BDS/GPS/Galileo多频观测值精度评估及随机模型精化

赵兴旺，陈健，刘超，刘春阳，樊亚; ZHAO Xingwang; CHEN Jian; LIU Chao; LIU Chunyang; FAN Ya

引 en

BDS/GPS/Galileo多频观测值精度评估及随机模型精化

赵兴旺¹
机构：
1. 安徽理工大学空间信息与测绘工程学院/矿山采动灾害空天地协同监测与预警安徽普通高校重点实验室/矿区环境与灾害协同监测煤炭行业工程研究中心,淮南, 232001
×
，陈健¹
机构：
1. 安徽理工大学空间信息与测绘工程学院/矿山采动灾害空天地协同监测与预警安徽普通高校重点实验室/矿区环境与灾害协同监测煤炭行业工程研究中心,淮南, 232001
×
，刘超¹
机构：
1. 安徽理工大学空间信息与测绘工程学院/矿山采动灾害空天地协同监测与预警安徽普通高校重点实验室/矿区环境与灾害协同监测煤炭行业工程研究中心,淮南, 232001
×
，刘春阳¹
机构：
1. 安徽理工大学空间信息与测绘工程学院/矿山采动灾害空天地协同监测与预警安徽普通高校重点实验室/矿区环境与灾害协同监测煤炭行业工程研究中心,淮南, 232001
×
，樊亚²
机构：
2. 中国建筑材料工业地质勘查中心贵州总队,贵阳, 551400
×

1. 安徽理工大学空间信息与测绘工程学院/矿山采动灾害空天地协同监测与预警安徽普通高校重点实验室/矿区环境与灾害协同监测煤炭行业工程研究中心,淮南, 232001；
2. 中国建筑材料工业地质勘查中心贵州总队,贵阳, 551400；

Precision estimation of the BDS/GPS/Galileo multi-frequency observations and stochastic model refining

ZHAO Xingwang¹
Affiliation：
1. School of Spatial Information and Geomatics Engineering/Key Laboratory of Aviation-aerospace-ground Cooperative Monitoring and Early Warning of Coal Mining-induced Disasters of Anhui Higher Education Institutes/Coal Industry Engineering Research Center of Mining Area Environmental and Disaster Cooperative Monitoring,Anhui University of Science & Technology,Huainan 232001
×
，CHEN Jian¹
Affiliation：
1. School of Spatial Information and Geomatics Engineering/Key Laboratory of Aviation-aerospace-ground Cooperative Monitoring and Early Warning of Coal Mining-induced Disasters of Anhui Higher Education Institutes/Coal Industry Engineering Research Center of Mining Area Environmental and Disaster Cooperative Monitoring,Anhui University of Science & Technology,Huainan 232001
×
，LIU Chao¹
Affiliation：
1. School of Spatial Information and Geomatics Engineering/Key Laboratory of Aviation-aerospace-ground Cooperative Monitoring and Early Warning of Coal Mining-induced Disasters of Anhui Higher Education Institutes/Coal Industry Engineering Research Center of Mining Area Environmental and Disaster Cooperative Monitoring,Anhui University of Science & Technology,Huainan 232001
×
，LIU Chunyang¹
Affiliation：
1. School of Spatial Information and Geomatics Engineering/Key Laboratory of Aviation-aerospace-ground Cooperative Monitoring and Early Warning of Coal Mining-induced Disasters of Anhui Higher Education Institutes/Coal Industry Engineering Research Center of Mining Area Environmental and Disaster Cooperative Monitoring,Anhui University of Science & Technology,Huainan 232001
×
，FAN Ya²
Affiliation：
2. Guizhou Branch of China National Geological Exploration Center of Building Materials Industry,Guiyang 551400
×

1. School of Spatial Information and Geomatics Engineering/Key Laboratory of Aviation-aerospace-ground Cooperative Monitoring and Early Warning of Coal Mining-induced Disasters of Anhui Higher Education Institutes/Coal Industry Engineering Research Center of Mining Area Environmental and Disaster Cooperative Monitoring,Anhui University of Science & Technology,Huainan 232001；
2. Guizhou Branch of China National Geological Exploration Center of Building Materials Industry,Guiyang 551400；

