow><mrow><mi>i</mi></mrow></msub><mo>+</mo><msubsup><mrow><mi>T</mi></mrow><mrow><mi>r</mi></mrow><mrow><mi>s</mi></mrow></msubsup><mo>+</mo><msub><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mi>P</mi><mo>,</mo></mrow></msub></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078601&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078596&type= 70.95066071 5.07999992 式中，上标 <math id="M2"><mi>s</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078603&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078614&type= 1.26999998 2.79399991 和下标 <math id="M3"><mi>r</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078605&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078616&type= 1.69333339 2.79399991 、 <math id="M4"><mi>i</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078619&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078617&type= 1.10066664 2.79399991 分别代表卫星、接收机以及频点编号； <math id="M5"><mi>P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078607&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078621&type= 2.62466669 2.79399991 为伪距观测值； <math id="M6"><mi>ρ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078612&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078624&type= 2.11666679 3.64066648 表示卫星和接收机间的几何距离； <math id="M7"><mi>c</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078633&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078631&type= 1.52400005 2.79399991 为真空中的光速； <math id="M8"><msup><mrow><mi>t</mi></mrow><mrow><mi>s</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078627&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078626&type= 2.11666679 3.04800010 和 <math id="M9"><msub><mrow><mi>t</mi></mrow><mrow><mi>r</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078644&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078643&type= 2.11666679 3.72533321 分别代表卫星和接收机钟差； <math id="M10"><msubsup><mrow><mi>b</mi></mrow><mrow><mi>r</mi><mo>,</mo><mi>i</mi></mrow><mrow><mi>s</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078636&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078645&type= 4.40266657 3.97933316 为接收机伪距偏差； <math id="M11"><msubsup><mrow><mi>I</mi></mrow><mrow><mi>r</mi></mrow><mrow><mi>s</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078638&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078646&type= 2.62466669 3.97933316 和 <math id="M12"><msubsup><mrow><mi>T</mi></mrow><mrow><mi>r</mi></mrow><mrow><mi>s</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078640&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078649&type= 3.89466691 3.97933316 分别为电离层延迟和对流层延迟； <math id="M13"><msub><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mi>P</mi><mo>,</mo></mrow></msub></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078651&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078650&type= 4.99533367 3.72533321 为伪距观测噪声，服从白噪声分布。假设不存在接收机伪距偏差，零基线的伪距双差观测值仅包含观测噪声；对于距离不超过2 km的短基线，由于电离层和对流层延迟具有强空间相关性，伪距双差几乎可以消除大气延迟、卫星和接收机钟差的影响［ 24 24 ］。因此，在某一历元 <math id="M14"><mi>k</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078688&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078670&type= 1.69333339 2.79399991 ，接收机 <math id="M15"><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078655&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078654&type= 2.62466669 3.72533321 、 <math id="M16"><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078657&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078656&type= 2.62466669 3.72533321 和卫星 <math id="M17"><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078892&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078873&type= 2.45533323 3.72533321 、 <math id="M18"><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078674&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078673&type= 2.45533323 3.72533321 的双差伪距观测方程为： <math display="block" id="M19"><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>P</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup><msub><mrow><mo stretchy="false">(</mo><mi>k</mi><mo stretchy="false">)</mo></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>ρ</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup><msub><mrow><mo stretchy="false">(</mo><mi>k</mi><mo stretchy="false">)</mo></mrow><mrow><mi>i</mi></mrow></msub><mo>+</mo><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>b</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup><msub><mrow><mo stretchy="false">(</mo><mi>k</mi><mo stretchy="false">)</mo></mrow><mrow><mi>i</mi></mrow></msub><mo>+</mo><mtext> </mtext><mi mathvariant="normal">Δ</mi><mo>∇</mo><mi>ε</mi><msub><mrow><mo stretchy="false">(</mo><mi>k</mi><mo