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Volume 47 Issue 9
Sep.  2022
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LI Haodong, ZHAO Qile, TAO Jun, LONG Yuhao. FCB Estimation and Ambiguity Resolution of BDS-3[J]. Geomatics and Information Science of Wuhan University, 2022, 47(9): 1439-1446. doi: 10.13203/j.whugis20200168
 Citation: LI Haodong, ZHAO Qile, TAO Jun, LONG Yuhao. FCB Estimation and Ambiguity Resolution of BDS-3[J]. Geomatics and Information Science of Wuhan University, 2022, 47(9): 1439-1446.

# FCB Estimation and Ambiguity Resolution of BDS-3

##### doi: 10.13203/j.whugis20200168
Funds:

The National Key Research and Development Program of China 2017YFB0503400

the National Natural Science Foundation of China 41774035

the National Natural Science Foundation of China 41674004

• Author Bio:

LI Haodong, master, mainly engaged in precise GNSS positioning technology. E-mail: haodongli@whu.edu.cn

• Corresponding author: TAO Jun, PhD candidate. E-mail: jtaowhu@whu.edu.cn
• Publish Date: 2022-09-05
•   Objectives  Precise point positioning (PPP) combines the advantages of standard point position‍ing (SPP) and relative positioning, which can achieve centimeter level positioning. With the development of BeiDou satellite navigation system (BDS), more and more BDS satellites begin to provide global positioning, navigation and timing services, which also promotes the development of multi-frequency and multi-system PPP. For a long time, because of the atmospheric delay and hardware delay of satellite and receiver, the ambiguity of PPP is not an integer. PPP needs a long time to converge, which greatly lim‍its its application.The ambiguity can be restored to integer and the convergence time can be shortened with the help of fractional cycle bias (FCB).  Methods  In order to improve the effect of precise point positioning-ambiguity resolution (PPP-AR) of BDS as a whole, we estimate the FCBs of GPS and BDS based on the observation data from August 1 to August 31 in 2020 of globally distributed stations. The single difference between satellites is used to eliminate the influence of hardware delay at the receivers, and the single differ‍ence ambiguity vector is solved by the whole network adjustment to obtain the FCB estimation of each satellite.  Results  The results of the time series of BDS-3 wide lane (WL) and narrow lane (NL) FCBs show that the WL FCBs has long-term stability, the change of BDS-3 WL FCBs in 31 days is less than 0.2 weeks, and the change of GPS WL FCBs is less than 0.1 weeks. The FCBs of BDS-3 NL can keep stable for a period of time, and the change is less than 0.1 weeks. The percentages of GPS WL and NL FCBs residuals within 0.15 weeks are 99.8% and 99.3% respectively, and the percentages of BDS-3 are 99.7% and 98.1% respectively. In order to reflect the improvement effect of FCBs on PPP, static and dynamic PPP-AR tests were carried out at 8 stations around the world. The results show that under the static condition, the average fixed time and convergence time of BDS-3 are 31.5 min and 24.9 min respectively, which is 24.8% shorter than the float PPP. The errors in E, N and U directions are 1.03 cm, 0.60 cm and 1.72 ‍cm respectively, and the fixed rate is 89.8%. Under the dynamic condition, the average fixed time and convergence time of BDS-3 are 33.3 min and 50.7 min respectively, which is 17.4% shorter than the float PPP. The errors in E, N and U directions are 2.57 cm, 2.29 cm and 3.71 cm respectively, and the fixed rate is 83.9%.  Conclusions  PPP-AR can shorten the convergence time of PPP to a certain extent, but the improvement of positioning accuracy is not obvious after complete convergence. BDS-3 FCBs stability is lim‍it‍ed by precision products and observation data, and its PPP-AR is slightly worse than GPS.
