GPSRTK点位测量随机误差二维空间分布模式研究
|
摘要
矢量空间数据的可用性取决于其空间位置不确定性,直接受控于点元位置误差的二维空间概率分布模式。应用GPS RTK技术,对选定测量点的空间位置进行重复观测,累积观测20 d,采用一维、二维正态分布检验与数学模型拟合3种分析方法,研究了GPS RTK测点误差空间概率分布模式。结果表明,GPS RTK测点误差空间分布呈现为具有一定方向的二维正态分布形式,并且这种分布形式的显著性随着点元位置观测时间的缩短而不断提升。所得到的GPS RTK测点误差空间概率分布模式可为其测点误差空间分布影响因素分析与数学预测模型构建奠定基础,并有助于推动矢量空间数据位置不确定性的理论研究。
The spatial position uncertainty influences the availability of the vector spatial data,which is directly controlled by the two-dimensional probability distribution model of the point's position errors. This paper studies the spatial distribution model of GPS RTK positioning random error,which has repeatedly measured the selected points for 20 days. Then the one-and two-dimensional normal distribution tests and two-dimensional normal distribution fitting are employed to analyze the distribution model. The results show that the GPS RTK positioning random error fits directional two-dimensional normal distribution model and the significance is enhanced constantly along with the observation time shorten. The research results can build foundation for analyzing the influencing factors of the distribution model of positioning random error and establishing the mathematic forecasting model. Besides,contribute to promote the theoretical research of position uncertainty for spatial vector data.
The spatial position uncertainty influences the availability of the vector spatial data,which is directly controlled by the two-dimensional probability distribution model of the point's position errors. This paper studies the spatial distribution model of GPS RTK positioning random error,which has repeatedly measured the selected points for 20 days. Then the one-and two-dimensional normal distribution tests and two-dimensional normal distribution fitting are employed to analyze the distribution model. The results show that the GPS RTK positioning random error fits directional two-dimensional normal distribution model and the significance is enhanced constantly along with the observation time shorten. The research results can build foundation for analyzing the influencing factors of the distribution model of positioning random error and establishing the mathematic forecasting model. Besides,contribute to promote the theoretical research of position uncertainty for spatial vector data.
引文
[1]Shi Wenzhong.Principle of Modelling Uncertainties in Spatial Data and Analysis[M].Beijing:Science Press,2005(史文中.空间数据与空间分析不确定性原理[M].北京:科学出版社,2005)
[2]Li Deren,Peng Meiyun,Zhang Juqing.Modelling Positional Uncertainty of Line Primitives in GIS[J].Journal of Wuhan Technical University of Surveying and Mapping,1995,20(4):283-288(李德仁,彭美云,张菊清.GIS中线要素的定位不确定性模型研究[J].武汉测绘科技大学学报,1995,20(4):283-288)
[3]Zhang Guoqin,Zhu Changqing,Li Guozhong.A Positional UncertaintyεEModel for Line Segment Considering Error Ellipse Long Semi-axis as Error Band Width[J].Geomatics and Information Science of Wuhan University,2010,35(4):495-499(张国芹,朱长青,李国重.以误差椭圆长半轴表示带宽的线元位置不确定性εE模型[J].武汉大学学报·信息科学版,2010,35(4):495-499)
[4]Bian Yuxia,Liu Xuejun,Zhen Yan.Uncertainty Measurment Model of Three-Dimensional Polygon[J].Geomatics and Information Science of Wuhan University,2015,40(1):26-31(卞玉霞,刘学军,甄艳.三维空间多边形的位置不确定性度量模型[J].武汉大学学报·信息科学版,2015,40(1):26-31)
[5]Meng Xiaolin,Shi Wenzhong,Liu Dajie.Statistical Tests of the Distribution of Errors in Manually Digitized Cartographic Lines[J].Geographic Information Sciences,1998,4(1):52-58