stretchy="false">)</mo></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078659&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078675&type= 92.54067230 4.82600021 式中， <math id="M20"><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>P</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup><msub><mrow><mo stretchy="false">(</mo><mi>k</mi><mo stretchy="false">)</mo></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078676&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078660&type= 17.44133186 4.82600021 和 <math id="M21"><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>ρ</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup><msub><mrow><mo stretchy="false">(</mo><mi>k</mi><mo stretchy="false">)</mo></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078678&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078662&type= 16.84866714 4.82600021 分别为双差伪距观测值和几何距离； <math id="M22"><mi mathvariant="normal">Δ</mi><mo>∇</mo><mi>ε</mi><msub><mrow><mo stretchy="false">(</mo><mi>k</mi><mo stretchy="false">)</mo></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078666&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078664&type= 12.86933327 4.48733330 为双差伪距观测噪声； <math id="M23"><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>b</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup><msub><mrow><mo stretchy="false">(</mo><mi>k</mi><mo stretchy="false">)</mo></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078680&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078668&type= 16.84866714 4.82600021 为 <math id="M24"><mi>k</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078688&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078670&type= 1.69333339 2.79399991 历元的双差接收机伪距偏差。零基线的双差几何距离 <math id="M25"><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>ρ</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup><msub><mrow><mo stretchy="false">(</mo><mi>k</mi><mo stretchy="false">)</mo></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078692&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078690&type= 16.84866714 4.82600021 为零，短基线的双差几何距离可通过广播星历以及IGS提供的站坐标消除。因此，双差接收机伪距偏差 <math id="M26"><mi mathvariant="normal">Δ</mi><mo>∇</mo><msub><mrow><msubsup><mrow><mi>b</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078835&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078840&type= 11.59933376 4.74133301 可表示为： <math display="block" id="M27"><mi mathvariant="normal">Δ</mi><mo>∇</mo><msub><mrow><msubsup><mrow><mi>b</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mi>E</mi><mo stretchy="false">{</mo><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup><msub><mrow><mo stretchy="false">(</mo><mi>k</mi><mo stretchy="false">)</mo></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">}</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078696&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078684&type= 40.30133438 4.91066647 式中， <math id="M28"><mi>E</mi><mo stretchy="false">{</mo><mo>•</mo><mo stretchy="false">}</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078700&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078698&type= 8.55133343 3.55599999 为数学期望； <math id="M29"><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup><msub><mrow><mo stretchy="false">(</mo><mi>k</mi><mo stretchy="false">)</mo></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078871&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078867&type= 16.76399994 4.82600021 为不含几何距离的双差伪距观测值。为了分析不同卫星的双差接收机伪距偏差的特性，分别以G01、C12、E01作为GPS、BDS、Galileo的基准星。因此，3个系统的接收机伪距偏差表达式为： <math display="block" id="M30"><mfenced open="{" close="" separators="|"><mrow><mtable><mtr><mtd><mi mathvariant="normal">Δ</mi><mo>∇</mo><msub><mrow><msubsup><mrow><mi>b</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">G</mi><mn mathvariant="normal">01</mn><msub><mrow><mi>s</mi></mrow><mrow><mi>l</mi></mrow></msub></mrow></msubsup></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mi>E</mi><mo stretchy="false">{</mo><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">G</mi><mn mathvariant="normal">01</mn><msub><mrow><mi>s</mi></mrow><mrow><mi>l</mi></mrow></msub></mrow></msubsup><msub><mrow><mo stretchy="false">(</mo><mi>k</mi><mo stretchy="false">)</mo></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">}</mo><mo stretchy="false">(</mo><mi>l</mi><mo>=</mo><mn mathvariant="normal">1,2</mn><mo>,</mo><mo>⋯</mo><mo>,</mo><msub><mrow><mi>n</mi></mrow><mrow><mi mathvariant="normal">G</mi></mrow></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi mathvariant="normal">Δ</mi><mo>∇</mo><msub><mrow><msubsup><mrow><mi>b</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">C</mi><mn