•  [1] Zumberge J F, Heflin M B, Jefferson D C, et al. Precise Point Positioning for the Efficient and Robust Analysis of GPS Data from Large Networks[J]. Journal of Geophysical Research: Solid Earth, 1997, 102(B3): 5005-5017 [2] Geng J H, Shi C, Ge M R, et al. Improving the Estimation of Fractional-Cycle Biases for Ambiguity Resolution in Precise Point Positioning[J]. Journal of Geodesy, 2012, 86(8): 579-589 [3] 张辉, 郝金明, 刘伟平, 等. 估计接收机差分码偏差的GPS/BDS非组合精密单点定位模型[J]. 武汉大学学报·信息科学版, 2019, 44(4): 495-500 Zhang Hui, Hao Jinming, Liu Weiping, et al. GPS/ BDS Precise Point Positioning Model with Receiver DCB Parameters for Raw Observations[J]. Geomatics and Information Science of Wuhan University, 2019, 44(4): 495-500 [4] Montenbruck O, Steigenberger P, Prange L, et al. The Multi-GNSS Experiment(MGEX)of the International GNSS Service(IGS): Achievements, Prospects and Challenges[J]. Advances in Space Research, 2017, 59(7): 1671-1697 [5] 赵昂, 杨元喜, 许扬胤, 等. GNSS单系统及多系统组合完好性分析[J]. 武汉大学学报·信息科学版, 2020, 45(1): 72-80 Zhao Ang, Yang Yuanxi, Xu Yangyin, et al. Integrity Analysis of GNSS Single System and Multi-System Combination[J]. Geomatics and Information Science of Wuhan University, 2020, 45(1): 72-80 [6] Shi C, Zhao Q L, Hu Z G, et al. Precise Relative Positioning Using Real Tracking Data from COM PASS GEO and IGSO Satellites[J]. GPS Solutions, 2013, 17(1): 103-119 [7] 何义磊. 北斗三号最简系统卫星信号质量分析[J]. 武汉大学学报·信息科学版, 2020, 45 (3): 394-402 He Yilei. Quality Analysis of Satellite Signal for BDS-3 Simplest System[J]. Geomatics and Information Science of Wuhan University, 2020, 45(3): 394-402 [8] Li X X, Zhang X H. Improving the Estimation of Uncalibrated Fractional Phase Offsets for PPP Ambiguity Resolution[J]. Journal of Navigation, 2012, 65(3): 513-529 [9] Li P, Zhang X H, Guo F. Ambiguity Resolved Precise Point Positioning with GPS and BeiDou[J]. Journal of Geodesy, 2017, 91(1): 25-40 [10] Ge M, Gendt G, Rothacher M, et al. Resolution of GPS Carrier-Phase Ambiguities in Precise Point Positioning(PPP)with Daily Observations[J]. Journal of Geodesy, 2008, 82(7): 389-399 [11] Laurichesse D, Mercier F, Berthias J P, et al. Integer Ambiguity Resolution on Undifferenced GPS Phase Measurements and Its Application to PPP and Satellite Precise Orbit Determination[J]. Navigation, 2009, 56(2): 135-149 [12] Collins P, Bisnath S, Lahaye F, et al. Undifferenced GPS Ambiguity Resolution Using the Decoupled Clock Model and Ambiguity Datum Fixing [J]. Navigation, 2010, 57(2): 123-135 [13] Geng J H, Meng X L, Dodson A H, et al. Integer Ambiguity Resolution in Precise Point Positioning: Method Comparison[J]. Journal of Geodesy, 2010, 84(9): 569-581 [14] Shi J B, Gao Y. A Comparison of Three PPP Integer Ambiguity Resolution Methods[J]. GPS Solutions, 2014, 18(4): 519-528 [15] Zhang X H, Wu M K, Liu W K, et al. Initial Assessment of the COMPASS/BeiDou-3: New-Generation Navigation Signals[J]. Journal of Geodesy, 2017, 91(10): 1225-1240 [16] Wanninger L, Beer S. BeiDou Satellite-Induced Code Pseudorange Variations: Diagnosis and Therapy[J]. GPS Solutions, 2015, 19(4): 639-648 [17] 楼益栋, 龚晓鹏, 辜声峰, 等. 北斗卫星伪距码偏差特性及其影响分析[J]. 武汉大学学报·信息科学版, 2017, 42(8): 1040-1046 Lou Yidong, Gong Xiaopeng, Gu Shengfeng, et al. The Characteristic and Effect of Code Bias Variations of BeiDou[J]. Geomatics and Information Science of Wuhan University, 2017, 42(8): 1040 1046 [18] Li X X, Li X, Yuan Y Q, et al. Multi-GNSS Phase Delay Estimation and PPP Ambiguity Resolution: GPS, BDS, GLONASS, Galileo[J]. Journal of Geodesy, 2018, 92(6): 579-608 [19] Liu Y Y, Ye S R, Song W W, et al. Estimating the Orbit Error of BeiDou GEO Satellites to Improve the Performance of Multi-GNSS PPP Ambiguity Resolution[J]. GPS Solutions, 2018, 22(3), DOI:org/ 10.1007/s10291-018-0751-9 [20] Qu L Z, Du M Y, Wang J, et al. Precise Point Positioning Ambiguity Resolution by Integrating BDS 3e into BDS-2 and GPS[J]. GPS Solutions, 2019, 23(3), DOI: org/ 10.1007/s10291-019-0854-y [21] Jiang W P, Zhao W, Chen H, et al. Analysis of BDS Fractional Cycle Biases and PPP Ambiguity Resolution[J]. Sensors (Basel, Switzerland), 2019, 19(21), DOI: org/org/ 10.3390/s19214725 [22] Hu J H, Zhang X H, Li P, et al. Multi-GNSS Fractional Cycle Bias Products Generation for GNSS Ambiguity-Fixed PPP at Wuhan University[J]. GPS Solutions, 2019, 24(1), DOI: org/ 10.1007/s10291-019-0929-9
###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

