基于几何相关的GPS观测量随机误差模型的研究

doi:10.11959/j.issn.1000-436x.2019188

通信学报 ›› 2019, Vol. 40 ›› Issue (9): 74-85.doi: 10.11959/j.issn.1000-436x.2019188

基于几何相关的GPS观测量随机误差模型的研究

周桃云^1,²,廉保旺¹,杨冬冬¹,张怡¹,蔡成林³

¹ 西北工业大学电子信息学院，陕西西安 710129
² 湖南人文科技学院信息学院，湖南娄底 417000
³ 湘潭大学信息工程学院，湖南湘潭 411105

修回日期:2019-07-02 出版日期:2019-09-25 发布日期:2019-09-28
作者简介:周桃云（1981- ），女，湖南娄底人，西北工业大学博士生，主要研究方向为卫星导航与定位技术。|廉保旺（1962- ），男，河南焦作人，博士，西北工业大学教授、博士生导师，主要研究方向为卫星通信导航与测控、室内定位技术、软件无线电技术、嵌入式系统设计。|杨冬冬（1994- ），男，河南焦作人，西北工业大学硕士生，主要研究方向为卫星导航与定位技术。|张怡（1966- ），女，陕西西安人，博士，西北工业大学教授、博士生导师，主要研究方向为通信、导航、遥测遥控系统的信息传输与处理、卫星导航与定位技术、无线通信与软件无线电。|蔡成林（1969- ），男，湖南娄底人，博士，湘潭大学教授、博士生导师，主要研究方向为卫星导航与无线通信。
基金资助:
国家自然科学基金资助项目(61301094);国家自然科学基金资助项目(61771150);国家重大科技专项基金资助项目(GFZX0301040115);湖南省科技创新计划基金资助项目(2018GK2014);湖南省科技创新计划基金资助项目(2018RS3089);广西科技计划项目合同基金资助项目(AB17129028);湖南省教育厅科学研究基金资助项目(18B458)

Research on GPS geometry-based observational stochastic error model

Taoyun ZHOU^1,²,Baowang LIAN¹,Dongdong YANG¹,Yi ZHANG¹,Chenglin CAI³

¹ School of Electronics and Information,Northwestern Polytechnical University,Xi’an 710129,China
² School of Information,Hunan University of Humanities,Science and Technology,Loudi 417000,China
³ College of Information Engineering，Xiangtan University,Xiangtan 411105,China

Revised:2019-07-02 Online:2019-09-25 Published:2019-09-28
Supported by:
The National Natural Science Foundation of China(61301094);The National Natural Science Foundation of China(61771150);The National Science and Technology Major Projects of China(GFZX0301040115);The Science and Technology Innovation Plan of Hunan Province(2018GK2014);The Science and Technology Innovation Plan of Hunan Province(2018RS3089);The National Research and Development Contracts of Guangxi Province(AB17129028);The Scientific Research Fund of Hunan Provincial Education Department(18B458)

摘要/Abstract

摘要：

针对传统方法考虑随机误差影响因素不够全面的问题，建立了一种更加真实的GPS观测量随机误差模型。该方法在几何相关功能模型中引入了误差修正项，采用了一种以空间换时间的改进LS-VCE算法对模型进行求解，采集了2组真实的GPS实测数据对模型进行性能评估，并利用该模型解算了载波相位整周模糊度。实验结果表明，所提方法在模型精度、模型求解复杂度及整周相位模糊度解算成功率等方面均优于传统方法。

关键词: 最小二乘方差分量估计, 随机误差模型, 几何相关模型, 整周模糊度解算

Abstract:

Aiming at the problem of not enough influencing factors were considered in traditional methods,a much more realistic stochastic model was built.In which error corrections were introduced into the geometry-based function model,an improved least squares variance component estimation (LS-VCE) algorithm with space-for-time was used to solve the model,two sets of real GPS data were collected to evaluate the performance of the model,and with which the carrier phase integer ambiguity was solved.The experimental results show that the proposed methods are superior to the traditional methods in terms of model accuracy,model solution complexity and integer ambiguity resolution.

Key words: LS-VCE, stochastic error model, geometry-based observation model, IAR

中图分类号:

TN961

周桃云,廉保旺,杨冬冬,张怡,蔡成林. 基于几何相关的GPS观测量随机误差模型的研究[J]. 通信学报, 2019, 40(9): 74-85.