mathvariant="normal">12</mn><msub><mrow><mi>s</mi></mrow><mrow><mi>l</mi></mrow></msub></mrow></msubsup></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mi>E</mi><mo stretchy="false">{</mo><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">C</mi><mn mathvariant="normal">12</mn><msub><mrow><mi>s</mi></mrow><mrow><mi>l</mi></mrow></msub></mrow></msubsup><msub><mrow><mo stretchy="false">(</mo><mi>k</mi><mo stretchy="false">)</mo></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">}</mo><mo stretchy="false">(</mo><mi>l</mi><mo>=</mo><mn mathvariant="normal">1,2</mn><mo>,</mo><mo>⋯</mo><mo>,</mo><msub><mrow><mi>n</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi mathvariant="normal">Δ</mi><mo>∇</mo><msub><mrow><msubsup><mrow><mi>b</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">E</mi><mn mathvariant="normal">01</mn><msub><mrow><mi>s</mi></mrow><mrow><mi>l</mi></mrow></msub></mrow></msubsup></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mi>E</mi><mo stretchy="false">{</mo><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">E</mi><mn mathvariant="normal">01</mn><msub><mrow><mi>s</mi></mrow><mrow><mi>l</mi></mrow></msub></mrow></msubsup><msub><mrow><mo stretchy="false">(</mo><mi>k</mi><mo stretchy="false">)</mo></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">}</mo><mo stretchy="false">(</mo><mi>l</mi><mo>=</mo><mn mathvariant="normal">1,2</mn><mo>,</mo><mo>⋯</mo><mo>,</mo><msub><mrow><mi>n</mi></mrow><mrow><mi mathvariant="normal">E</mi></mrow></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078718&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078704&type= 71.28932953 17.01799965 式中， <math id="M31"><mi mathvariant="normal">Δ</mi><mo>∇</mo><msub><mrow><msubsup><mrow><mi>b</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">G</mi><mn mathvariant="normal">01</mn><msub><mrow><mi>s</mi></mrow><mrow><mi>l</mi></mrow></msub></mrow></msubsup></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078707&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078705&type= 13.03866673 4.74133301 、 <math id="M32"><mi mathvariant="normal">Δ</mi><mo>∇</mo><msub><mrow><msubsup><mrow><mi>b</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">C</mi><mn mathvariant="normal">12</mn><msub><mrow><mi>s</mi></mrow><mrow><mi>l</mi></mrow></msub></mrow></msubsup></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078723&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078721&type= 12.95400047 4.74133301 、 <math id="M33"><mi mathvariant="normal">Δ</mi><mo>∇</mo><msub><mrow><msubsup><mrow><mi>b</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">E</mi><mn mathvariant="normal">01</mn><msub><mrow><mi>s</mi></mrow><mrow><mi>l</mi></mrow></msub></mrow></msubsup></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078712&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078724&type= 12.86933327 4.74133301 分别为以G01、C12、E01为基准星的接收机伪距偏差； <math id="M34"><mi>l</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078728&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078727&type= 1.26999998 2.79399991 为卫星编号； <math id="M35"><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">G</mi><mn mathvariant="normal">01</mn><msub><mrow><mi>s</mi></mrow><mrow><mi>l</mi></mrow></msub></mrow></msubsup><msub><mrow><mo stretchy="false">(</mo><mi>k</mi><mo stretchy="false">)</mo></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078731&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078729&type= 18.20333290 4.82600021 、 <math id="M36"><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">C</mi><mn mathvariant="normal">12</mn><msub><mrow><mi>s</mi></mrow><mrow><mi>l</mi></mrow></msub></mrow></msubsup><msub><mrow><mo stretchy="false">(</mo><mi>k</mi><mo stretchy="false">)</mo></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078749&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078748&type= 18.11866570 4.82600021 、 <math id="M37"><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">E</mi><mn mathvariant="normal">01</mn><msub><mrow><mi>s</mi></mrow><mrow><mi>l</mi></mrow></msub></mrow></msubsup><msub><mrow><mo stretchy="false">(</mo><mi>k</mi><mo stretchy="false">)</mo></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078752&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078735&type= 18.03400040 4.82600021 分别为以G01、C12、E01作为基准星的双差伪距观测值； <math id="M38"><msub><mrow><mi>n</mi></mrow><mrow><mi mathvariant="normal">G</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078755&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078753&type= 3.55599999 3.72533321 、 <math id="M39"><msub><mrow><mi>n</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078741&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078759&type= 3.47133350 3.72533321 、 <math id="M40"><msub><mrow><mi>n</mi></mrow><mrow><mi mathvariant="normal">E</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078761&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078743&type= 3.38666677 3.72533321 分别为GPS、BDS、Galileo的卫星数。