Figures(7)  / Tables(3)

## FCB Estimation and Ambiguity Resolution of BDS-3

##### doi: 10.13203/j.whugis20200168
###### 1. GNSS Research Center, Wuhan University, Wuhan 430079, China2. School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China3. Shanghai Key Laboratory of Space Navigation and Positioning Techniques, Shanghai 200030, China
Funds:

The National Key Research and Development Program of China 2017YFB0503400

the National Natural Science Foundation of China 41774035

the National Natural Science Foundation of China 41674004

• Author Bio:

• ###### Corresponding author:TAO Jun, PhD candidate. E-mail: jtaowhu@whu.edu.cn

Abstract:   Objectives  Precise point positioning (PPP) combines the advantages of standard point position‍ing (SPP) and relative positioning, which can achieve centimeter level positioning. With the development of BeiDou satellite navigation system (BDS), more and more BDS satellites begin to provide global positioning, navigation and timing services, which also promotes the development of multi-frequency and multi-system PPP. For a long time, because of the atmospheric delay and hardware delay of satellite and receiver, the ambiguity of PPP is not an integer. PPP needs a long time to converge, which greatly lim‍its its application.The ambiguity can be restored to integer and the convergence time can be shortened with the help of fractional cycle bias (FCB).  Methods  In order to improve the effect of precise point positioning-ambiguity resolution (PPP-AR) of BDS as a whole, we estimate the FCBs of GPS and BDS based on the observation data from August 1 to August 31 in 2020 of globally distributed stations. The single difference between satellites is used to eliminate the influence of hardware delay at the receivers, and the single differ‍ence ambiguity vector is solved by the whole network adjustment to obtain the FCB estimation of each satellite.  Results  The results of the time series of BDS-3 wide lane (WL) and narrow lane (NL) FCBs show that the WL FCBs has long-term stability, the change of BDS-3 WL FCBs in 31 days is less than 0.2 weeks, and the change of GPS WL FCBs is less than 0.1 weeks. The FCBs of BDS-3 NL can keep stable for a period of time, and the change is less than 0.1 weeks. The percentages of GPS WL and NL FCBs residuals within 0.15 weeks are 99.8% and 99.3% respectively, and the percentages of BDS-3 are 99.7% and 98.1% respectively. In order to reflect the improvement effect of FCBs on PPP, static and dynamic PPP-AR tests were carried out at 8 stations around the world. The results show that under the static condition, the average fixed time and convergence time of BDS-3 are 31.5 min and 24.9 min respectively, which is 24.8% shorter than the float PPP. The errors in E, N and U directions are 1.03 cm, 0.60 cm and 1.72 ‍cm respectively, and the fixed rate is 89.8%. Under the dynamic condition, the average fixed time and convergence time of BDS-3 are 33.3 min and 50.7 min respectively, which is 17.4% shorter than the float PPP. The errors in E, N and U directions are 2.57 cm, 2.29 cm and 3.71 cm respectively, and the fixed rate is 83.9%.  Conclusions  PPP-AR can shorten the convergence time of PPP to a certain extent, but the improvement of positioning accuracy is not obvious after complete convergence. BDS-3 FCBs stability is lim‍it‍ed by precision products and observation data, and its PPP-AR is slightly worse than GPS.

