Technique PPP-RTK combines the advantages of both the Precise Point Positioning(PPP)and the Real-Time Kinematic(RTK)positioning.With the emergence of multi-frequency Global Navigation Satellite System(GNSS)observation...Technique PPP-RTK combines the advantages of both the Precise Point Positioning(PPP)and the Real-Time Kinematic(RTK)positioning.With the emergence of multi-frequency Global Navigation Satellite System(GNSS)observations,it is preferable to formulate PPP-RTK functional models based on original(undiferenced and uncombined)observations.While there exist many variants of the undiferenced and uncombined PPP–RTK models,a unifed theoretical framework needs developing to link these variants.In this contribution,we formulate a class of undiferenced and uncombined PPP-RTK functional models in a systematic way and cast them in a unifed framework.This framework classifes the models into a code-plus-phase category and a phase-only category.Each category covers a variety of measurement scenarios on the network side,ranging from small-,medium-to large-scale networks.For each scenario,special care has been taken of the distinct ionospheric constraints and the diference between Code Division Multiple Access(CDMA)and Frequency Division Multiple Access(FDMA)signals.The key to systematically formulating these models lies in how to deal with the rank defciency problems encountered.We opt for the Singularity-basis(S-basis)theory,giving rise to the full-rank observation equations in which the estimable parameters turn out to be the functions of original parameters and those selected as the S-basis.In the sequel,it becomes straightforward to derive for each scenario the user model as it,more or less,amounts to the single-receiver network model.Benefting from the presented theoretical framework,the relationships and diferences between various undiferenced and uncombined PPP-RTK models become clear,which can lead to the better use of these models in a specifc situation.展开更多
There is increasing concern about the uncombined(UC)observation model in the field of global navigation satellite system(GNSS).Based on the global positioning system(GPS)and the third-generation BeiDou navigation sate...There is increasing concern about the uncombined(UC)observation model in the field of global navigation satellite system(GNSS).Based on the global positioning system(GPS)and the third-generation BeiDou navigation satellite system(BDS-3),this study processed the UC precision orbit determination(POD)for single and dual systems.First,a UC observation model suitable for multi-GNSS POD was derived,and the ionospheric-free(IF)combination observation model was presented.Although the ambiguity parameters of UC and IF strategies were different after reparameterization,the difference could be removed when processing ambiguity resolution,and the equivalence was proved theoretically.To demonstrate the accuracy of BDS-3 orbits fully,the observation data of approximately 1 month were selected for determining the precise orbit for global positioning system(GPS)only,BDS-3 only,and GPS/BDS-3 systems based on the UC and IF models.The orbit precision of BDS-3 satellites was validated by using metrics,including comparison with precision products released by Wuhan University,orbit boundary discontinuity,and satellite laser ranging(SLR)residuals.The results show that the orbit accuracies of the IF and UC models are almost the same,the difference in orbits is approximately several millimeters,and the clock difference is within 0.01 ns.The GPS/BDS-3 combined solution shows better accuracy compared to other solutions.The average accuracies in the R and 3D directions are approximately 4 and 15 cm,and the clock standard deviation is approximately 0.2 ns compared to external orbit product.The root mean square of SLR residuals is approximately 4 cm.展开更多
Ionospheric delay modeling is not only important for Global Navigation Satellite System(GNSS)based space weather study and monitoring,but also an efficient tool to speed up the convergence time of Precise Point Positi...Ionospheric delay modeling is not only important for Global Navigation Satellite System(GNSS)based space weather study and monitoring,but also an efficient tool to speed up the convergence time of Precise Point Positioning(PPP).In this study,a novel model,denoted as Quasi-4-Dimension Ionospheric Modeling(Q4DIM)is proposed for wide-area high precision ionospheric delay correction.In Q4DIM,the Line Of Sight(LOS)ionospheric delays from a GNSS station network are divided into different clusters according to not only the location