若卫星 <math id="M41"><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078892&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078873&type= 2.45533323 3.72533321 和基准星 <math id="M42"><msub><mrow><mi>s</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">f</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078839&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078822&type= 3.64066648 3.72533321 共视，则卫星 <math id="M43"><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078892&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078873&type= 2.45533323 3.72533321 的接收机伪距偏差可由式（4）式（4）求得；若卫星 <math id="M44"><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078890&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078887&type= 2.45533323 3.72533321 不与基准星 <math id="M45"><msub><mrow><mi>s</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">f</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078787&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078776&type= 3.64066648 3.72533321 共视但与 <math id="M46"><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078892&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078873&type= 2.45533323 3.72533321 共视，则卫星 <math id="M47"><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078890&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078887&type= 2.45533323 3.72533321 相对基准星 <math id="M48"><msub><mrow><mi>s</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">f</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078839&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078822&type= 3.64066648 3.72533321 的接收机伪距偏差 <math id="M49"><mi mathvariant="normal">Δ</mi><mo>∇</mo><msub><mrow><msubsup><mrow><mi>b</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">f</mi></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078806&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078809&type= 12.10733318 4.74133301 为： <math display="block" id="M50"><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">Δ</mi><mo>∇</mo><msub><mrow><msubsup><mrow><mi>b</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">f</mi></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mi mathvariant="normal">Δ</mi><mo>∇</mo><msub><mrow><msubsup><mrow><mi>b</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">f</mi></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msubsup></mrow><mrow><mi>i</mi></mrow></msub><mo>+</mo><mi mathvariant="normal">Δ</mi><mo>∇</mo><msub><mrow><msubsup><mrow><mi>b</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo></mtd></mtr><mtr><mtd><mtext> </mtext><mi>E</mi><mo stretchy="false">{</mo><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">f</mi></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msubsup><msub><mrow><mo stretchy="false">(</mo><mi>k</mi><mo stretchy="false">)</mo></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">}</mo><mo>+</mo><mi>E</mi><mo stretchy="false">{</mo><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup><msub><mrow><mo stretchy="false">(</mo><mi>k</mi><mo stretchy="false">)</mo></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">}</mo></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078824&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078807&type= 61.29866791 10.49866676 式中， <math id="M51"><mi mathvariant="normal">Δ</mi><mo>∇</mo><msub><mrow><msubsup><mrow><mi>b</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">f</mi></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msubsup></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078818&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078816&type= 12.10733318 4.74133301 为卫星 <math id="M52"><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078892&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078873&type= 2.45533323 3.72533321 相对基准星 <math id="M53"><msub><mrow><mi>s</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">f</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078839&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078822&type= 3.64066648 3.72533321 的接收机伪距偏差； <math id="M54"><mi mathvariant="normal">Δ</mi><mo>∇</mo><msub><mrow><msubsup><mrow><mi>b</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078835&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078840&type= 11.59933376 4.74133301 为卫星 <math id="M55"><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078890&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078887&type= 