作者简介:

赵兴旺,男,博士,教授,主要从事GNSS高精度导航定位等方面的研究工作.xwzhao2008@126.com

中图分类号:P228.4

文献标识码:A

DOI:10.13878/j.cnki.jnuist.2022.06.010

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出版信息

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目录contents

摘要 Abstract
关键词 Keywords
0 引言
1 单差残差模型
2 基于单差残差的BDS/GPS/Galileo随机模型精化
3 数据采集与结果分析
3.1 BDS/GPS/Galileo数据质量评估
3.2 BDS/GPS/Galileo随机模型系数确定
4 结论
参考文献

摘要

随机模型的优劣直接影响GNSS精密定位的精度以及可靠性.通过MEGX观测网CUT0、CUT2和CUTA测站连续10 d观测数据,基于短基线单差模型方法求解各系统单差残差的时间序列,并推导出BDS/GPS/Galileo卫星观测值噪声.统计观测值噪声随高度角变化的情况,通过最小二乘拟合方法确定精化的随机模型.结果表明:Galileo的4个频点的伪距观测值精度约20~50 cm,E5频点的精度最高,E1最低,E5a和E5b基本相当;载波相位观测值精度约1~3 mm,E5频点的精度明显高于E1、E5a和E5b.BDS载波观测值精度约1~3 mm,B1、B2、B3精度基本相当,其伪距观测值精度约30~50 cm,B1精度最低,B2和B3相差不多.GPS L1伪距观测值精度约63 cm,L2伪距观测值精度约42 cm,载波相位精度约3 mm.基于单差模型对各系统观测值进行精度估计,在短基线情况下,BDS/GPS/Galileo载波相位观测值精度基本相当,而Galileo E5伪距观测值精度明显优于其他卫星系统伪距观测值精度.各类型卫星观测值的残差分析可为定位中随机模型的建立提供依据.

Abstract

The accuracy of stochastic model directly affects the precision and reliability of GNSS precision positioning.With 10-day observation data of CUT0,CUT2 and CUTA stations in MEGX observation network,the residuals time series of GNSS were solved by single-difference model using short baseline method.According to the statistically observed noises changing with the elevation angle,a refined stochastic model is established via the least-square method.The results show that the range of pseudo-range observation precision lies in 20-50 cm,30-50 cm and 42-63 cm for Galileo,BDS and GPS,respectively;and the carrier phase observation precision falls within the scope of 1-3 mm for Galileo and BDS,and on 3 mm for GPS.For the four frequencies of Galileo,E5 is most accurate in both pseudo-range observation and carrier phase;the accuracies of B1,B2,B3 of BDS are roughly the same;the L2 of GPS is more accurate in pseudo-range observation with precision of 42 cm than L1 of 63 cm,and both L1 and L2 have carrier phase precision of 3 mm.From the above precision estimations based on single-difference model,it can be concluded that in case of short baseline,BDS/GPS/Galileo have roughly same precision in carrier phase observation values,while Galileo E5 outperforms the other satellite systems in pseudo-range observations.Residual analysis of satellite observations provides a basis for the establishment of stochastic models in positioning.

关键词

BDS/GPS/Galileo ；单差残差；随机模型；精度估计

Keywords

BDS/GPS/Galileo ； single-difference residuals ； stochastic model ； precision estimation