of latitude and longitude,but also satellite elevation and azimuth.Both Global Ionosphere Map(GIM)and Slant Ionospheric Delay(SID)models that are traditionally used for wide-area and regional ionospheric delay modeling,respectively,can be regarded as the special cases of Q4DIM by defining proper grids in latitude,longitude,elevation,and azimuth.Thus,Q4DIM presents a resilient model that is capable for both wide-area coverage and high precision.Four different sets of clusters are defined to illustrate the properties of Q4DIM based on 200 EUREF Permanent Network(EPN)stations.The results indicate that Q4DIM is compatible with the GIM products.Moreover,it is proved that by inducting the elevation and azimuth angle dependent residuals,the precision of the 2-dimensional GIM-like model,i.e.,Q4DIM 2-Dimensional(Q4DIM-2D),is improved from around 1.5 Total Electron Content Units(TECU)to better than 0.5 TECU.In addition,treating Q4DIM as a 4-dimensional matrix in latitude,longitude,elevation,and azimuth,whose sparsity is less than 5%,can result in its feasibility in a bandwidth-sensitive applications,e.g.,satellite-based Precising Point Positioning Real-Time Kinematic(PPP-RTK)service.Finally,the advantages of Q4DIM in PPP over the 2-dimensional models are demonstrated with the one month's data from 30 EPN stations in both high solar activity year 2014 and low solar activity year 2020.展开更多
为满足单系统单基线双频数据条件下的实时精密定位需求,提出一种双频非组合实时精密定位技术,基于站间-星间载波相位及伪距观测量双差观测模型,实现单系统单基线双频非组合RTK(Real Time Kinematic).通过分析双差模型观测量冗余度,确立...为满足单系统单基线双频数据条件下的实时精密定位需求,提出一种双频非组合实时精密定位技术,基于站间-星间载波相位及伪距观测量双差观测模型,实现单系统单基线双频非组合RTK(Real Time Kinematic).通过分析双差模型观测量冗余度,确立模型残余误差处理策略,设定状态向量,推导并建立状态预测方程及测量方程,实时更新状态向量变换矩阵,根据随机模型调整两种观测量数据的权重,最后利用扩展卡尔曼滤波器技术得到实时定位结果.文中基于几组中长基线实验,通过考察定位结果的三维定位误差及整周模糊度成功固定率,验证该方法的有效性.实验结果表明,在中长基线条件下进行实时定位,该方法精度可以达到厘米级,基线长度为135.6 km时,整周模糊度固定成功率为97.3%,东向、北向、天向的CEP95定位误差分别为1.35 cm、1.84 cm、7.08 cm.双频非组合技术充分利用差分技术的优势消除与距离无关的相关误差,并有效地避免了观测值组合过程所引起的观测噪声,可以实现中长基线条件下的厘米级实时定位.展开更多
在Trip软件的基础上实现了北斗三频无电离层两两组合、三频消电离层组合和三频非组合精密单点定位(precise point positioning,PPP)算法。利用12个陆态网观测站的北斗三频观测数据对3种三频PPP定位模型及传统的双频无电离层组合PPP模型...在Trip软件的基础上实现了北斗三频无电离层两两组合、三频消电离层组合和三频非组合精密单点定位(precise point positioning,PPP)算法。利用12个陆态网观测站的北斗三频观测数据对3种三频PPP定位模型及传统的双频无电离层组合PPP模型的定位性能进行分析。试验结果表明,对大多数测站,3种三频PPP模型静态定位精度水平方向优于1cm,高程方向优于2cm,动态定位精度水平方向优于4cm,高程方向优于6cm;3种三频PPP模型静态收敛时间约为120min,动态收敛时间约180min;相比于传统的双频PPP模型,三频PPP模型的定位精度有所提高,其中,三频非组合模型静态单天解RMS在水平方向和高程方向分别提高36.1%和6.3%,动态单天解RMS在水平方向和高程方向分别提高9.1%和6.3%。展开更多
基金This work was partially funded by the National Natural Science Foundation of China(Grant Nos.41774042,42174034)the Key Research and Development Plan of Hubei Province(Grant No.2020BHB014)+1 种基金the Scientifc Instrument Developing Project of the Chinese Academy of Sciences(Grant No.YJKYYQ20190063)The frst author is supported by the CAS Pioneer Hundred Talents Program。
文摘Technique PPP-RTK combines the advantages of both the Precise Point Positioning(PPP)and the Real-Time Kinematic(RTK)positioning.With the emergence of multi-frequency Global Navigation Satellite System(GNSS)observations,it is preferable to formulate PPP-RTK functional models based on original(undiferenced and uncombined)observations.While there exist many variants of the undiferenced and uncombined PPP–RTK models,a unifed theoretical framework needs developing to link these variants.In this contribution,we formulate a class of undiferenced and uncombined PPP-RTK functional models in a systematic way and cast them in a unifed framework.This framework classifes the models into a code-plus-phase category and a phase-only category.Each category covers a variety of measurement scenarios on the network side,ranging from small-,medium-to large-scale networks.For each scenario,special care has been taken of the distinct ionospheric constraints and the diference between Code Division Multiple Access(CDMA)and Frequency Division Multiple Access(FDMA)signals.The key to systematically formulating these models lies in how to deal with the rank defciency problems encountered.We opt for the Singularity-basis(S-basis)theory,giving rise to the full-rank observation equations in which the estimable parameters turn out to be the functions of original parameters and those selected as the S-basis.In the sequel,it becomes straightforward to derive for each scenario the user model as it,more or less,amounts to the single-receiver network model.Benefting from the presented theoretical framework,the relationships and diferences between various undiferenced and uncombined PPP-RTK models become clear,which can lead to the better use of these models in a specifc situation.