2.45533323 3.72533321 相对卫星 <math id="M56"><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078892&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078873&type= 2.45533323 3.72533321 的接收机伪距偏差； <math id="M57"><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">f</mi></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msubsup><msub><mrow><mo stretchy="false">(</mo><mi>k</mi><mo stretchy="false">)</mo></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078850&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078857&type= 17.27199936 4.82600021 为卫星 <math id="M58"><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078892&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078873&type= 2.45533323 3.72533321 相对基准星 <math id="M59"><msub><mrow><mi>s</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">f</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078866&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078864&type= 3.64066648 3.72533321 的双差伪距观测值； <math id="M60"><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup><msub><mrow><mo stretchy="false">(</mo><mi>k</mi><mo stretchy="false">)</mo></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078871&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078867&type= 16.76399994 4.82600021 为卫星 <math id="M61"><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078890&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078887&type= 2.45533323 3.72533321 相对卫星 <math id="M62"><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078892&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078873&type= 2.45533323 3.72533321 的双差伪距观测值。 2　数据说明 1 本文数据采用多GNSS实验（the multi-GNSS experiment，MGEX）全球跟踪网16个测站构成的9条零/短基线，时间跨度为2019年年积日第300—360天，数据采样间隔为30 s。为了削弱多路径误差影响，卫星截止高度角取30°。对于BDS，因地球同步轨道（geostationary Earth orbit，GEO）卫星轨道精度较差，本文暂不考虑。根据接收机的生产厂商和型号将基线分为3组：相同厂商且相同型号接收机组（第1组）、不同厂商接收机组（第2组）、相同厂商但不同型号接收机组（第3组），详细信息见表1 表1 。此外，对于GPS的L1、L2、L5频点，本文使用的观测值类型分别为C1C、C2W、C5Q/C5X；对于BDS的B1I、B2I、B3I频点，本文使用的观测值类型分别为C2I、C7I、C6I；对于Galileo的E1、E5a、E5b频点，本文使用的观测值类型分别为C1C/C1X、C5Q/C5X、C7Q/C7X。分组基线接收机1 接收机2 长度/m 3 1 MAT1_MATE Leica Gr30 Leica Gr30 10.7 USN7_USN8 Sept Polarx5tr Sept Polarx5tr 0 ZIM2_ZIM3 Trimble Netr9 Trimble Netr9 0 3 2 WTZR_WTZZ Leica Gr50 Javad Tre_3 1.6 CHPI_CHPG Sept Polarx5 Trimble Netr9 1 850.5 STR1_STR2 Sept Polarx5tr Trimble Netr9 70.3 3 3 MAT1_MATG Leica Gr30 Leica Gr10 9.6 WTZ3_WTZZ Javad Tre_G3th Javad Tre_3 67.1 YAR2_YAR3 Sept Polarx4tr Sept Polarx5 18.2 3　接收机伪距偏差分析 1 3.1　相同厂商相同型号接收机伪距偏差 2 以基线USN7_USN8为例，GPS、BDS和Galileo的接收机伪距偏差分别如图 1 1 （a）~ 1 1 （c）所示。由图1 图1 可知，3系统的伪距偏差分别不超过7.5、8.5、5.0 cm，其中GPS L2频点伪距偏差明显小于L1和L5频点；BDS B3I频点伪距偏差最小，B1I频点伪距偏差最大；而Galileo不同频点的伪距偏差量级几乎一致。值得注意的是，图1 图1 中部分卫星和频点观测数据缺失，因为对于GPS，测试期间G04和G18处于非健康状态，且仅Block II-F和Block III-A卫星提供L5频点信号；对于BDS-2，基线USN7_USN8位于美国，无法接收到倾斜同步轨道（inclined geosynchronous orbit，IGSO）卫星信号；对于BDS-3，由于测试期间接收机固件未升级，无法接收C37以上卫星信号，且BDS-3不提供B2I频点信号。本文用相同频点接收机伪距偏差的最大值与最小值之差表示该频点的最大伪距偏差。相同厂商且相同型号接收机组成的3条基线MAT1_MATE、USN7_USN8、ZIM2_ZIM3在各频点的最大伪距偏差分别如图 2 2 （a）~ 2 2 （c）所示。从图2 图2 中可以看出，各系统各频点的接收机最大伪距偏差值较小，均不超过25 cm，这可能是由于相同厂商相同型号的接收机硬件配置差异不大，测量的伪距一致性较好。 3.2　不同厂商接收机伪距偏差分析 2 以基线STR1_STR2为例，各系统接收机伪距偏差如图3 图3 所示。GPS L5频点的伪距偏差整体稍大于L1频点，最大可达80 cm，L2频点伪距偏差最小，不超过15 cm。对于BDS，B1I频点伪距偏差明显大于B2I和B3I，最大可达160 cm。值得注意的是，BDS-3卫星的B1I频点伪距偏差明显大于BDS-2，且接收机伪距偏差符号表现出系统性，这可能是由BDS-3和BDS-2卫星间的系统性偏差所引起［ 27 27 - 28 28 27-28 ］。对于Galileo，接收机伪距偏差整体上小于GPS和BDS，其中E1频点伪距偏差稍大于E5a和E5b频点，最大值约为31 cm，表明不同类型接收机间的Galileo伪距一致性优于GPS和BDS。为了分析接收机伪距偏差的稳定性，以STR1_STR2为例，GPS、BDS、Galileo典型卫星的L1、B1I、E1频点伪距偏差时间序列见图4 图4 。可以看出，伪距偏差时间序列较为平稳，未见明显的趋势性变化。图5 图5 给出了STR1_STR2两个月的伪距偏差标准差（standard deviation， STD），由图5 图5 可知，GPS和Galileo各频点接收机伪距偏差STD均不超过10 cm，BDS除C23和C24卫星在B1I频点的STD达12 cm，其余卫星各频点的STD同样不超过10 cm。上述结果表明，接收机伪距偏差具有较好的稳定性。图 6 6 （a）~ 6 6 （c）分别为基线WTZR_WTZZ、CHPI_CHPG、STR1_STR2各频点的最大伪距偏差。可以看出，3条基线中B1I频点伪距偏差最大，可达180 cm；L5频点最大伪距偏差仅次于B1I频点，最大约为100 cm；L1频点最大伪距偏差低于B1I和L5频点，但高于其他频点，最大值约为60 cm；E5a频点伪距偏差最小，最大不超过25 cm。Galileo最大伪距偏差总体上优于GPS和BDS。由于图6 图6 中不同厂商的接收机采用了不同的相关器间隔和前端带宽设计，其接收机伪距偏差明显大于图2 图2 中相同厂商相同型号接收机的伪距偏差。 3.3　相同厂商不同型号接收机伪距偏差分析 2 以MAT1_MATE为例，各系统接收机伪距偏差如图7 图7 所示。GPS各频点伪距偏差量级相近，除G32号卫星的L5频点伪距偏差达到34 cm，其余卫星各频点均不超过20 cm。BDS B1I频点伪距偏差明显大于B2I，最大值可达35 cm，由于接收机无法接收到B3I频点信号，造成该频点数据缺失。Galileo各频点伪距偏差均低于20 cm，低于GPS和BDS。伪距偏差STD如图8 图8 所示，所有系统各频点均不超过10 cm，表明伪距偏差具有良好的稳定性。图9 图9 给出了基线MAT1_MATE、WTZ3_WTZZ、YAR2_YAR3在各频点的最大伪距偏差。可以看出，3条基线各频点的最大伪距偏差值均不超过90 cm，其量级低于图6 图6 中不同厂商接收机的伪距偏差但高于图2 图2 中相同厂商相同型号接收机的伪距偏差。对于基线MAT1_MATE、YAR2_YAR3，B1I频点伪距偏差最大，L5频点次之。需要说明的是，基线MAT1_MATE无法接收到B3I频点信号；基线WTZ3_WTZZ的测站WTZ3无法接收到BDS信号和Galileo E5b频点信号；基线YAR2_YAR3的测站YAR2无法接收到Galileo E01卫星信号，因此造成了相应的结果缺失。 4　接收机伪距偏差对定位影响 1 由§3.2可知接收机伪距偏差在不同厂商的接收机间可达1.6 m，对基于伪距观测值的精密定位的影响无法忽略。因此，本节研究接收机伪距偏差对双差模糊度固定以及伪距相对定位的影响。 