[6]Lan Yueming,Yang Xiaomei.The Distribution Test of Manual Digitization Map Error[J].Bulletin of Surveying and Mapping,2003(4):42-44(蓝悦明,杨晓梅.手工数字化地图误差的分布检验[J].测绘通报,2003(4):42-44)
[7]Yang Yuanxi.Discussion on “A New Measure of Positional Error”[J].Acta Geodaetica et Cartographica Sinica,2009,38(8):280-282(杨元喜.关于“新的点位误差度量”的讨论[J].测绘学报,2009,38(8):280-282)
[8]Luo X,Mayer M,Heck B.On the Probability Distribution of GNSS Carrier Phase Observations[J].GPS Solution,2011,15(4):369-379
[9]Lan Yueming,Wang Nan.The Study of Probability Density Function for GPS RTK Observations[J].Bulletin of Surveying and Mapping,2011(2):6-7(蓝悦明,王楠.GPS RTK观测数据的概率密度函数研究[J].测绘通报,2011(2):6-7)
[10]Zhou Fangbin,Zhu Jianjun,Chen Yongqi.Analysis of Error Distribution for GPS RTK Observations by Entropy[J].Bulletin of Surveying and Mapping,2012(11):19-20(周访滨,朱建军,陈永奇.GPS RTK观测数据误差分布的熵分析[J].测绘通报,2012(11):19-20)
[11]Militino A F,Ugarte M D,Iribas J,et al.Mapping GPS Positional Errors Using Spatial Linear Mixed Models[J].Journal of Geodesy,2013,87(7):675-685
[12]Ragheb A E,Clarke P J,Edwards S J.GPS Side-real Filtering:Coordinate-and Carrier-Phase-Level Strategies[J].Journal of Geodesy,2007,81(5):325-335
[13]Yuan Linguo,Huang Dingfa,Ding Xiaoli,et al.On the Influence of Signal Multipath Effects in GPS Carrier Phase Surveying[J].Acta Geodaetica et Cartographica Sinica,2004,33(3):210-215(袁林果,黄丁发,丁晓利,等.GPS载波相位测量中的信号多路径效应影响研究[J].测绘学报,2004,33(3):210-215)
[14]Teunissen P J G,Odolinski R,Odijk D.Instantaneous Bei Dou+GPS RTK Positioning with High Cut-Off Elevation Angles[J].Journal of Geodesy,2014,88(4):335-350
[15]Gao Huixuan.Applied Multivariate Statistical Ana-lysis[M].Beijing:Peking University Press,2005(高惠璇.应用多元统计分析[M].北京:北京大学出版社,2005)
[16]Szekely G J,Rizzo M L.A New Test for Multivariate Normality[J].Journal of Multivariate Analysis,2005,93(1):58-80
[17]Zhu Ning,Zhao Xiaoxiao,Tang Qinghua.Comparison of Three Methods for Multivariate Normality Test and SAS Program Design[J].Journal of Suzhou University(Natural Science Edition),2012,28(3):20-25(朱宁,赵肖肖,唐庆华.多元正态性检验三种方法的比较及SAS程序设计[J].苏州大学学报(自然科学版),2012,28(3):20-25)
[18]Nordhausen K,Oja H,Tyler D E.Tools for Exploring Multivariate Data:The Package ICS[J].Journal of Statistical Software,2008,28(6):1-31
[19]Ilmomen P,Oja H,Serfling R.On Invariant Coordinate System(ICS)Functionals[J].International Statistical Review,2012,80(1):93-110
[20]Kankainen A,Taskinen S,Oja H.Test of Multinormality Based on Location Vectors and Scatter Matrices[J].Statistical Methods&Applications,2007,16(3):357-379
[21]Zhang Zhenglu,Fan Guoqing,Zhang Songlin,et al.General Reliability of Measurement[J].Geomatics and Information Science of Wuhan University,2012,37(5):577-581(张正禄,范国庆,张松林,等.测量的广义可靠性研究[J].武汉大学学报·信息科学版,2012,37(5):577-581)
[22]Santerre R.Impact of GPS Satellite Sky Distribution[J].Manuscripta Geodaetica,1991,16:28-53
[2]Li Deren,Peng Meiyun,Zhang Juqing.Modelling Positional Uncertainty of Line Primitives in GIS[J].Journal of Wuhan Technical University of Surveying and Mapping,1995,20(4):283-288(李德仁,彭美云,张菊清.GIS中线要素的定位不确定性模型研究[J].武汉测绘科技大学学报,1995,20(4):283-288)
[3]Zhang Guoqin,Zhu Changqing,Li Guozhong.A Positional UncertaintyεEModel for Line Segment Considering Error Ellipse Long Semi-axis as Error Band Width[J].Geomatics and Information Science of Wuhan University,2010,35(4):495-499(张国芹,朱长青,李国重.以误差椭圆长半轴表示带宽的线元位置不确定性εE模型[J].武汉大学学报·信息科学版,2010,35(4):495-499)