基金National Natural Science Foundation of China(Grant Nos.41674016,41874041,41704035,41904039)by State Key Laboratory of Geo-Information Engineering,NO.SKLGIE2018-M-2-1.
文摘There is increasing concern about the uncombined(UC)observation model in the field of global navigation satellite system(GNSS).Based on the global positioning system(GPS)and the third-generation BeiDou navigation satellite system(BDS-3),this study processed the UC precision orbit determination(POD)for single and dual systems.First,a UC observation model suitable for multi-GNSS POD was derived,and the ionospheric-free(IF)combination observation model was presented.Although the ambiguity parameters of UC and IF strategies were different after reparameterization,the difference could be removed when processing ambiguity resolution,and the equivalence was proved theoretically.To demonstrate the accuracy of BDS-3 orbits fully,the observation data of approximately 1 month were selected for determining the precise orbit for global positioning system(GPS)only,BDS-3 only,and GPS/BDS-3 systems based on the UC and IF models.The orbit precision of BDS-3 satellites was validated by using metrics,including comparison with precision products released by Wuhan University,orbit boundary discontinuity,and satellite laser ranging(SLR)residuals.The results show that the orbit accuracies of the IF and UC models are almost the same,the difference in orbits is approximately several millimeters,and the clock difference is within 0.01 ns.The GPS/BDS-3 combined solution shows better accuracy compared to other solutions.The average accuracies in the R and 3D directions are approximately 4 and 15 cm,and the clock standard deviation is approximately 0.2 ns compared to external orbit product.The root mean square of SLR residuals is approximately 4 cm.
基金National Natural Science Foundation of China(42174029).
文摘Ionospheric delay modeling is not only important for Global Navigation Satellite System(GNSS)based space weather study and monitoring,but also an efficient tool to speed up the convergence time of Precise Point Positioning(PPP).In this study,a novel model,denoted as Quasi-4-Dimension Ionospheric Modeling(Q4DIM)is proposed for wide-area high precision ionospheric delay correction.In Q4DIM,the Line Of Sight(LOS)ionospheric delays from a GNSS station network are divided into different clusters according to not only the location of latitude and longitude,but also satellite elevation and azimuth.Both Global Ionosphere Map(GIM)and Slant Ionospheric Delay(SID)models that are traditionally used for wide-area and regional ionospheric delay modeling,respectively,can be regarded as the special cases of Q4DIM by defining proper grids in latitude,longitude,elevation,and azimuth.Thus,Q4DIM presents a resilient model that is capable for both wide-area coverage and high precision.Four different sets of clusters are defined to illustrate the properties of Q4DIM based on 200 EUREF Permanent Network(EPN)stations.The results indicate that Q4DIM is compatible with the GIM products.Moreover,it is proved that by inducting the elevation and azimuth angle dependent residuals,the precision of the 2-dimensional GIM-like model,i.e.,Q4DIM 2-Dimensional(Q4DIM-2D),is improved from around 1.5 Total Electron Content Units(TECU)to better than 0.5 TECU.In addition,treating Q4DIM as a 4-dimensional matrix in latitude,longitude,elevation,and azimuth,whose sparsity is less than 5%,can result in its feasibility in a bandwidth-sensitive applications,e.g.,satellite-based Precising Point Positioning Real-Time Kinematic(PPP-RTK)service.Finally,the advantages of Q4DIM in PPP over the 2-dimensional models are demonstrated with the one month's data from 30 EPN stations in both high solar activity year 2014 and low solar activity year 2020.
文摘在Trip软件的基础上实现了北斗三频无电离层两两组合、三频消电离层组合和三频非组合精密单点定位(precise point positioning,PPP)算法。利用12个陆态网观测站的北斗三频观测数据对3种三频PPP定位模型及传统的双频无电离层组合PPP模型的定位性能进行分析。试验结果表明,对大多数测站,3种三频PPP模型静态定位精度水平方向优于1cm,高程方向优于2cm,动态定位精度水平方向优于4cm,高程方向优于6cm;3种三频PPP模型静态收敛时间约为120min,动态收敛时间约180min;相比于传统的双频PPP模型,三频PPP模型的定位精度有所提高,其中,三频非组合模型静态单天解RMS在水平方向和高程方向分别提高36.1%和6.3%,动态单天解RMS在水平方向和高程方向分别提高9.1%和6.3%。