4.1　伪距偏差对宽巷模糊度固定的影响 2 基于双频伪距和载波相位观测值的MW（Melbourne-Wübbena）组合通常应用于宽巷模糊度解算，计算公式为［ 11 11 ］： <math display="block" id="M63"><mtable columnalign="left"><mtr><mtd><msubsup><mrow><mi>M</mi></mrow><mrow><mi>r</mi></mrow><mrow><mi>s</mi></mrow></msubsup><mo>=</mo><mfenced separators="|"><mrow><mfrac><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac><mo>-</mo><mfrac><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfrac></mrow></mfenced><mo>-</mo><mfenced separators="|"><mrow><mfrac><mrow><msub><mrow><mi>f</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>f</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mo stretchy="false">(</mo><msub><mrow><mi>f</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>f</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><msub><mrow><mi>λ</mi></mrow><mrow><mi>w</mi></mrow></msub></mrow></mfrac></mrow></mfenced><mo>=</mo></mtd></mtr><mtr><mtd><mo stretchy="false">(</mo><msubsup><mrow><mi>N</mi></mrow><mrow><mi>r</mi><mo>,</mo><mi>M</mi></mrow><mrow><mi>s</mi></mrow></msubsup><mo>+</mo><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>r</mi><mo>,</mo><mi>M</mi></mrow></msub><mo>-</mo><msubsup><mrow><mi>ϕ</mi></mrow><mrow><mi>M</mi></mrow><mrow><mi>s</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>+</mo><msubsup><mrow><mi>B</mi></mrow><mrow><mi>r</mi><mo>,</mo><mi>M</mi></mrow><mrow><mi>s</mi></mrow></msubsup></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078971&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078968&type= 56.64199829 17.10266685 式中， <math id="M64"><msubsup><mrow><mi>M</mi></mrow><mrow><mi>r</mi></mrow><mrow><mi>s</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078991&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078986&type= 4.91066647 3.97933316 为MW组合观测值， <math id="M65"><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079005&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078995&type= 3.64066648 3.72533321 、 <math id="M66"><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079009&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45078998&type= 3.64066648 3.72533321 分别为频点1、2的载波相位观测值； <math id="M67"><msub><mrow><mi>λ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079018&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079013&type= 2.96333337 3.72533321 、 <math id="M68"><msub><mrow><mi>λ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079025&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079015&type= 2.96333337 3.72533321 分别为频点1、2的波长； <math id="M69"><msub><mrow><mi>f</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079036&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079034&type= 2.96333337 4.57200003 、 <math id="M70"><msub><mrow><mi>f</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079029&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079027&type= 2.96333337 4.57200003 分别为频点1、2的信号频率； <math id="M71"><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079048&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079030&type= 3.72533321 3.72533321 、 <math id="M72"><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079051&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079049&type= 3.72533321 3.72533321 为分别为频点1、2的伪距观测值； <math id="M73"><msub><mrow><mi>λ</mi></mrow><mrow><mi>w</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079055&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079043&type= 3.47133350 3.72533321 为宽巷波长； <math id="M74"><msubsup><mrow><mi>N</mi></mrow><mrow><mi>r</mi><mo>,</mo><mi>M</mi></mrow><mrow><mi>s</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079058&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079046&type= 6.68866634 4.06400013 为具有整周特性的宽巷模糊度； <math id="M75"><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>r</mi><mo>,</mo><mi>M</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079078&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079060&type= 5.92666674 4.57200003 和 <math id="M76"><msubsup><mrow><mi>ϕ</mi></mrow><mrow><mi>M</mi></mrow><mrow><mi>s</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079067&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079080&type= 4.14866638 4.82600021 分别为与接收机和卫星相关的相位硬件延迟； <math id="M77"><msubsup><mrow><mi>B</mi></mrow><mrow><mi>r</mi><mo>,</mo><mi>M</mi></mrow><mrow><mi>s</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079087&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079069&type= 6.26533365 3.97933316 为接收机伪距偏差对MW组合的影响。