0 引言
随着GPS、BDS和Galileo系统的不断完善，全球导航卫星系统（Global Navigation Satellite System，GNSS）定位技术的应用领域也逐渐扩大和深化.多系统多频GNSS融合数据处理的发展成为趋势，不同星座、不同观测值的联合解算比单系统更复杂.因此，获取更加可靠的多系统多频GNSS融合定位的随机模型还需进一步研究.
近年来，有大量学者对BDS/GPS/Galileo的精密定位开展了相关研究^[1-2].GNSS精密定位需要准确的确定函数模型和随机模型.函数模型建立了观测值与坐标参数、模糊度参数以及大气延迟等估计参数之间的相互关系; 随机模型刻画了观测值的精度及其相关关系，其优劣直接影响多系统GNSS组合定位的精度以及可靠性^[3].因此，分析不同类型卫星观测值的精度和随机统计特性是很有必要的.随机模型主要有三种类型:基于卫星高度角模型、基于信噪比（Signal to Noise Ratio，SNR）模型和验后方差分量估计模型.张小红等^[4]对北斗二代观测值展开质量分析，比较分析了高度角和信噪比加权的随机模型; Li等^[5]系统研究了BDS随机模型对可靠性统计检验的影响; 黄令勇等^[6]提出一种利用单站数据估计BDS伪距随机模型的算法; 严丽等^[7]研究出结合迭代最小二乘和最小范数二次无偏估计的方法，能够实时地估计北斗卫星观测值的方差; 刘一等^[8]提出一种基于指数函数的随机模型; 吴琼宝等^[9]对BDS/GPS星载观测数据进行了质量评估; Yan等^[10]提出一种BDS/GPS具有积分常数的随机模型; 虞顺等^[11]进行了Galileo数据质量分析并简要地评估了Galileo单点定位的精度; Prochniewicz等^[12]详细研究了多GNSS定位随机模型的建模问题; Hou等^[13]提出一种联合估计观测噪声和过程噪声的方法; Kiliszek等^[14]比较了选取多种不同的观测值加权函数对精密定位的影响.
综上所述，现有研究主要针对单系统的观测值精度进行分析，但关于Galileo四频观测值精度及多卫星系统的观测值精度对比研究较少.本文通过短基线单差残差分析BDS/GPS/Galileo不同类型卫星的观测值精度，并采用最小二乘拟合方法分别得到各系统卫星伪距和载波相位的高度角随机模型，建立起适用于各系统的定位随机模型.
1 单差残差模型
单差模型得到的残差是各卫星联合平差的结果，该方法未引入卫星之间的相关性且更易解算出与卫星相关的随机误差项.忽略对流层误差、电离层误差以及多路径误差等影响，零基线的站间单差观测方程表示为

\{\begin{matrix} Δ P_{k l, i}^{s, s y s} = Δ ρ_{k l}^{s} + c \cdot Δ δ t_{k l} + c \cdot Δ b_{k l, i}^{s y s} + Δ ε_{p}, \\ Δ Φ_{k l, i}^{s, s y s} = Δ ρ_{k l}^{s} + c \cdot Δ δ t_{k l} + \\ λ_{i} (Δ N_{k l, i}^{s} + Δ B_{k l, i}^{s y s}) + Δ ε_{Φ}, \end{matrix}

(1)

式中:Δ为单差算子; k和l分别为两测站接收机，s为观测到的卫星; P和Φ分别为伪距观测值和载波相位观测值; i为信号频率; 上标sys为不同卫星系统（GPS、BDS和Galileo）; ρ为卫星到测站间的几何距离; c为真空光速; b和B分别为伪距和载波相位硬件延迟; δt为接收机钟差; λ和N分别为载波相位的波长和整周模糊度; ε_P和ε_Φ分别为伪距观测噪声和载波相位观测噪声.对于GPS、BDS和Galileo是CDMA信号体制的系统，可将式（1）中的载波相位和伪距观测值改为如下形式:

\begin{matrix} Δ Φ_{k l, i}^{s s y s} = Δ ρ_{k l}^{s} + c \cdot Δ δ t_{k l} + λ_{i} Δ B_{k l, i}^{s y s} + \\ λ_{i} (Δ N_{k l, i}^{s} - Δ N_{k l, i}^{r} + Δ N_{k l, i}^{r}) + Δ ε_{Φ} = \\ Δ ρ_{k l}^{s} + c \cdot \overset{\bar{}}{Δ δ t_{Φ}} + λ_{i} \nabla Δ N_{k l, i}^{r s} + Δ ε_{Φ}, \end{matrix}

(2)

Δ P_{k l, i}^{s, s y s} = Δ ρ_{k l}^{s} + c \cdot \bar{Δ δ t_{P}} + Δ ε_{P},

(3)