Taoyun ZHOU,Baowang LIAN,Dongdong YANG,Yi ZHANG,Chenglin CAI. Research on GPS geometry-based observational stochastic error model[J]. Journal on Communications, 2019, 40(9): 74-85.

图/表 14

图1

图2

图3

图4

表1

表2

表3

图5

表4

图6

表5

表6

图7

图8

参考文献 23

[1]	冯威 . GPS中央差分定位系统理论与应用研究[D]. 成都:西南交通大学, 2013.
	FENG W . Theory and applications of GPS central differential posi-tioning system[D]. Chengdu:Southwest Jiaotong University, 2013.
[2]	AMIRI- SIMKOOEI A R , JAZAERI S , FARZANEH ZANGENEH-NEJAD F . Role of stochastic model on GPS integer ambiguity resolution success rate[J]. GPS Solution, 2016,20(1): 51-61.
[3]	SONY. 武汉大学测绘学院测量平差学科组.误差理论与测量平差基础（第3版）[M]. 武汉: 武汉大学出版社, 2014.
	Department of Surveying Adjustment,School of Geodesy and Geomatics,Wuhan University. Theory of errors and basis of surveying adjustment (3rd Edition)[M]. Wuhan: Wuhan University PressPress, 2014.
[4]	RAO C R . Estimation of variance and covariance componentsMINQUE theory[J]. Journal of Multivariate Analysis, 1971,1(3): 257-275.
[5]	KOCH K R . Sch?tzung von varianzkomponenten[J]. Allgemeine Vermessungs Nachrichten, 1978,85: 264-269.
[6]	KUBIK K . The estimation of the weights of measured quantities within the method of least squares[J]. Bulletin Géodésique, 1970,95(1): 21-40.
[7]	KOCH K R . Bayesian inference for variance components[J]. Manuscripta Geodaetica, 1987,12: 309-313.
[8]	TEUNISSEN P . Towards a least-squares framework for adjusting and testing of both functional and stochastic models[R]. Delft University of Technology, 1988.
[9]	AMIRISIMKOOEI A R . Least-squares variance component estimation theory and GPS applications[D]. Netherlands:Delft University of Technology, 2007.
[10]	TEUNISSEN P J G , AMIRISIMKOOEI A R . Least-squares variance component estimation[J]. Journal of Geodesy, 2008,82(2): 65-82.
[11]	AMIRISIMKOOEI A R . Application of least squares variance component estimation to errors-in -variables models[J]. Journal of Geodesy, 2013,87(10-12): 935-944.
[12]	TEUNISSEN P J G . A canonical theory for short GPS baselines.Part III:the geometry of the ambiguity search space[J]. Journal of Geodesy, 1997,71(8): 486-501.
[13]	TEUNISSEN P J G . A canonical theory for short GPS baselines.Part IV:precision versus reliability[J]. Journal of Geodesy, 1997,71(9): 513-525.
[14]	WANG J , STEWART M P , TSAKIRI M . Stochastic modeling for static GPS baseline data processing[J]. Journal of Surveying Engineering, 1998,124(4): 171-181.
[15]	TEUNISSEN P J G , JONKAN N F , TIBERIUS C C J M . Weighting GPS dual frequency observations:bearing the cross of cross-correlation[J]. GPS Solutions, 1998,2(2): 28-37.
[16]	HARTINGER H , BRUNNER F K . Variances of GPS phase observations:the sigma-? model[J]. GPS Solutions, 1999,2(4): 35-43.
[17]	WANG J , SATIRAPOD C , RIZOS C . Stochastic assessment of GPS carrier phase measurements for precise static relative positioning[J]. Journal of Geodesy, 2002,76(2): 95-104.
[18]	AMIRI-SIMKOOEI A R , JAZAERI S ， ZANGENEH-NEIAD F . Role of stochastic model on GPS integer ambiguity resolution success rate[J]. GPS Solutions, 2016,20(1): 51-61
[19]	AMIRI-SIMKOOEI A R , TIBERIUS C C J M . Assessing receiver noise using GPS short baseline time series[J]. GPS Solutions, 2007,11(1): 21-35.
[20]	AMIRI-SIMKOOEI A R , TEUNISSEN P J G , TERIUS C C J M . Application of least-squares variance component estimation to GPS observables[J]. Journal of Surveying Engineering, 2009,135(4): 149-160.
[21]	AMIRI-SIMKOOEI A R , ZANGENEH-NEJAD F , ASGARI J . Least-squares variance component estimation applied to GPS geometry-based observation model[J]. Journal of Surveying Engineering, 2013,139(4): 176-187.
[22]	ZANGENEH-NEJAD F , AMIRI-SIMKOOEI A R , SHARIFI M A . Recursive least squares with real time stochastic modeling:application to GPS relative positioning[J]. 2017,XLII-4/W4:531-536.
[23]	LI B F . Stochastic modeling of triple-frequency BeiDou signals:estimation,assessment and impact analysis[J]. Journal of Geodesy, 2016,90(7): 593-610.