根据式（6）式（6），构造双差形式的MW组合，计算公式为： <math display="block" id="M78"><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>M</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup><mo>=</mo><mfenced separators="|"><mrow><mfrac><mrow><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>L</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mn mathvariant="normal">1</mn></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup></mrow><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac><mo>-</mo><mfrac><mrow><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>L</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mn mathvariant="normal">2</mn></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup></mrow><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfrac><mo>-</mo><mfrac><mrow><msub><mrow><mi>f</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mi mathvariant="normal">Δ</mi><mo>∇</mo><msub><mrow><msubsup><mrow><mi>P</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>f</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mi mathvariant="normal">Δ</mi><mo>∇</mo><msub><mrow><msubsup><mrow><mi>P</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mo stretchy="false">(</mo><msub><mrow><mi>f</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>f</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><msub><mrow><mi>λ</mi></mrow><mrow><mi>w</mi></mrow></msub></mrow></mfrac></mrow></mfenced><mo>+</mo><mfrac><mrow><msub><mrow><mi>f</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>b</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mn mathvariant="normal">1</mn></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup><mo>+</mo><msub><mrow><mi>f</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>b</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mn mathvariant="normal">2</mn></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup></mrow><mrow><mo stretchy="false">(</mo><msub><mrow><mi>f</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>f</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><msub><mrow><mi>λ</mi></mrow><mrow><mi>w</mi></mrow></msub></mrow></mfrac><mo>=</mo><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>N</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup><mo>+</mo><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>B</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079073&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079089&type= 153.16200256 16.08666801 <math display="block" id="M79"><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>B</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup><mo>=</mo><mfrac><mrow><msub><mrow><mi>f</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mi mathvariant="normal">Δ</mi><mo>∇</mo><msub><mrow><msubsup><mrow><mi>b</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>f</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mi mathvariant="normal">Δ</mi><mo>∇</mo><msub><mrow><msubsup><mrow><mi>b</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mo stretchy="false">(</mo><msub><mrow><mi>f</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>f</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><msub><mrow><mi>λ</mi></mrow><mrow><mi>w</mi></mrow></msub></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079093&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079076&type= 50.54600143 9.31333351 式中， <math id="M80"><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>M</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079108&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079096&type= 12.27666664 3.80999994 为双差MW组合观测值； <math id="M81"><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>L</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mn mathvariant="normal">1</mn></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079112&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079109&type= 12.02266598 3.80999994 、 <math id="M82"><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>L</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mn mathvariant="normal">2</mn></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079100&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079114&type= 12.10733318 3.80999994 分别为频点1、2的双差载波相位观测值； <math id="M83"><mi mathvariant="normal">Δ</mi><mo>∇</mo><msub><mrow><msubsup><mrow><mi>P</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079119&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079117&type= 12.61533356 4.74133301 、 <math id="M84"><mi mathvariant="normal">Δ</mi><mo>∇</mo><msub><mrow><msubsup><mrow><mi>P</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079122&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079106&type= 12.61533356 4.74133301 分别为频点1、2的双差伪距观测值； <math id="M85"><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>b</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mn mathvariant="normal">1</mn></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079141&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079138&type= 11.51466751 3.80999994 、 <math id="M86"><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>b</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mn mathvariant="normal">2</mn></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079146&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=45079129&type= 11.59933376 3.80999994 分别为频点1、2的双差接收机伪距偏差； <math id="M87"><mi mathvariant="normal">Δ</mi><mo>∇</mo><msubsup><mrow><mi>N</mi></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn 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为双差接收机伪距偏差对双差MW组合的影响。