式中:r表示参考卫星; $\overset{\bar{}}{Δ δ t_{Φ}}$ ， $\bar{Δ δ t_{P}}$ 分别表示等效载波钟差和等效伪距钟差，其具体表达式为

\{\begin{matrix} \bar{Δ δ t_{Φ}} = Δ δ t_{k l} + λ_{i} Δ B_{k l, i}^{s y s} + λ_{i} Δ N_{k l, i}^{r}, \\ \bar{Δ δ t_{P}} = Δ δ t_{k l} + c \cdot Δ b_{k l, i}^{s y s} . \end{matrix}

(4)

利用式（4），通过最小二乘估计出每个历元单差形式下的载波和伪距观测残差，对其进行相应的统计即可以获得随机模型参数.
2 基于单差残差的BDS/GPS/Galileo随机模型精化
本节旨在建立与高度角相关的GPS、BDS和Galileo观测值随机模型.用卫星高度角的正弦三角函数来表示非差观测值的中误差:

σ = \sqrt{m^{2} + \frac{n^{2}}{{s i n}^{2} (θ)}},

(5)

式（5）中，m，n均为经验系数，θ为卫星高度角.
根据式（4）中计算得到伪距和载波相位观测值的单差残差，可以建立适用于GPS、BDS、Galileo观测值的随机模型.首先，根据单差残差时间序列分别计算在高度角区间内每度的所有残差值的标准差，该偏差反映了观测值标准差随高度角的关系; 进而根据标准差和高度角的关系采用最小二乘估计方法解算经验模型的系数.
对于式（5）所示的正弦函数形式，待求参数为m，n，建立如下的观测方程:

[\begin{matrix} {\hat{σ}}_{1}^{2} \\ {\hat{σ}}_{2}^{2} \\ ⋮ \\ {\hat{σ}}_{j}^{2} \end{matrix}] = [\begin{matrix} 1 & \frac{1}{\sin^{2} (θ_{1})} \\ 1 & \frac{1}{\sin^{2} (θ_{2})} \\ ⋮ & ⋮ \\ 1 & \frac{1}{\sin^{2} (θ_{j})} \end{matrix}] [\begin{matrix} m^{2} \\ n^{2} \end{matrix}] .

(6)

令:

\begin{matrix} A = [\begin{matrix} 1 & \frac{1}{\sin^{2} (θ_{1})} \\ 1 & \frac{1}{\sin^{2} (θ_{2})} \\ ⋮ & ⋮ \\ 1 & \frac{1}{\sin^{2} (θ_{j})} \end{matrix}], \\ L = [\begin{matrix} {\hat{σ}}_{1}^{2} & {\hat{σ}}_{2}^{2} & \dots & {\hat{σ}}_{j}^{2} \end{matrix}], X = [\begin{matrix} m^{2} \\ n^{2} \end{matrix}] . \end{matrix}

(7)

式中，j为卫星数，根据最小二乘原理，可求解出模型系数:

X = {(A^{T} P A)}^{- 1} A^{T} P L,

(8)

