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Volume 47 Issue 9
Sep.  2022
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Article Contents

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. doi: 10.13203/j.whugis20200168

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

More Information
  • 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
  • Received Date: 2021-12-13
  • 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.
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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

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. doi: 10.13203/j.whugis20200168
  • 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。

  • 利用北斗三号卫星伪距和相位观测值构建如下观测方程:

    式中,Pr,isLr,is分别表示接收机r在卫星si个频率上(i=b1/b3)的伪距和相位观测值;ρrs是卫星和接收机之间的几何距离;dtrdts分别为接收机钟差和卫星钟差,Trs是卫星和接收机之间的对流层延迟;Ir,is是频率i上的电离层延迟;br,ibis分别是接收机端和卫星端在频率i上的伪距硬件延迟;Br,iBis分别为接收机端和卫星端在频率i上的相位硬件延迟;λiNr,is分别为第i个频率的波长和整周模糊度;er,isεr,is分别为频率i上的伪距和相位观测值噪声。为了消除电离层的影响,通常会利用BDS-3卫星b1b3频段观测值构建非差无电离层组合观测值(ionospheric-free,IF):

    式中,br,IFbr,IFs分别表示BDS-3卫星无电离层组合伪距观测值在接收机端和卫星端的的硬件延迟;Br,IFBr,IFs分别表示BDS-3卫星无电离层组合相位观测值在接收机端和卫星端的硬件延迟;λIF表示无电离层组合观测值的波长;Nr,IFs表示无电离层组合观测值的整周模糊度;er,IFsεr,IFs分别表示无电离层组合观测值的伪距和相位噪声。在PPP模糊度固定过程中,通常把无电离层组合观测值的浮点型模糊度分解为整数型的宽巷(wide-lane,WL)模糊度和浮点型的窄巷(narrow-lane,NL)模糊度:

    式中,N~r,IFs表示非差无电离层组合观测值的浮点模糊度;Nr,WLsN˜r,NLs分别表示整数型宽巷模糊度和浮点型窄巷模糊度。

  • 为了消除观测粗差、提高FCB产品的可靠性和精度,通常选择多个测站的观测数据利用整体网平差求解。对于某个地面参考站网,假设有r‍个测站、共s颗卫星,每个测站可观测到的卫星数为si(sis,i=1, 2r),则模糊度参数和FCB之间的关系为:

    式中,niNi是第i个测站相位观测值的浮点与整数模糊度向量;brbs分别为r×1维接收机FCB和s×1维卫星FCB;Risi×s维系数矩阵,其第i列元素为1,其余元素为0;Sisi×s‍ ‍维系数矩阵,其每行对应卫星的元素为-‍1,其他元素为0。由于方程秩亏数为1,无法直接求解,因此选取观测数量最多、平均高度角最大的一颗卫星作为参考星进行星间单差消除接收机端的影响,利用最小二乘估计得到FCB产品。

    浮点宽巷模糊度参数可以通过Melbourne-Wubbena(MW)公式得到,BDS-3卫星的HMW(Hatch-MW)组合观测值可以表示为:

    式中,N˜r,WLs是浮点宽巷模糊度;Nr,WLs是其整数部分;dr,WLdr,WLs是接收机端和卫星端硬件延迟的小数部分;λWL是宽巷波长。

    宽巷固定较为简单,测站选取的不同以及测站分布等因素估计出的同一单差对的宽巷FCB具有良好的一致性。使用的测站越多,估计的FCB产品可靠性越高。得到宽巷浮点模糊度参数之后,可以利用式(4)进行求解。

    根据式(3)可知,BDS-3卫星浮点窄巷模糊度参数可以利用浮点无电离层组合观测值模糊度和整数宽巷模糊度得到:

    式中,Nr,NLs是窄巷模糊度的整数部分;dr,NLdNLs分别为接收机端硬件延迟和卫星端硬件延迟的小数部分。得到浮点窄巷模糊度之后,与宽巷固定方法相同,利用星间单差和最小二乘即可得到BDS-3卫星窄巷FCB估计值。