由式（7）式（7）、式（8）式（8）可知，与接收机和卫星相关的非整周相位硬件延迟可通过双差消除，而接收机伪距偏差对MW组合的影响无法通过双差消除，需要进行接收机伪距偏差改正以削弱其影响。选取GPS L1、L2频点，Galileo E1、E5a频点以及BDS B1I、B3I频点构造MW组合，并研究接收机伪距偏差对宽巷模糊度解算的影响。以基线USN7_USN8、WTZR_WTZZ、WTZ3_WTZZ为例，统计伪距偏差改正前/后GPS双差宽巷模糊度非整周部分在各区间的百分比，如图10 图10 所示。可以看出，基线USN7_USN8的非整周部分均方根（root mean square， RMS）明显小于基线WTZR_WTZZ、WTZ3_WTZZ的，这是由于基线USN7_USN8的接收机为相同厂商相同型号，接收机伪距偏差量级及其对双差宽巷模糊度解算的影响较小。此外，对于部分误差（如多路径误差、几何距离误差等），短基线的消除或削弱程度不如零基线。伪距偏差改正后，3条基线宽巷模糊度非整周部分的正态分布特性更加显著，RMS值分别从0.039、0.200、0.159 周降低到0.028、0.146、0.100 周，分别降低了22%、27%、37%。基于相同方法统计了伪距偏差改正前后GPS、BDS、Galileo双差MW组合的宽巷模糊度非整周部分RMS，结果见表2 表2 。由表2 表2 可知，伪距偏差改正后，GPS、BDS、Galileo非整周部分RMS分别从0.092、0.170、0.065 周减小到0.076、0.123、0.056 周，分别降低了17%、22%、14%。 3 系统 4 第1组 4 第2组 4 第3组 2 ZIM2_ZIM3 2 USN7_USN8 2 WTZR_WTZZ 2 CHPI_CHPG 2 WTZ3_WTZZ 2 YAR2_YAR3 改正前改正后改正前改正后改正前改正后改正前改正后改正前改正后改正前改正后 BDS 0.250 0.220 0.140 0.080 GPS 0.029 0.014 0.039 0.028 0.200 0.146 0.140 0.130 0.159 0.100 0.080 0.078 Galileo 0.023 0.009 0.044 0.026 0.120 0.090 0.088 0.083 0.111 0.096 4.2　伪距偏差对伪距相对定位的影响 2 选取2019年年积日第300、330、359天的数据，以基线STR1_STR2为例，图11 图11 给出了接收机伪距偏差改正前后的GPS、BDS、Galileo的L1、B1I、 E5a频点伪距相对定位误差时间序列图。由图11 图11 可知，伪距偏差改正后3系统的相对定位精度在东（east，E）、北（north， N）、天（up， U）方向均有所提高，GPS和Galileo的三维定位误差RMS分别从142.0、97.5 cm下降到137.1、93.2 cm。由于BDS在基线STR1_STR2的接收机伪距偏差比GPS和Galileo的量级大，因此定位精度的提高幅度更大，E、N、U方向的定位误差RMS分别从0.826、0.836、1.472 m下降到0.607、0.647、1.272 m，定位精度分别提高27%、38%、13%。接收机伪距偏差改正前后的表1 表1 中每组2条基线伪距相对定位三维误差统计结果见表３表３。可以看出，偏差改正后，相对定位精度整体上均有所提高，其中基线USN7_USN8的三维定位误差在改正前后变化不大，其原因是USN7_USN8的各系统伪距偏差量级较小。总体上，接收机伪距偏差改正后，相同厂商相同型号接收机、不同厂商接收机、相同厂商不同型号接收机的平均三维定位误差分别从56.6、84.7、89.8 cm降低到54.4、76.8、84.9 cm；GPS、BDS、Galileo的平均三维定位误差分别从84.4、77.3、60.0 cm下降到了80.1、72.1、57.0 cm。 3 系统 4 第1组 4 第2组 4 第3组 2 ZIM2_ZIM3 2 USN7_USN8 2 WTZR_WTZZ 2 CHPI_CHPG 2 WTZ3_WTZZ 2 YAR2_YAR3 改正前改正后改正前改正后改正前改正后改正前改正后改正前改正后改正前改正后 BDS 53.1 50.8 73.1 73.1 92.1 80.0 90.9 84.4 GPS 43.3 41.6 76.9 75.2 78.4 70.1 94.7 91.4 150.0 145.2 60.3 56.6 Galileo 25.1 23.4 65.3 62.5 70.2 62.1 88.2 80.6 57.8 53.5 5　结语 1 本文基于并置接收机双差法确定了GPS、BDS、Galileo的接收机伪距偏差，并按照接收机厂商和型号分为3组基线：相同厂商相同型号接收机、不同厂商接收机、相同厂商不同型号接收机，分别对其伪距偏差特性进行了分析。结果显示，相同厂商相同型号接收机伪距偏差最小，所有系统各频点伪距偏差均不超过10 cm；相同厂商不同型号接收机其次，偏差值最大约45 cm；不同厂商接收机伪距偏差最大，BDS B1I频点可达160 cm，表明接收机伪距偏差与其硬件配置（如相关器间隔、前端带宽设计等）有关。3个系统中，Galileo接收机伪距偏差明显小于GPS和BDS，各系统的伪距偏差具有良好的稳定性，60 d内的STD不超过12 cm。本文还研究了接收机伪距偏差对双差宽巷模糊度解算和伪距相对定位的影响。伪距偏差改正后，GPS、BDS、Galileo双差MW组合宽巷模糊度非整周部分RMS分别从0.092、0.170、0.065周降低到0.076、0.123、0.056 周，分别降低17%、22%、14%；对伪距相对定位的影响与伪距偏差的量级相关，偏差改正后GPS、BDS、Galileo的平均三维定位误差分别从84.4、77.3、60.0 cm下降到了80.1、72.1、57.0 cm。本文采用的伪距偏差确定方法是基于并置接收机的双差法，结果表明伪距偏差对模糊度解算和相对定位精度有重要影响。由于双差法要求测站分布为零基线或者短基线，因此在后续工作中将使用非差估计方法标定接收机伪距偏差，根据接收机类型发布接收机伪距偏差改正产品，这对多模GNSS精密数据处理有重要意义。此外，下一步将以BDS-3新体制信号的接收机伪距偏差以及BDS-2和BDS-3之间的系统性偏差为重点开展研究工作。参考文献 Montenbruck O . 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Improving BDS-2 and BDS-3 Joint Precise Point Positioning with Time Delay Bias Estimation 10.13203/j.whugis20210276 P228 A 1671-8860（2023）07-1134-12 耿涛,李钟兴,谢新，等.GNSS接收机伪距偏差确定方法及其对定位的影响[J].武汉大学学报（信息科学版）,2023,48(7):1134-1145.DOI: 10.13203/j.whugis20210276 http://dx.doi.org/10.13203/j.whugis20210276 耿涛,李钟兴,谢新，等.GNSS接收机伪距偏差确定方法及其对定位的影响[J].武汉大学学报（信息科学版）,2023,48(7):1134-1145.DOI:10.13203/j.whugis20210276 GENG Tao,LI Zhongxing,XIE Xin,et al.GNSS Receiver-Related Pseudorange Bias Determination Method and Its Effect on Positioning[J].Geomatics and Information Science of Wuhan University,2023,48(7):1134-1145.DOI: 10.13203/j.whugis20210276 http://dx.doi.org/10.13203/j.whugis20210276 GENG Tao,LI Zhongxing,XIE Xin,et al.GNSS Receiver-Related Pseudorange Bias Determination Method and Its Effect on Positioning[J].Geomatics and Information Science of Wuhan University,2023,48(7):1134-1145.DOI:10.13203/j.whugis20210276 国家自然科学基金（41974036）；湖北省自然科学基金（2019CFA051）；中央高校基本科研业务费专项资金（2042021kf0062）；中国博士后科学基金（2020M682482）。 2021-09-06 2023-07-05 2023-06-29 39072392 武汉大学学报（信息科学版） 7 48

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GNSS Receiver-Related Pseudorange Bias Determination Method and Its Effect on Positioning

DOI：10.13203/j.whugis20210276