[4]Bian Yuxia,Liu Xuejun,Zhen Yan.Uncertainty Measurment Model of Three-Dimensional Polygon[J].Geomatics and Information Science of Wuhan University,2015,40(1):26-31(卞玉霞,刘学军,甄艳.三维空间多边形的位置不确定性度量模型[J].武汉大学学报·信息科学版,2015,40(1):26-31)
[5]Meng Xiaolin,Shi Wenzhong,Liu Dajie.Statistical Tests of the Distribution of Errors in Manually Digitized Cartographic Lines[J].Geographic Information Sciences,1998,4(1):52-58
[6]Lan Yueming,Yang Xiaomei.The Distribution Test of Manual Digitization Map Error[J].Bulletin of Surveying and Mapping,2003(4):42-44(蓝悦明,杨晓梅.手工数字化地图误差的分布检验[J].测绘通报,2003(4):42-44)
[7]Yang Yuanxi.Discussion on “A New Measure of Positional Error”[J].Acta Geodaetica et Cartographica Sinica,2009,38(8):280-282(杨元喜.关于“新的点位误差度量”的讨论[J].测绘学报,2009,38(8):280-282)
[8]Luo X,Mayer M,Heck B.On the Probability Distribution of GNSS Carrier Phase Observations[J].GPS Solution,2011,15(4):369-379
[9]Lan Yueming,Wang Nan.The Study of Probability Density Function for GPS RTK Observations[J].Bulletin of Surveying and Mapping,2011(2):6-7(蓝悦明,王楠.GPS RTK观测数据的概率密度函数研究[J].测绘通报,2011(2):6-7)
[10]Zhou Fangbin,Zhu Jianjun,Chen Yongqi.Analysis of Error Distribution for GPS RTK Observations by Entropy[J].Bulletin of Surveying and Mapping,2012(11):19-20(周访滨,朱建军,陈永奇.GPS RTK观测数据误差分布的熵分析[J].测绘通报,2012(11):19-20)
[11]Militino A F,Ugarte M D,Iribas J,et al.Mapping GPS Positional Errors Using Spatial Linear Mixed Models[J].Journal of Geodesy,2013,87(7):675-685
[12]Ragheb A E,Clarke P J,Edwards S J.GPS Side-real Filtering:Coordinate-and Carrier-Phase-Level Strategies[J].Journal of Geodesy,2007,81(5):325-335
[13]Yuan Linguo,Huang Dingfa,Ding Xiaoli,et al.On the Influence of Signal Multipath Effects in GPS Carrier Phase Surveying[J].Acta Geodaetica et Cartographica Sinica,2004,33(3):210-215(袁林果,黄丁发,丁晓利,等.GPS载波相位测量中的信号多路径效应影响研究[J].测绘学报,2004,33(3):210-215)
[14]Teunissen P J G,Odolinski R,Odijk D.Instantaneous Bei Dou+GPS RTK Positioning with High Cut-Off Elevation Angles[J].Journal of Geodesy,2014,88(4):335-350
[15]Gao Huixuan.Applied Multivariate Statistical Ana-lysis[M].Beijing:Peking University Press,2005(高惠璇.应用多元统计分析[M].北京:北京大学出版社,2005)
[16]Szekely G J,Rizzo M L.A New Test for Multivariate Normality[J].Journal of Multivariate Analysis,2005,93(1):58-80
[17]Zhu Ning,Zhao Xiaoxiao,Tang Qinghua.Comparison of Three Methods for Multivariate Normality Test and SAS Program Design[J].Journal of Suzhou University(Natural Science Edition),2012,28(3):20-25(朱宁,赵肖肖,唐庆华.多元正态性检验三种方法的比较及SAS程序设计[J].苏州大学学报(自然科学版),2012,28(3):20-25)
[18]Nordhausen K,Oja H,Tyler D E.Tools for Exploring Multivariate Data:The Package ICS[J].Journal of Statistical Software,2008,28(6):1-31
[19]Ilmomen P,Oja H,Serfling R.On Invariant Coordinate System(ICS)Functionals[J].International Statistical Review,2012,80(1):93-110
[20]Kankainen A,Taskinen S,Oja H.Test of Multinormality Based on Location Vectors and Scatter Matrices[J].Statistical Methods&Applications,2007,16(3):357-379
[21]Zhang Zhenglu,Fan Guoqing,Zhang Songlin,et al.General Reliability of Measurement[J].Geomatics and Information Science of Wuhan University,2012,37(5):577-581(张正禄,范国庆,张松林,等.测量的广义可靠性研究[J].武汉大学学报·信息科学版,2012,37(5):577-581)
[22]Santerre R.Impact of GPS Satellite Sky Distribution[J].Manuscripta Geodaetica,1991,16:28-53