式中，P为观测值权阵，A为系数矩阵，L为观测值阵.
3 数据采集与结果分析
3.1 BDS/GPS/Galileo数据质量评估
选取位于澳大利亚科廷大学短基线CUT0、CUT2和CUTA测站连续10 d观测数据，采集时间为2018-12-16—2018-12-25，接收机类型为TRIMBLE NETR9.采用单差模型，计算得到BDS、GPS和Galileo伪距和载波相位观测值的单差残差.为了分析BDS、GPS和Galileo系统不同频率伪距和载波相位观测值单差残差的特性，图1—3分别给出了短基线下BDS IGSO（C08）、GPS IIF（G06）、Galileo IOV（E19）3种卫星类型的伪距和载波相位单差残差的时间序列.通过单差残差的时间序列，进而得到BDS、GPS和Galileo非差伪距和载波相位观测值精度的统计结果，如表1—3所示.从图1和表1可知:BDS载波观测值精度约1~3 mm，其伪距观测值精度约30~50 cm，B1、B2、B3载波观测值精度基本相当，B1伪距观测值精度最低; BDS的IGSO和GEO卫星运行轨迹约1 d，MEO卫星运行轨迹约7 d; GEO和IGSO卫星相比，MEO卫星伪距和载波相位观测值精度较低，其主要原因是MEO观测时段中，低高度角观测值比例较大，导致观测值精度较差.从图2和表2可知:GPS L1伪距观测值精度约63 cm，L2伪距观测值精度约42 cm; 载波相位精度约3 mm; GPS卫星运行轨迹周期约1 d.从图3和表3可知:Galileo的4个频点的伪距观测值精度约20~50 cm，载波相位观测值精度约1~3 mm; E5频点载波观测值精度最高，E1最低，E5a和E5b基本相当，而E5 频点伪距观测值精度明显要优于E1、E5a、E5b频点.综上可得:在短基线情况下，BDS、GPS和Galileo载波相位观测值精度基本相当，而Galileo E5伪距观测值精度明显优于其他卫星系统伪距观测值精度.
图1 短基线情况下，C08卫星单差残差（左:载波相位; 右:伪距）
Fig.1 Single difference residuals of C08 satellite in short baseline (left:carrier phase; right:pseudo-range)
图2 短基线情况下，G06卫星载波相位和伪距单差残差（左:载波相位; 右:伪距）
Fig.2 Single difference residuals of G06 satellite in short baseline (left:carrier phase; right:pseudo-range)
图3 短基线情况下，E19卫星载波相位和伪距单差残差（左:载波相位; 右:伪距）
Fig.3 Single difference residuals of E19 satellite in short baseline (left:carrier phase; right:pseudo-range)
表1 BDS非差伪距和载波相位观测值精度
Table1 Accuracies of BDS non-difference pseudo-range and carrier phase observations
3.2 BDS/GPS/Galileo随机模型系数确定
图4给出了Galileo IOV卫星的每一度高度角的载波残差标准差值.从图4中可以看出:卫星高度角越低，伪距残差标准差越大; BDS和GPS卫星也具有相同结论.根据式（8）计算方法，可得到Galileo FOC和IOV卫星、BDS IGSO和MEO卫星以及GPSIIR-A/B、IIR-M和IIF卫星不同频率下伪距和载波相位观测值的模型系数，如表4—6所示.图5—7分别给出了载波相位拟合随机模型曲线.
表2 GPS非差伪距和载波相位观测值精度
Table2 Accuracies of GPS non-difference pseudo-range and carrier phase observations
从表4和图5可以发现:FOC卫星E5频点伪距观测值的模型系数m=0.052 2，n=0.023 6，IOV卫星E5频点伪距观测值的模型系数m=0.052 1，n=0.025 0; FOC卫星E5频点载波相位观测值的模型系数m=0.947 7，n=0.583 9，IOV卫星E5频点载波相位观测值的模型系数为m=0.787 6，n=0.789 0.E5频点的观测值精度要明显高于E1、E5a和E5b频点观测值的精度.
表3 Galileo系统非差伪距和载波相位观测值精度
Table3 Accuracies of Galileo non-difference pseudo-range and carrier phase observations