LI Haodong, ZHAO Qile, TAO Jun, LONG Yuhao. FCB Estimation and Ambiguity Resolution of BDS-3[J]. Geomatics and Information Science of Wuhan University, 2022, 47(9): 1439-1446. doi: 10.13203/j.whugis20200168
 Citation: LI Haodong, ZHAO Qile, TAO Jun, LONG Yuhao. FCB Estimation and Ambiguity Resolution of BDS-3[J]. Geomatics and Information Science of Wuhan University, 2022, 47(9): 1439-1446.
• 精密单点定位技术（precise point position‍ing，PPP）融合了单点定位和相对定位的优点，利用单个测站即可实现厘米级的高精度定位[1-3]。近年来，全球导航卫星系统（global navigation satellite system，GNSS）的发展对于提高PPP定位精度、减少PPP收敛时间、扩大PPP应用场景等做出了卓越的贡献[4-5]。北斗卫星导航系统（BeiDou nav‍igation satellite system，BDS）由地球静止轨道卫星（geostationary earth orbit，GEO）、中圆地球轨道卫星（medium earth orbit，MEO）、倾斜地球同步轨道卫星（inclined geosynchronous satellite orbit，IGSO）组成混合星座，已经成为全球GNSS领域的研究热点之一[6-7]。这种独特的星座设计使得北斗卫星在亚太地区可见卫星数明显多于其他地区。随着BDS-3卫星全球组网完成，北斗系统开始提供全球性的定位、导航、授时服务。

PPP需要很长的收敛时间才能达到较高的定位精度，这极大地限制了PPP的应用，而精密单点定位-模糊度固定（precise point position‍ing-ambiguity resolution，PPP-AR）技术可以很好地弥补这个缺陷。众多的研究表明，在卫星端和接收机端都存在着硬件延迟，且难以将它们与模糊度参数分离，导致模糊度参数失去整数特性而无法直接固定[8-9]。将模糊度参数恢复为整数的主要方法包括利用小数周偏差产品（fractional cycle bias，FCB）、钟差去耦模型法及整数钟法[10-12]。有学者通过对3种方法进行对比分析，验证了3种方法在估计FCB时的等价性[13-14]。BDS-2卫星除了硬件延迟外还存在伪距码偏差[15]，这增加了BDS-2卫星PPP模糊度固定的难度。对于IGSO和MEO卫星，伪距码偏差可以通过高度角模型进行削弱或者改正[16]。但GEO卫星由于高度角始终不变，因此无法利用该模型进行改正[17]。GEO卫星精密产品精度较差，一般在估计北斗卫星FCB时都将其与ISGO和MEO分开估计[18-19]。文献[20-21]指出北斗系统GEO卫星和非GEO卫星在某些接收机端存在卫星类型间偏差（inter-satellite-type bias，ISTB），并通过对该偏差的深入研究验证了将GEO卫星与非GEO卫星分开估计FCB方法的合理性。结果表明，利用单北斗PPP-AR可以在静态条件下将收敛时间从56.0 ‍min缩短到43.6 min，动态条件下可以从71.6 min缩短到63.7 min。2019-04-01起，武汉大学测绘学院开始为用户提供GPS、伽利略、北斗、准天顶卫星系统（quasi-zenith satellite system，QZSS）4个系统的宽巷和窄巷FCB产品，其窄巷FCB产品的标准差（standard deviation，STD）分别为0.021、0.021、0.057和0.010周[22]

现有研究对北斗卫星的FCB估计主要集中在BDS-‍2及BDS-2和GPS的组合，本文重点研究BDS-3的FCB的时变特性，并利用该产品进行模糊度固定。

Reference (22)

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