  • 本文选取全球均匀分布的约140个测站2020-08-01—2020-08-31(年积日214天~244天)共31 d的观测数据进行GPS、BDS双系统FCB估计,观测数据采样间隔为30 s。为了解决中国区域测站稀疏的问题,采用了部分中海北斗导航技术有限公司的自建站。使用武汉大学精密轨道和钟差产品,卫星截止高度角为10°。其中宽巷FCB每天估计一组,窄巷FCB每15 min估计一组。

  • 宽巷模糊度利用HMW组合观测值得到,该观测值可以消除所有几何项误差的影响,且北斗卫星宽巷的波长约为85 cm,远大于硬件延迟和观测噪声等残余误差的影响,因此宽巷FCB应该较为稳定。图 1表示年积日214天~244天可观测的BDS-3卫星的宽巷FCB时间序列。

    Figure 1.  Variation of BDS-3 WL FCB

    图 1可以看出,宽巷FCB具有长期稳定性,BDS-3卫星宽巷FCB在31 d内的变化小于0.2 ‍周,GPS卫星更加明显,小于0.1周。由式(6)可知,窄巷模糊度参数是利用无电离层组合模糊度分解后得到的。无电离层组合模糊度利用几何相关方程滤波得到,易受平差模型和观测误差的影响。且窄巷波长更短,在长时间内难以保持稳定,因此每隔15 min估计一组窄巷FCB。

    2020年年积日220天可解算的BDS‍-‍3卫星窄巷FCB时间序列如图 2所示。

    Figure 2.  Variation of BDS-3 NL FCB on DOY 220 of 2020

    图 2可以看出,BDS-3卫星窄巷FCB在一段时间内保持稳定,变化小于0.1周,可以达到与全球定位系统(global positioning system,GPS)卫星相当的精度。卫星精密产品精度、伪距码偏差改正效果、可观测卫星数等均会对窄巷FCB估计值的稳定性造成一定的影响。

    GPS和BDS-3卫星宽巷、窄巷FCB的残差分布见图 3,可以评定FCB产品的精度和一致性。

    Figure 3.  Residual Distributions of WL and NL FCB Estimates for GPS and BDS-3

    图 3可以看出,宽巷残差分布相对于窄巷更加集中。GPS卫星宽巷和窄巷残差在±‍0.15周内所占比例分别为99.8%、99.3%,BDS‍-3卫星宽巷和窄巷残差在±‍0.15周内所占比例分别为99.7%、98.1%;GPS卫星宽巷和窄巷残差在±0.10周内占比分别为99.2%、97.4%,BDS-3卫星宽巷和窄巷残差在±0.10周内占比分别为98.3%、94.1%。受观测数据和精密产品的限制,BDS-‍3卫星的FCB产品相对于GPS略差。

  • 为体现FCB产品对于PPP的提升效果,选择全球均分分布的8个测站分别在静态和动态条件下用单GPS、单BDS-3、BDS-2/3、GPS+BDS-3共4种模式进行PPP-AR解算,并对定位结果进行统计分析。将平面、高程和三维误差达到10 ‍cm以内并在之后的10 min内保持稳定的时刻定义为收敛时间。将固定卫星数大于等于4颗的历元视为固定,固定历元占总历元的百分比为历元固定率,将10 min内保持固定的首‍个固定历元称为首次固定时间(time to first fixed,TTFF)。

  • AREG测站2020年年积日220天不同模式下浮点解和固定解的坐标偏差时间序列见图 4

    Figure 4.  Results of Static Float PPP and PPP-AR at AREG

    图 4可以看出,静态条件下浮点解和固定解在收敛之后都可以达到厘米级的定位精度,但固定解的收敛时间小于浮点解,说明模糊度固定能够加快PPP收敛。

    为充分体现模糊度固定的效果,表 1给出了所有测站静态条件下各种模式浮点解和固定解的平均收敛时间。从表 1可以看出,模糊度固定可以减少PPP收敛所需时间。单BDS-3受到观测数据和精密产品等的影响收敛时间最长,进行模糊度固定后在水平、高程和三维方向的收敛时间分别缩短了24.6%、30.6%、24.8%。