基线长度/m	改进前/s	改进后/s	效率提高
2.791 2	546	165	69.8%
0	351	101	71.2%

基线长度/m	观测量类型	标准差（迭代后）/m	观测量方差	标准差（迭代前）/m
	L₁伪距	0.291 2	0.089 7	0.294 2
2.791 2	L₁载波相位	0.002 2	4.982 2×10^-6	0.001 7
	L₂伪距	0.309 4	0.101 0	0.279 4
	L₂载波相位	0.002 9	9.381 6×10^-6	0.002 4
	L₁伪距	0.213 4	0.046 7	0.219 4
0	L₁载波相位	0.001 0	1.130 4×10^-6	0.001 0
	L₂伪距	0.188 4	0.036 2	0.179 9
	L₂载波相位	0.001 3	1.824 9×10^-6	0.001 3

基线长度/m	相关类型	相关系数（迭代后）	协方差	相关系数（迭代前）
	L₁-L₂伪距	0.102 2	0.0100	0.039 7
	L₁伪距-L₁相位	0.016 0	1.025 8×10^-5	-0.001 9
2.791 2	L₂伪距-L₁相位	-0.008 4	-6.255 2×10^-6	-0.032 7
	L₁伪距-L₂相位	0.021 1	1.795 8×10^-5	0.021 8
	L₂伪距-L₂相位	0.006 9	7.679 4×10-^-6	-0.007 5
	L₁-L₂相位	0.665 2	4.539 3×10^-6	0.300 2
	L₁伪距-L₂伪距	0.122 8	0.0051	0.108 4
	L₁伪距-L₁相位	-0.005 7	-1.018 8×10^-6	-0.003 9
0	L₂伪距-L₁相位	-0.008 8	-1.775 4×10^-6	-0.007 2
	L₁伪距-L₂相位	-0.007 5	-1.930 4×10-⁶	-0.007 1
	L₂伪距-L₂相位	-0.008 3	-2.067 1×10^-6	-0.004 7
	L₁-L₂相位	0.782 2	1.138 7×10^-6	0.739 9

基线长度/m	迭代前		迭代后
基线长度/m	a	b	a	b
2.791 2	0.563 9	-0.020 4	0.492 9	-0.099 9
0	0.746 2	0.215 4	0.605 1	0.072 8

基线长度/m	历元	相关系数（迭代后）	时间相关性	相关系数（迭代前）
	1	1.000 0	0.051 4	1.000 0
	2	0.693 5	0.050 7	0.475 4
2.791 2	3	0.683 2	0.050 9	0.462 0
	4	0.672 0	0.051 6	0.450 4
	5	0.658 4	0.054 8	0.437 1
	1	1.000 0	0.016 4	1.000 0
	2	0.151 3	0.012 0	0.114 2
0	3	0.116 4	0.014 0	0.084 7
	4	0.104 8	0.018 4	0.076 7
	5	0.100 3	0.032 3	0.073 0

基于几何相关的GPS观测量随机误差模型的研究

Research on GPS geometry-based observational stochastic error model

在线阅读

PDF下载

可视化

摘要/Abstract

引用本文

使用本文

图/表 14

参考文献 23

相关文章 0

Metrics

推荐阅读 0

数据类型	模型类型	短基线解算正确率	零基线解算正确率
	1	1.252%	3.478%
	2	84.033%	98.949%
L₁	3	87.428%	99.193%
	4	92.549%	99.629%
	1	2.675%	11.237%
L₂	2	91.602%	99.785%
	3	93.805%	99.789%
	4	95.714%	99.847%