图4 Galileo IOV卫星载波残差标准差与高度角关系
Fig.4 Relationship between standard deviation of Galileo IOV satellite carrier phase residual and elevation angle
表4 Galileo伪距和载波相位观测值模型系数拟合值
Table4 The fitted values of Galileo pseudo-range and carrier phase observation
图5 Galileo载波拟合随机模型曲线
Fig.5 Galileo carrier fitting curves of stochastic model
图6 BDS相位拟合随机模型曲线
Fig.6 BDS carrier phase fitting curves of stochastic model
图7 GPS载波拟合随机模型曲线
Fig.7 GPS carrier fitting curves of stochastic model
表5 BDS伪距和载波相位观测值模型系数拟合值
Table5 The fitted values of BDS pseudo-range and carrier phase observation
从表5和图6可以看出:BDS IGSO卫星B3频点伪距观测值的模型系数m=0.147 1，n=1.144 4，MEO卫星B3频点伪距观测值的模型系数m=0.181 3，n=0.143 9; IGSO卫星B3频点载波相位观测值的模型系数m=1.225 1，n=1.014 6，MEO卫星B3频点载波相位观测值的模型系数m=1.327 8，n=0.957 1.B2和B3频点的伪距观测值精度要高于B1频点观测值的精度; B3频点的相位观测值的精度要高于B1和B2频点的相位观测值精度.
表6 GPS伪距和载波相位观测值模型系数拟合值
Table6 The fitted values of GPS pseudo-range and carrier phase observation
从表6和图7可知:GPS IIR-A/B卫星L2频点伪距观测值的模型系数m=0.286 4，n=0.099 0，IIR-M卫星L2频点伪距观测值的模型m=0.007 6，n=0.200 4，IIF卫星L2频点伪距观测值的模型系数m=0.141 1，n=0.177 0; L2频点的伪距观测值精度要高于L1频点观测值的精度.IIR-A/B卫星L1频点载波相位观测值的模型系数m=1.128 2，n=0.935 2，IIR-M卫星L1频点载波相位观测值的模型系数m=1.389 0，n=0.821 9，IIF卫星L1频点载波相位观测值的模型系数m=0.436 4，n=1.199 8; L1频点的相位观测值的精度与L2频点的相位观测值精度相当.
4 结论
本文对BDS/GPS/Galileo观测值精度进行分析，通过单差残差统计结果拟合GNSS不同卫星伪距和载波相位高度角随机模型的系数，精化了随机模型.
1）Galileo的4个频点的伪距观测值精度约20~50 cm，载波相位观测值精度约1~3 mm; BDS载波观测值精度约1~3 mm，其伪距观测值精度约30~50 cm; GPS L1伪距观测值精度约63 cm，L2伪距观测值精度约42 cm; 载波相位精度约3 mm.在短基线情况下，BDS、GPS和Galileo载波相位观测值精度基本相当，而Galileo E5伪距观测值精度明显优于其他卫星系统伪距观测值精度.
2）卫星高度角越高，伪距和载波观测值残差标准差越小.Galileo伪距和载波观测值精度E5频点皆高于E1、E5a、E5b.FOC卫星E5频点伪距观测值随机模型采用的系数为m=0.052 2，n=0.023 6，IOV卫星E5的系数为m=0.052 1，n=0.025 0; FOC卫星E5频点载波观测值随机模型采用的系数为m=0.947 7，n=0.583 9，IOV卫星E5的系数为m=0.787 6，n=0.789 0.BDS B2和B3伪距观测值精度高于B1，B3载波观测值精度高于B2和B1; GPS L2频点伪距观测值精度高于L1，载波观测值精度二者基本相当.
参考文献
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- [14] Kiliszek D,Kroszczyński K,Araszkiewicz A.Analysis of different weighting functions of observations for GPS and Galileo precise point positioning performance[J].Remote Sensing,2022,14(9):2223