    定位模式 浮点解 固定解
    水平 高程 三维 水平 高程 三维
    GPS 9.0 14.1 16.1 6.5 10.4 11.7
    BDS-3 17.5 26.8 33.1 13.2 18.6 24.9
    BDS-2/3 13.8 18.9 29.9 12.4 17.7 23.3
    GPS+BDS-3 8.1 11.3 15.1 5.8 8.0 10.5

    Table 1.  Convergence Time of Static Float PPP and PPP-AR/min

    表 2中记录了静态条件下完全收敛之后东、北、天共3个方向的平均均方根误差(root mean square error,RMSE)。为了反映所有测站多天的固定解定位结果,统计了每个测站31 d解算结果的平均TTFF、历元固定率和东、北、天3个方向的RMSE。TTFF和历元固定率的柱状图如图 5所示。

    定位模式 静态 动态
    TTFF/min 固定率/% 东/cm 北/cm 天/cm TTFF/min 固定率/% 东/cm 北/cm 天/cm
    GPS 21.0 95.9 0.93 0.64 1.34 29.5 93.4 1.75 1.54 3.05
    BDS-3 31.5 89.8 1.03 0.60 1.72 33.3 83.9 2.57 2.29 3.71
    BDS-2/3 27.0 92.4 0.94 0.73 1.39 29.4 88.3 1.99 1.70 3.28
    GPS+BDS-3 13.2 98.7 0.90 0.50 1.15 16.7 98.2 1.56 1.34 2.42

    Table 2.  Statistical Results of Static and Kinematic PPP-AR Solutions in Different Positioning Strategies

    Figure 5.  Average Values of TTFFs and Fixing Rates of Four Groups of Static PPP-AR

    相对于单GPS系统,加入BDS-3卫星后固定时间和历元固定率都有一定的提升,能更快地完成模糊度的正确固定,从而实现厘米级的定位精度。随着可视北斗卫星数目的增加,用来进行固定的候选模糊度数量随之增加,从而显著减少了首次固定时间。

    表 2可以看出,BDS-2/3的定位精度已经达到和GPS相当的水平,随着北斗卫星精密产品的完善和提高,定位精度会进一步提高。GPS+BDS-3在所有模式中的效果最好,TTFF为13.2 ‍min,定位结果时间序列稳定性已经达到了很高的水平。由于可用卫星数较少,因此BDS‍-3卫星TTFF较长,其中PNGM测站所需时间最长,达到了37.7 min。加入GPS卫星之后,单BDS-3的TTFF有了一定的提升,说明多系统融合可以显著改善各单系统的缺陷。在历元固定率方面,所有测站都超过了85%。其中LEIJ测站由于其位于欧洲区域,可视北斗卫星数较少,部分历元只能观测到4颗北斗卫星,因此其BDS-3历元固定率最低,只有86.9%。加入GPS系统之后,历元固定率可以达到96.8%。

    表 2还可以看出,4种模式静态PPP-AR都可以达到很高的精度。BDS-3定位结果相对于单GPS系统较差,一方面是由于BDS卫星精密轨道钟差产品精度较低,另一方面是因为GPS卫星全为MEO,南北方向和东西方向上的空间几何构型更好。与单GPS相比,GPS+BDS‍-3在东、北、天3个方向定位精度分别提升了3.2%、10.7%、5.1%,提升效果并不明显,但可以显著减少TTFF和收敛时间并提升历元固定率,这说明利用估计的FCB产品可以实现BDS-3卫星模糊度的正确固定。

  • 选择相同的观测数据进行4种模式下的动态PPP-AR解算,图 6绘制了AREG测站2020年年积日220天的动态解算结果的坐标差序列。从图 6可以看出,与静态结果相比,动态解算结果存在一定的波动,其中,GPS+BDS-3定位效果最好,只需要大约10 min就可以实现模糊度正确固定,并在之后的时间内保持稳定,水平方向精度在1~2 cm,高程方向精度在2~3 cm。单BDS-3系统需要33 min实现模糊度的正确固定,BDS‍-‍2/‍3解算效果相比于BDS-3有一定提升,需要25 min实现模糊度固定。单BDS-3和BDS‍-‍2/‍3在某个时间段内浮点解和固定解都出现了跳动,可能是由于该时刻观测数据出现问题导致模糊度需要重新固定。与静态模式类似,当PPP完全收敛后,浮点解和固定解都能达到较高的精度,但固定解的收敛时间更短。

