北斗三号卫星FCB估计及其模糊度固定

FCB Estimation and Ambiguity Resolution of BDS‑3

随着北斗卫星导航系统(BeiDou navigation satellite system,BDS)的建设和完善,更多的北斗在轨卫星开始提供全球性的定位、导航、授时服务。为了验证北斗系统整体精密单点定位⁃模糊度固定(precise point positioning⁃ambiguity resolution,PPP⁃AR)的效果,基于全球分布的测站2020-08-01—2020-08-31共31 d的观测数据进行GPS、BDS双系统相位小数周偏差(fractional cycle bias,FCB)估计,并对其中BDS⁃3卫星FCB产品时变特性进行分析。结果表明,大部分BDS⁃3卫星宽巷FCB在31 d内保持相对稳定,变化小于0.2周,窄巷FCB在1 d之内的变化小于0.1周。利用估计的FCB产品进行动态和静态PPP⁃AR解算。单BDS⁃3静态PPP⁃AR的历元固定率可以达到89.8%,东、北、天3个方向的均方根误差(root mean square error,RMSE)分别为0.94 cm、0.73 cm和1.39 cm,动态PPP⁃AR的历元固定率为83.9%,东、北、天3个方向的RMSE分别为1.99 cm、1.70 cm和3.28 cm。

Objectives:Precise point positioning(PPP)combines the advantages of standard point posi⁃tioning(SPP)and relative positioning,which can achieve centimeter level positioning.With the develop⁃ment 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 re⁃ceiver,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⁃am⁃biguity resolution(PPP⁃AR)of BDS as a whole,we estimate the FCBs of GPS and BDS based on the ob⁃servation data from August 1 to August 31 in 2020 of globally distributed stations.The single difference be⁃tween satellites is used to eliminate the influence of hardware delay at the receivers,and the single dif⁃ference 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 re⁃siduals 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 condi⁃tion,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 im⁃provement 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.