基本信息

中图分类号: P228.4
文献标识码: A
DOI: 10.13878/j.cnki.jnuist.2022.06.010

基金信息

安徽省自然科学基金(2108085QD171,2208085MD101)；
安徽高校自然科学研究重点项目(KJ2021A0443)；

引用信息

稿件历史

收稿日期: 2022-08-02

参考文献

[1] 刘琳.GNSS观测值精度估计及随机模型精化方法研究[D].武汉:武汉大学,2019;LIU Lin.Research on method of GNSS observation precision estimation and stochastic model refinement[D].Wuhan:Wuhan University,2019
[2] 刘琳,席瑞杰.GPS/GLONASS/BDS/Galileo系统载波相位观测值质量对比分析[J].全球定位系统,2019,44(1):16-22;LIU Lin,XI Ruijie.Quality contrast and analysis of carrier phase observations in GPS/GLONASS/BDS/Galileo system[J].GNSS World of China,2019,44(1):16-22
[3] 刘永建,江勇.北斗GEO/IGSO/MEO卫星观测值精度分析及随机模型精化[J].全球定位系统,2018,43(1):1-6;LIU Yongjian,JIANG Yong.Precision analysis of the BDS GEO/IGSO/MEO observables and stochastic model refining[J].GNSS World of China,2018,43(1):1-6
[4] 张小红,丁乐乐.北斗二代观测值质量分析及随机模型精化[J].武汉大学学报·信息科学版,2013,38(7):832-836;ZHANG Xiaohong,DING Lele.Quality analysis of the second generation compass observables and stochastic model refining[J].Geomatics and Information Science of Wuhan University,2013,38(7):832-836
[5] Li B F,Zhang L,Verhagen S.Impacts of BeiDou stochastic model on reliability:overall test,w-test and minimal detectable bias[J].GPS Solutions,2017,21(3):1095-1112
[6] 黄令勇,吕志平,吕浩,等.北斗三频伪距相关随机模型单站建模方法[J].测绘学报,2016,45(S2):165-171;HUANG Lingyong,LÜ Zhiping,LÜ Hao,et al.The BDS triple frequency pseudo-range correlated stochastic model of single station modeling method[J].Acta Geodaetica et Cartographica Sinica,2016,45(S2):165-171
[7] 严丽,李萌,梅熙,等.实时估计不同类型北斗卫星观测值的随机模型[J].武汉大学学报·信息科学版,2017,42(2):263-269;YAN Li,LI Meng,MEI Xi,et al.Real-time estimating different types of BDS observations stochastic model[J].Geomatics and Information Science of Wuhan University,2017,42(2):263-269
[8] 刘一,边少锋,纪兵,等.北斗三号卫星观测信息高度角相关随机模型统计特性分析[J/OL].武汉大学学报·信息科学版:1-12[2022-05-22].DOI:10.13203/j.whugis20220021;LIU Yi,BIAN Shaofeng,JI Bing,et al.Analysis of statistic testing of elevation-dependent stochastic models of BDS-3 satellite observation[J/OL].Geomatics and Information Science of Wuhan University:1-12[2022-05-22].DOI:10.13203/j.whugis20220021
[9] 吴琼宝,赵春梅.星载GPS/BDS数据质量评估与分析[J].导航定位学报,2018,6(1):81-84,107;WU Qiongbao,ZHAO Chunmei.Quality evaluation and analysis on spaceborne GPS/BDS data[J].Journal of Navigation and Positioning,2018,6(1):81-84,107
[10] Yan L,Huang D F,Li M,et al.BDS/GPS stochastic model refinement and assessment using satellite elevation angle and SNR[C]//第六届中国卫星导航学术年会论文集:S06北斗/GNSS测试评估技术,2015:22
[11] 虞顺,吴明魁,刘万科,等.Galileo导航系统观测值的质量分析[J].测绘地理信息,2019,44(3):51-56;YU Shun,WU Mingkui,LIU Wanke,et al.Quality analysis of Galileo guided system observations[J].Journal of Geomatics,2019,44(3):51-56
[12] Prochniewicz D,Wezka K,Kozuchowska J.Empirical stochastic model of multi-GNSS measurements[J].Sensors(Basel,Switzerland),2021,21(13):4566
[13] Hou P Y,Zha J P,Liu T,et al.LS-VCE applied to stochastic modeling of GNSS observation noise and process noise[J].Remote Sensing,2022,14(2):258
[14] Kiliszek D,Kroszczyński K,Araszkiewicz A.Analysis of different weighting functions of observations for GPS and Galileo precise point positioning performance[J].Remote Sensing,2022,14(9):2223

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BDS/GPS/Galileo多频观测值精度评估及随机模型精化

Precision estimation of the BDS/GPS/Galileo multi-frequency observations and stochastic model refining

摘要

Abstract

关键词

Keywords

0 引言

1 单差残差模型

(1)

(2)

(3)

(4)

2 基于单差残差的BDS/GPS/Galileo随机模型精化

(5)

(6)

(7)

(8)

3 数据采集与结果分析

3.1 BDS/GPS/Galileo数据质量评估

3.2 BDS/GPS/Galileo随机模型系数确定

4 结论

参考文献

基本信息

基金信息

引用信息

稿件历史

参考文献