    Figure 6.  Results of Kinematic Float PPP and PPP-AR at AREG

    为了充分反映模糊度固定对于加快收敛的效果,表 3给出了所有测站动态条件下各种模式浮点解和固定解的平均收敛时间。从表 3可以看出,模糊度固定可以显著提高动态PPP的收敛时间。对于单BDS-3系统,在水平、高程、三维的收敛时间分别减少了11.7%、22.3%、17.4%。经过模糊度固定后,GPS+BDS-3在水平方向只需要7.8 ‍min的收敛时间,随着多频多系统的发展,收敛时间将会进一步缩短。

    定位模式 浮点解 固定解
    水平 高程 三维 水平 高程 三维
    GPS 16.3 24.0 35.5 12.0 16.1 24.5
    BDS-3 44.5 56.0 61.4 39.3 43.5 50.7
    BDS-2/3 27.9 39.5 45.8 24.1 35.1 40.4
    GPS+BDS-3 11.2 17.8 24.6 7.8 12.0 15.7

    Table 3.  Convergence Time of Kinematic Float PPP and PPP-AR/min

    为了反映所有测站多天的动态解算结果,图 7绘制了31 d的动态解算的平均TTFF、历元固定率的柱状图。表 2中记录了动态条件下完全收敛之后东、北、天共3个方向的RMSE值。

    Figure 7.  Average Values of TTFFs and Fixing Rates of Four Groups of Kinematic PPP-AR

    图 7中可以看出,AREG测站单BDS-3固定时间最长,需要38.5 min。由于DARW位于亚太地区,可用北斗卫星较多,因此只需要24 min就可以实现模糊度的正确固定。从历元固定率上看,所有测站单BDS-3历元固定率都超过了80%。其中LEIJ测站固定率最低,只有80.5%,加入GPS卫星之后,历元固定率可以提高到97.4%,提升了20.99%。

    表 2的数据可以看出,4种模式下动态PPP-AR的定位精度在东和北方向大约2~3 ‍cm,在天方向大约为3~4 cm。受到北斗卫星精密产品和可视卫星数的影响,单BDS-3定位精度较差,加入BDS-2卫星后精度略差于GPS。在GPS固定效果较差的测站,加入BDS-3卫星后TTFF和历元固定率都有了较大的提高。

  • 本文基于全球约140个测站共31 d的观测数据进行GPS、BDS双系统FCB估计,并对BDS-3卫星宽巷、窄巷FCB的时变特性进行分析。选择了8个测试站利用估计的FCB产品进行不同模式下的静态、动态PPP-AR定位解算,并对定位结果进行分析。

    从BDS-3的FCB产品时变特性上看,宽巷FCB具有长期稳定性,31 d内的变化不超过0.2 ‍周。窄巷FCB在一天之内可以保持相对稳定,变化不超过0.1 ‍周。部分BDS-3卫星受到精密产品精度和观测数据较少的影响,在几个小时的短时间保持稳定,在两个连续观测时段之间存在一定偏差。

    从静态PPP-AR定位结果上看,单BDS-3需要20~30 min才能实现完全收敛,加入GPS卫星之后可以缩短至10 min。在模糊度固定方面,单BDS-3的固定时间较长,需要30 min才能实现正确固定,加入GPS卫星可以减少到13.2 min。单BDS-3历元固定率为89.8%,加入GPS卫星后可以提高到98.7%。模糊度正确固定之后,单BDS‍-‍3的定位精度可以达到水平方向1 cm,高程方向1.5 cm。从动态PPP-AR定位结果上看,收敛时间、固定时间与历元固定率趋势与静态PPP‍-‍AR基本类似,加入GPS系统固定时间可以从33.3 min缩小到16.7 min。单BDS-3在正确固定模糊度的前提下可以达到水平方向2~3 cm、高程方向3~4 cm的定位精度,略低于单GPS。

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